Timely and informative data dissemination in communication networks is essential for enhancing system performance and energy efficiency, as it reduces the transmission of outdated or redundant data. Timeliness metrics, such as Age of Information (AoI), effectively quantify data freshness; however, these metrics fail to account for the intrinsic informativeness of the content itself. To address this limitation, content-based metrics have been proposed that combine both timeliness and informativeness. Nevertheless, existing studies have predominantly focused on evaluating average metric values, leaving the complete distribution—particularly in multi-hop networkscenarios—largely unexplored. In this paper, we provide a comprehensive analysis of the stationary distribution of the Version Age of Information (VAoI), a content-based metric, under various scheduling policies, including randomized stationary, uniform, and threshold-based policies, with transmission constraints in single-hop and multi-hop networks. We derive closed-form expressions for the stationary distribution and average VAoI under these scheduling approaches. Furthermore, for thresholdbasedscheduling, we analytically determine the optimal threshold value that minimizes VAoI and derive the corresponding optimal VAoI in closed form. Numerical evaluations verify our analytical findings and provide valuable insights into leveraging VAoI in the design of efficient communication networks.

This paper addresses query scheduling for goaloriented semantic communication in pull-based status update systems. We consider a system where multiple sensing agents (SAs) observe a source characterized by various attributes and provide updates to multiple actuation agents (AAs), which act upon the received information to fulfill their heterogeneous goals at the endpoint. A hub serves as an intermediary, querying the SAs for updates on observed attributes and maintaining a knowledge base, which is then broadcast to the AAs. The AAs leverage the knowledge to perform their actions effectively. To quantify the semantic value of updates, we introduce agrade of effectiveness(GoE) metric. Furthermore, we integrate cumulative perspective theory(CPT) into the long-term effectiveness analysis to account for risk awareness and loss aversion in the system. Leveraging this framework, we compute effect-aware scheduling policies aimed at maximizing the expected discounted sum of CPT-based total GoE provided by the transmitted updates while complying with a given query cost constraint. To achieve this, we propose amodel-basedsolution based on dynamic programming andmodel-freesolutions employing state-of-the-art deep reinforcement learning (DRL) algorithms. Our findings demonstrate that effect-aware scheduling significantly enhances the effectiveness of communicated updates compared to benchmark scheduling methods, particularly in settings with stringent cost constraints where optimal query scheduling is vital for system performance and overall effectiveness.

In this work, we study the freshness and significance of information in an IoT status update system in which an Energy Harvesting (EH) device samples an information source and forwards update packets to a destination node via a direct channel. We introduce and optimize a semantics-aware metric, Query Version Age of Information (QVAoI), in the system along with other metrics: Query Age of Information (QAoI), Version Age of Information (VAoI), and Age of Information (AoI). We formulate the optimization problem as a Markov Decision Process to determine the optimal transmission policy at the device, which decides the time slots for transmitting updates, subject to the device's battery energy limitations and the energy arrivals. Furthermore, we derive closed-form expressions for the average update rate and the QVAoI for a unit-capacity battery, serving as analytical benchmarks. We compare the performance of QVAoI-Optimal, QAoI-Optimal, VoI-Optimal, and AoI-Optimal policies with a baseline greedy policy. All semantics-aware policies achieve better performance than the greedy policy. The QVAoI-Optimal policy, in particular, demonstrates a significant performance improvement either by providing fresher, more relevant, and more valuable updates with the same energy arrivals or by reducing the number of transmissions in the system while maintaining the same level of freshness and information significance as the QAoI-Optimal and other policies.

We consider semantics-aware remote estimation of a discrete-state Markov source with both normal (low-priority) and alarm (high-priority) states. Erroneously announcing a normal state at the destination when the source is actually in an alarm state (i.e., missed alarm) incurs a significantly higher cost than falsely announcing an alarm state when the source is in a normal state (i.e., false alarm). Moreover, consecutive estimation errors may cause significant lasting impacts, such as maintenance costs and misoperations. Motivated by this, we introduce two new metrics, the Age of Missed Alarm (AoMA) and the Age of False Alarm (AoFA), to capture the lasting impacts incurred by different estimation errors. Notably, these two age processes evolve interdependently and distinguish between different error types. Our goal is to design a transmission policy that achieves an optimized trade-off between lasting impact and communication cost. The problem is formulated as a countably infinite-state Markov decision process (MDP) with an unbounded cost function. We show the existence of a simple switching policy with distinct thresholds for each age process and derive closed-form expressions for its performance. For symmetric and non-prioritized sources, we show that the optimal policy reduces to a threshold policy with identical thresholds. For numerical tractability, we propose a finite-state approximate MDP and prove that it converges exponentially fast to the original MDP in the truncation size. Finally, we develop an efficient search algorithm to compute the optimal switching policy and validate our theoretical findings with numerical results.

This paper studies semantics-aware remote estimation of Markov sources. We leverage two complementary information attributes: the urgency of lasting impact, which quantifies thesignificanceof consecutive estimation error at the transmitter, and the age of information (AoI), which captures thepredictabilityof outdated information at the receiver. The objective is to minimize the long-run average lasting impact subject to a transmission frequency constraint. The problem is formulated as a constrained Markov decision process (CMDP) with potentially unbounded costs. We show the existence of an optimalsimple mixture policy, which randomizes between two neighboringswitching policiesat a common regeneration state. A closed-form expression for the optimal mixture coefficient is derived. Each switching policy triggers transmission only when the error holding time exceeds a threshold that depends on both the instantaneous estimation error and the AoI.We further derive sufficient conditions under which the thresholds are independent of the instantaneous error and the AoI. Finally, we propose a structure-aware algorithm, Insec-SPI, that computes the optimal policy with reduced computation overhead. Numerical results demonstrate that incorporating both the age and semantics of information significantly improves estimation performance compared to using either attribute alone.

In this paper, we investigate a model relevant to semantics-aware goal-oriented communications, and propose a new metric that incorporates the utilization of information in addition to its timelines. We consider the transmission of observations from an external process to a battery-powered receiver through status updates. These updates inform the receiver about the process status and enable actuation if sufficient energy is available. We focus on a wireless power transfer (WPT) model, where the receiver receives energy from a dedicated power transmitter.We analyze the Age of Information (AoI) and propose a new metric, theAge of Actuation (AoA), which is relevant when the receiver utilizes the status updates to perform actions in a timely manner. We provide analytical characterizations of the average AoA and the violation probability of the AoA, demonstrating that AoA generalizes AoI. Moreover, we introduce and analytically characterize the Probability ofMissing Actuation (PoMA); this metric becomes relevant also toquantify the incurred cost of a missed action. We formulate unconstrained and constrained optimization problems for all the metrics and present numerical evaluations of our analytical results. This proposed set of metrics goes beyond the traditional timeliness metrics since the synergy of different flows is now considered.

We investigate the role of channel access schemes in enhancing the timeliness of status updates in sensor networks. Specifically, we model the large-scale sensor network as a Poisson cellular network and derive the network average age of information (AoI) under five different channel access schemes: slotted ALOHA, frame slotted ALOHA, random scheduling, round robin, and channel-aware. These schemes are categorized based on random vs. scheduled access and non-channel-aware vs. channel-aware. Our goal is to investigate when the additional overhead and complexity introduced by scheduling and channel state information (CSI) are beneficial, enabling better decisions in network design. Our findings reveal that the effectiveness of these schemes is influenced by the signal-to-interference ratio (SIR) decoding threshold, which often reflects the length of communication data. For short-packet communications, the performance differences among various channel access strategies are minimal, and the gains from scheduling are limited. Additionally, the inclusion of extra CSI does not yield performance improvements; in fact, some simple scheduling strategies, along with channelaware strategy that leverage CSI, may not outperform basic random access methods. Among the protocols we examined, the round robin scheme achieves the best performance. In contrast, scheduled access schemes exhibit a clear performance advantage in long-packet communications. Furthermore, the channel-aware scheme significantly enhances the network AoI performance, particularly in networks with higher transmitter competition.

Federated learning facilitates collaborative model training across multiple clients while preserving data privacy. However, its performance is often constrained by limited communication resources, particularly in systems supporting a large number of clients. To address this challenge, integrating over-the-air computations into the training process has emerged as a promising solution to alleviate communication bottlenecks. The system significantly increases the number of clients it can support in each communication round by transmitting intermediate parameters via analog signals rather than digital ones. This improvement, however, comes at the cost of channel-induced distortions, such as fading and noise, which affect the aggregated global parameters. To elucidate these effects, this paper develops a theoretical framework to analyze the performance of over-the-air federated learning in large-scale client scenarios. Our analysis reveals three key advantages of scaling up the number of participating clients: (1) Enhanced Privacy: The mutual information between a client’s local gradient and the server’s aggregated gradient diminishes, effectively reducing privacy leakage. (2) Mitigation of Channel Fading: The channel hardening effect eliminates the impact of small-scale fading in the noisy global gradient. (3) Improved Convergence: Reduced thermal noise and gradient estimation errors benefit the convergence rate. These findings solidify over-the-air model training as a viable approach for federated learning in networks with a large number of clients. The theoretical insights are further substantiated through extensive experimental evaluations.

The Age of Information (AoI) has emerged as a critical metric for quantifying information freshness; however, its interplay with channel estimation in partially observable wireless systems remains underexplored. This work considers a transmitter-receiver pair communicating over an unreliable channel with time-varying reliability levels. The transmitter observes the instantaneous link reliability through a channel state information acquisition procedure, during which the data transmission is interrupted. This leads to a fundamental trade-off between utilizing limited network resources for either data transmission or channel state information acquisition to combat the channel aging effect. Assuming the wireless channel is modeled as a finite-state Markovian channel, we formulate an optimization problem as a partially observable Markov decision process (POMDP), obtain the optimal policy through the relative value iteration algorithm, and demonstrate the efficiency of our solution through simulations. To the best of our knowledge, this is the first work to aim for an optimal scheduling policy for data transmissions while considering the effect of channel state information aging.

Achieving flexible and efficient wireless resource sharing across diverse applications and services is among the key goals of the sixth-generation of mobile systems (6G). This work investigates the performance of a real-time system coexisting with a broadband service in a frame-based wireless channel. Specifically, we consider a remote tracking device that monitors an information source and transmits updates to a base station (BS) for real-time source reconstruction, and potential remote actuation. We revise the common idealized assumptions in real-time remote tracking studies, such as instantaneous feedback and pervasive wireless resources, as they do not hold in practical scenarios. We consider a monitoring device and a broadband user communicating with the BS via a grant-free access mechanism over wireless resources defined for either orthogonal or non-orthogonal access, with feedback scheduled at the end of each frame. We analyze system performance using goal-oriented performance metrics for real-time remote reconstruction, alongside throughput and energy efficiency for the broadband user. Our results show that the ‘Idealistic’ model considered in conventional studies achieves better performance but incurs disproportionately high overhead compared to the Frame-Based model. Moreover, within the Frame-Based model, orthogonal resource sharing is preferable for maximizing broadband throughput, while non-orthogonal sharing significantly improves energy efficiency.

Despite extensive research on Quality-of-Services (QoS) analysis of 5G networks, practical applications remain limited. This gap may be attributed to the lack of available tools and the complexity of developing or configuring technical systems to implement theoretical approaches. To address this, we developed an edge control system within a private 5G base station, utilizing Precision Time Protocol (PTP) to enable accurate Age of Information (AoI) measurements. Through analysis using AoI and Age of Actuation (AoA) metrics, we demonstrate the accomplishment of comparable results in an emulated Local Area Network (LAN), which offers greater accessibility and reduced complexity. We also test the reliability of network emulation application on system performance analysis.

We study the real-time remote tracking of a two-state Markov process powered by an energy harvesting source. The source dynamically decides whether to transmit over an unreliable channel based on the state of the system. This problem is formulated as a Markov decision process (MDP) to determine the optimal transmission policy that minimizes the average Version Innovation Age (VIA) as a key performance metric. We demonstrate that the optimal transmission policy is threshold-based, determined by the battery level, source state, and VIA value. We numerically validate the analytical structure of the optimal policy and compare its performance against two baseline policies under various system parameters, establishing the superior performance of our approach.

We study the semantics-aware remote state estimation of a Markov chain with prioritized states. The aim is to exploit the significance of information through the history of system realizations to determine the optimal timing of transmission, thereby reducing the amount of uninformative data transmitted in the network. To this end, we introduce the significanceaware Age of Consecutive Error (AoCE) that captures three semantic attributes: the significance of estimation error, the cost of consecutive error (or lasting impact, for short), and the urgency of lasting impact. We identify the optimal transmission problem as a countably infinite state Markov decision process (MDP) with unbounded costs. We give sufficient conditions under which an optimal policy exists to have bounded average costs. We show that the optimal policy exhibits a switching structure and, under certain conditions, degenerates into a simple threshold policy. A structured policy iteration (SPI) algorithm is proposed to compute an asymptotically optimal policy with reduced computation overhead. An important takeaway is that the more semantic attributes we utilize, the fewer transmissions are needed.

Full-duplex (FD) communication improves spectral efficiency by allowing simultaneous transmission and reception on the same frequency band. This paper analyzes a two-tier network consisting of macrocells and picocells, where base stations (BSs) operate in FD mode while users operate in half-duplex (HD) mode. However, interference remains a major challenge in these systems, significantly impacting coverage probability. To enhance network performance, we incorporate user offloading and resource partitioning. Offloading redistributes users from macrocells to picocells to balance the network load. However, offloaded users often experience lower SINR compared to those connected to macrocells. Resource partitioning is applied to mitigate this SINR degradation and reduce interference. This method allocates a fraction of time or frequency resources where macrocells remain inactive, allowing picocells to serve users with less interference. We derive analytical expressions for the downlink coverage probability, considering the effects of offloading, resource partitioning, and key network parameters. Our results indicate that load balancing by itself is insufficient; however, when resource partitioning is combined with offloading, DL coverage probability is significantly improved.

We investigate the role of channel access schemes in enhancing the timeliness of status updates in sensor networks. Specifically, we model the large-scale sensor network as a Poisson cellular network and derive the network average Age of Information (AoI) under two channel access schemes: random and scheduled access. Our findings reveal that the effectiveness of these schemes is influenced by the signal-to-interference ratio (SIR) decoding threshold, which often reflects the length of communication data. For short-packet communications, performance differences among various channel access strategies are minimal, and the gains from scheduling are limited; in fact, some simple scheduling strategies may not outperform basic random strategies. Conversely, scheduled access schemes demonstrate a distinct performance advantage for long-packet communications. The round robin scheme consistently yields the best performance among the four protocols we examined-slotted ALOHA, frame slotted ALOHA, random scheduling, and round robin scheduling. This is due to its ability to mitigate intra-cell interference and regularize both status updates and channel access periods for each sensor, which is particularly beneficial in reducing AoI.

Federated learning enables multiple clients to collaboratively train a common model while concurrently preserving data privacy. However, its performance is often constrained by limited communication resources, especially when the system encounters a large number of clients. Under those circumstances, integrating over-the-air computations into the model training procedure is considered an effective approach to coping with the communication bottleneck. Specifically, by uploading each client's intermediate parameters via analog transmissions instead of digital ones, the system can dramatically extend the number of clients it simultaneously supports in each communication round. However, that is achieved at the expense of introducing channel distortions, particularly fading and noise, in the aggregated global parameter. To demystify these effects, the present paper develops a theoretical framework to analyze the performance of the over-the-air federated model training process. Our analysis unveils a three-fold benefit from system scaling up, i.e., as the number of participating clients increases: (i) the privacy leakage, quantified by the mutual information between each client's locally possessed gradient and the edge's globally aggregated one, substantially decreases, (ii) the impairment of small-scale fading disappears due to the channel hardening effect, and (iii) the convergence rate is enhanced as thermal noise and gradient estimation error can be reduced. To that end, it establishes over-the-air model training as a viable approach for implementing federated learning in scenarios with a large number of clients. We corroborate the theoretical findings with extensive experiments.

We study the age of information (AoI) in a random access network consisting of multiple source-destination pairs, where each source node is empowered by energy harvesting capability. Every source node transmits a sequence of data packets to its destination using only the harvested energy. Each data packet is encoded with finite-length codewords, characterizing the nature of short codeword transmissions in random access networks. By combining tools from bulk-service Markov chains with stochastic geometry, we derive an analytical expression for the network average AoI and obtain closed-form results in two special cases, i.e., the small and large energy buffer size scenarios. Our analysis reveals the trade-off between energy accumulation time and transmission success probability. We then optimize the network average AoI by jointly adjusting the update rate and the blocklength of the data packet. Our findings indicate that the optimal update rate should be set to one in the energy-constrained regime where the energy consumption rate exceeds the energy arrival rate. This also means if the optimal blocklength of the data packet is pre-configured, an energy buffer size supporting only one transmission is sufficient.

This paper studies decision-making for goal-oriented effective communication. We consider an end-to-end status update system where a sensing agent (SA) observes a source, generates and transmits updates to an actuation agent (AA), while the AA takes actions to accomplish a goal at the endpoint. We integrate the push- and pull-based update communication models to obtain apush-and-pullmodel, which allows the transmission controller at the SA to decide whether to push an update to the AA and the query controller at the AA to pull updates by initiating queries at specific time instants. To gauge effectiveness, we utilize agrade of effectiveness(GoE) metric incorporating the updates’ freshness, usefulness, and the timeliness of actions as qualitative attributes. We then derive effect-aware policies to maximize the expected discounted sum of the updates’ effectiveness subject to induced costs. The effect-aware policy at the SA considers the potential effectiveness of communicated updates at the endpoint, while at the AA, it accounts for the probabilistic evolution of the source and importance of the generated updates. Our results show the proposed push-and-pull model outperforms models solely based on push- or pull-based updates both in terms of efficiency and effectiveness. Additionally, using effect-aware policies at both agents enhances effectiveness compared to periodic and/or probabilistic, effect-agnostic policies at either or both agents.

We consider a wireless networked control system (WNCS) with imperfect bidirectional links for real-time applications such as smart grids. To maintain the stability of WNCS, captured by the probability that plant state violates preset values, at minimal cost, heterogeneous physical processes are monitored by multiple sensors. This status information, such as dynamic plant state and Markov Process-based context information, is then received/estimated by the controller for remote control. However, scheduling multiple sensors and designing the controller with limited resources is challenging due to their coupling, delay, and transmission loss. We formulate a Constrained Markov Decision Problem (CMDP) to minimize violation probability with cost constraints. We reveal the relationship between the goal and different updating actions by analyzing the significance of information that incorporates goal-related usefulness and contextual importance. Subsequently, a goal-oriented deterministic scheduling policy is proposed. Two sensing-assisted control strategies and a control-aware estimation policy are proposed to improve the violation probability-cost tradeoff, integrated with the scheduling policy to form a goal-oriented co-design framework. Additionally, we explore retransmission in downlink transmission and qualitatively analyze its preference scenario. Simulation results demonstrate that the proposed goal-oriented co-design policy outperforms previous work in simultaneously reducing violation probability and cost.

This work studies the average Age of Information (AoI) of a remote monitoring setup in which a multi-sensor system observes independent sources and updates the status to a common monitor using orthogonal channels. Considering the limited buffer size at the sensors, we first model each sensor as a first-come-first-served M/M/1/1 queue. Leveraging tools from stochastic hybrid systems, we derive the average AoI of a homogeneous single-source multi-sensor system in which all sensors’ arrival and service rates are the same. We then extend the results to the multi-source, multi-sensor system. For a multi-source dual-sensor system, we present an approximate optimal arrival rate for a given sum arrival rate at a light load. For heterogeneous cases with different arrival and service rates at sensors, the average AoI is derived for the single-source dual-sensor and more general multi-source systems. Our analysis shows that the average AoI decreases by 16.44% and 21.44% for the dual-sensor and three-sensor systems, respectively, compared to the single-sensor system when the service rate and the total arrival rate of the sensors are normalized. Numerical results confirm that the average AoI performance of the single-source dual-sensor system outperforms the M/M/2 system at high system load.

In this work, we consider a real-time IoT monitoring system in which an energy harvesting sensor with a finite-size battery measures a physical process and transmits the status updates to an aggregator. The aggregator, equipped with caching capabilities, can serve the external requests of a destination network with either a stored update or a fresh update from the sensor. We assume the destination network acts as a gossiping network in which the update packets are forwarded among the nodes in a randomized setting. We utilize the Markov Decision Process framework to model and optimize the network’s average Version Age of Information (AoI) and obtain the optimal policy at the aggregator. We demonstrate analytically and verify numerically that the optimal policy structure conforms to a threshold policy regarding the Version AoI at the aggregator. Furthermore, we establish that the optimal policy is independent of the Version AoI value at the destination nodes. Through numerical results, we elucidate the impact of system parameters on the average Version AoI of the network and the rationale behind this impact. Additionally, the simulations unveil scenarios wherein the performance of the optimal policy significantly surpasses that of a set of baseline policies.

In Internet of Things (IoT) status update systems, where information is sampled and subsequently transmitted from a source to a destination node, the imperative necessity lies in maintaining the timeliness of information and updating the system with optimal frequency. Optimizing information freshness in resource-limited status update systems often involves Constrained Markov Decision Process (CMDP) problems with update rate constraints. Solving CMDP problems, especially with multiple constraints, is a challenging task. To address this, we present a token-based approach that transforms CMDP into an unconstrained MDP, simplifying the solution process. To demonstrate the comprehensiveness and effectiveness of the token-based approach, we apply this method to systems with one and two update rate constraints to optimize two distinct metrics: Age of Incorrect Information (AoII) and Age of Information (AoI), respectively, and explore the analytical and numerical aspects. Additionally, we introduce an iterative triangle bisection method for solving the CMDP problems with two constraints, comparing its results with the token-based MDP approach. The structure of the optimal token-based solution is studied analytically. Our numerical results show that the token-based approach yields superior performance over baseline policies, converging to the optimal policy as the maximum number of tokens increases.

This paper studies the remote estimation of multiple Markov sources over a lossy and rate-constrained channel. Unlike most existing studies that treat all source states equally, we exploit thesemantics of informationand consider that the remote actuator has different tolerances for the estimation errors. We aim to find an optimal scheduling policy that minimizes the long-termstate-dependentcosts of estimation errors under a transmission frequency constraint. The optimal scheduling problem is formulated as aconstrained Markov decision process(CMDP). We show that the optimal Lagrangian cost follows a piece-wise linear and concave (PWLC) function, and the optimal policy is, at most, a randomized mixture of two simple deterministic policies. By exploiting the structural results, we develop a newintersection searchalgorithm that finds the optimal policy using only a few iterations. We further propose a reinforcement learning (RL) algorithm to compute the optimal policy without knowinga priorithe channel and source statistics. To avoid the “curse of dimensionality” in MDPs, we propose an online low-complexitydrift-plus-penalty(DPP) algorithm. Numerical results show that continuous transmission is inefficient, and remarkably, our semantic-aware policies can attain the optimum by strategically utilizing fewer transmissions by exploiting the timing of the important information.

Using multiple sensors to update the status process of interest is promising in improving the information freshness. The unordered arrival of status updates at the monitor end poses a significant challenge in analyzing the timeliness performance of parallel updating systems. This work investigates the age of information (AoI) of a discrete-time dual-sensor status updating system. Specifically, the status update is generated following the zero-waiting policy. The two sensors are modeled as a geometrically distributed service time queue and a deterministic service time queue in parallel. We derive the analytical expressions for the average AoI and peak AoI using the graphical analysis method. Moreover, the connection of average AoI between discrete-time and continuous-time systems is also explored. It reveals that in dual-queue systems, the AoI results of continuous-time systems with exponential time distribution can be extended from the limit cases of discrete-time systems with geometric distribution. Numerical results validate the effectiveness of our analysis and further show that randomness of service time contributes more AoI reduction than determinacy of service time in dual-queue systems in most cases, which is different from what is known about the single-queue system.

We consider the problem of real-time remote monitoring of a two-state Markov process, where a sensor observes the source state and decides whether to transmit updates over an unreliable channel. We introduce a change-aware randomized stationary policy, in which the source is sampled probabilistically whenever its state changes, and a semantics-aware randomized stationary policy, in which sampling is performed probabilistically based on the current source state and whether the system was in sync in the previous time slot. We then propose two new performance metrics:the Version Innovation Age (VIA), which measures significant changes in content between versions, andthe Age of Incorrect Version (AoIV), which quantifies the outdated versions at the receiver compared to the source when the system is in an incorrect state. We analyze their performance under the proposed and other state-of-the-art sampling policies. Specifically, we derive closed-form expressions for the distributions and averages of VIA, AoIV, and the Age of Incorrect Information (AoII), and formulate three constrained optimization problems to minimize them while accounting for constraints on the time-averaged sampling cost and the reconstruction error. Finally, we compare various sampling and transmission policies and identify the conditions under which each policy performs best.

We consider a real-time state reconstruction system for industrial metaverse. The time-varying physical process states in real space are captured by multiple sensors via wireless links, and then reconstructed in virtual space. In this paper, we use the spatial-temporal correlation of the sensor data of interest to infer the real-time data of the target sensor to reduce the mean squared error (MSE) of reconstruction for industrial metaverse under short-packet transmission (SPT). Both synchronous and asynchronous transmission modes for multiple sensors are considered. It is proved that the average reconstruction MSE and average block error probability (BLEP) have a positive correlation under inference with synchronous transmission scheme, whereas they have a negative correlation under inference with asynchronous transmission scheme in certain conditions. Additionally, the average reconstruction MSE decreases monotonically with the mean squared spatial correlation (MSSC), which characterizes the global spatial correlation level. With a high BLEP or long transmission period, even under weak MSSC, the inference scheme still significantly reduces the average reconstruction MSE compared to the no inference case. Moreover, closed-form MSSC thresholds are derived for the superiority regions of the inference with synchronous transmission and inference with asynchronous transmission schemes, respectively. Adaptations of blocklength and time shift of asynchronous transmission are conducted to minimize the average reconstruction MSE. Simulation results show that the two inference schemes outperform the no inference case, with an average MSE reduction of more than 50%.

This paper considers the semantics-aware remote state estimation of an asymmetric Markov chain withprioritizedstates. Due to resource constraints, the sensor needs to trade off estimation quality against communication cost. The aim is to exploit thesignificanceof information through the history of system realizations to determine the optimal timing of transmission, thereby reducing the amount of uninformative data transmitted in the network. To this end, we introduce a new metric, thesignificance-aware Age of Consecutive Error(AoCE), that captures three semantic attributes: thesignificance of estimation error, thecost of consecutive error(orlasting impact, for short), and theurgency of lasting impact. Different costs and non-linear age functions are assigned to different estimation errors to account for their relative importance to system performance. We identify the optimal transmission problem as a countably infinite state Markov decision process (MDP) with unbounded costs. We first give sufficient conditions on the age functions, source pattern, and channel reliability so that an optimal policy exists to have bounded average costs. We show that the optimal policy exhibits aswitching structure. That is, the sensor triggers a transmission only when the system has been trapped in an error for a certain number of consecutive time slots. We also provide sufficient conditions under which the switching policy degenerates into a simplethreshold policy, i.e., featuring identical thresholds for all estimation errors. Furthermore, we exploit the structural results and develop astructured policy iteration(SPI) algorithm that considerably reduces computation overhead. Numerical results show that the optimal policy outperforms the classic rule-, distortion- and age-based policies. An important takeaway is thatthe more semantic attributes we utilize, the fewer transmissions are needed.

Diffusion models have been extensively utilized in AI-generated content (AIGC) in recent years, thanks to the superior generation capabilities. Combining with semantic communications, diffusion models are used for tasks such as denoising, data reconstruction, and content generation. However, existing diffusion-based generative models do not consider the stringent bandwidth limitation, which limits its application in wireless communication. This paper introduces a diffusion-driven semantic communication framework with advanced VAE-based compression for bandwidth-constrained generative model. Our designed architecture utilizes the diffusion model, where the signal transmission process through the wireless channel acts as the forward process in diffusion. To reduce bandwidth requirements, we incorporate a downsampling module and a paired upsampling module based on a variational auto-encoder with reparameterization at the receiver to ensure that the recovered features conform to the Gaussian distribution. Furthermore, we derive the loss function for our proposed system and evaluate its performance through comprehensive experiments. Our experimental results demonstrate significant improvements in pixel-level metrics such as peak signal to noise ratio (PSNR) and semantic metrics like learned perceptual image patch similarity (LPIPS). These enhancements are more profound regarding the compression rates and SNR compared to deep joint source-channel coding (DJSCC).

We consider a base station (BS) that receives version update packets from multiple streams and broadcasts them using non-orthogonal multiple access (NOMA) over a fading broadcast channel. Sequentially indexed packets arrive randomly, rendering previous ones obsolete. The version age of information (VAoI) at a user is defined as the difference between the latest packet’s version index at the BS and at the user. Our objective is to minimize the average VAoI across users, subject to an average power constraint at the BS, by optimally scheduling and transmitting packets with sufficient power for successful delivery. We consider channel-only stationary randomized policies (CO-SRP), making transmission decisions based on channel power gains, and obtain optimal CO-SRP, showing that VAoI achieved with CO-SRP is within twice the optimal VAoI. We also develop a Constrained Markov Decision Process (CMDP)-based solution, several heuristic benchmarks, and analyze CMDP policy properties. Simulations compare achievable VAoI and computational performance of various policies and reveal differences between optimizing AoI and VAoI. Notably, a scheme allowing transmission to at most one user at a time matches NOMA’s performance under strict power constraints but is outperformed when constraints are relaxed. Additionally, AoI-optimized policies result in higher VAoI compared to VAoI-optimized policies and vice versa, when user arrival rates are mismatched.

In this paper, we extend the metric of Age of Actuation (AoA), and we propose the Age of Actuated Information (AoAI) within a discrete-time system that integrates data caching and energy harvesting (EH). AoA evaluates the timeliness of actions irrespective of the age of the information, while AoAI considers the freshness of the utilized data packet. We analytically characterize the performance of AoA and AoAI for the system at hand. Our findings show that while AoAI consistently decreases with increased data and energy packet arrival rates, AoA shows a counter-intuitive behavior, with a potential increase under limited data or energy availability. These metrics go towards the semantics of information and goal-oriented communications since they consider the timeliness of the utilized information to perform an action.

We study a pull-based communication system where a sensing agent updates an actuation agent using a query control policy, which is adjusted in the evolution of an observed information source and the usefulness of each update for achieving a specific goal. For that, a controller decides whether to pull an update at each slot, predicting what is probably occurring at the source and how much effective impact that update could have at the endpoint. Thus, temporal changes in the source evolution could modify the query arrivals to capture important updates. The amount of impact is determined by a grade of effectiveness (GoE) metric, which incorporates both freshness and usefulness attributes of the communicated updates. Applying an iterative algorithm, we derive query decisions that maximize the longterm average GoE for the communicated packets, subject to cost constraints. Our analytical and numerical results show that the proposed query policy exhibits higher effectiveness than existing periodic and probabilistic query policies for a wide range of query arrival rates.

We optimize the Age of Information (AoI) in random access networks using the age-threshold slotted ALOHA (TSA) protocol. The network comprises multiple source-destination pairs, where each source sends a sequence of status update packets to its destination over a shared spectrum. The TSA protocol stipulates that a source node must remain silent until its AoI reaches a predefined threshold, after which the node accesses the radio channel with a certain probability. We derive analytical expressions for the transmission success probability and time-average AoI using stochastic geometry tools. Subsequently, we obtain closed-form expressions for the optimal update rate and age threshold that minimize the time-average AoI. In addition, we establish a scaling law for the time-average AoI in random access networks, revealing that the optimal time-average AoI increases linearly with the deployment density. Notably, the growth rate under TSA is half of that under conventional slotted ALOHA.

We consider the remote estimation of a discrete-state Markov source with normal and alarm states. Data significance is revealed via two semantic attributes: 1) Erroneously announcing a normal state at the destination when the source is actually in an alarm state (i.e., missed alarm error) incurs a significantly higher cost than falsely announcing an alarm state when the source is in a normal state (i.e., false alarm error). 2) Successive reception of an estimation error may cause significant lasting impact, e.g., maintenance cost and wrong operations. Motivated by this, we assign different costs to different estimation errors and introduce two new age metrics, namely the Age of Missed Alarm (AoMA) and the Age of False Alarm (AoFA), to account for the lasting impact incurred by different estimation errors. We aim to achieve an optimal trade-off between the cost of estimation error, lasting impact, and communication utilization. The problem is formulated as an infinite-state Markov decision process (MDP). We show that the optimal policy exhibits a switching structure, i.e., triggering transmissions only when the AoMA or AoFA exceeds a threshold. Numerical results underscore that our approach significantly reduces the amount of less important information transmitted in the networks.

This paper investigates goal-oriented communication for remote estimation of multiple Markov sources in resource-constrained networks. An agent decides the updating times of the sources and transmits the packet to a remote destination over an unreliable channel with delay. The destination is tasked with source reconstruction for actuation. We utilize the metric cost of actuation error (CAE) to capture the state-dependent actuation costs. We aim for a sampling policy that minimizes the long-term average CAE subject to an average resource constraint. We formulate this problem as an average-cost constrained Markov Decision Process (CMDP) and relax it into an unconstrained problem by utilizing Lyapunov drift techniques. Then, we propose a low-complexity drift-plus-penalty (DPP) policy for systems with known source/channel statistics and a Lyapunov optimization-based deep reinforcement learning (LO-DRL) policy for unknown environments. Our policies significantly reduce the number of uninformative transmissions by exploiting the timing of the important information.

Due to the fact that large swathes on Earth still lack broadband communication coverage, especially in remote/rural areas and developing countries, there have been several attempts, starting from 3GPP Release 17, to lay out the architectural amendments needed for the integration of terrestrial networks with their non-terrestrial counterparts. Such attempts have led to recent projects regarding such integration that consider either 5G/5G-Advanced networks or more revolutionary approaches for the forthcoming 6G networks. In this manuscript, we give an overview of the architectural framework, technical innovations, and considered use cases of the Horizon Europe ETHER project.

We leverage the Multiplicative Weight Update (MWU) method to develop a decentralized algorithm that significantly improves the performance of dynamic time division duplexing (D-TDD) in small cell networks. The proposed algorithm adaptively adjusts the time portion allocated to uplink (UL) and downlink (DL) transmissions at every node during each scheduled time slot, aligning the packet transmissions toward the most appropriate link directions according to the feedback of signal-to-interference ratio information. Our simulation results reveal that compared to the (conventional) fixed configuration of UL/DL transmission probabilities in D-TDD, incorporating MWU into D-TDD brings about a two-fold improvement of mean packet throughput in the DL and a three-fold improvement of the same performance metric in the UL, resulting in the D-TDD even outperforming Static-TDD in the UL. It also shows that the proposed scheme maintains a consistent performance gain in the presence of an ascending traffic load, validating its effectiveness in boosting the network performance. This work also demonstrates an approach that accounts for algorithmic considerations at the forefront when solving stochastic problems.

The problem of goal-oriented semantic filtering and timely source coding in multiuser communication systems is considered here. We study a distributed monitoring system in which multiple information sources, each observing a physical process, provide status update packets to multiple monitors having heterogeneous goals. Two semantic filtering schemes are first proposed as a means to admit or drop arrival packets based on their goal-dependent importance, which is a function of the intrinsic and extrinsic attributes of information and the probability of occurrence of each realization. Admitted packets at each sensor are then encoded and transmitted over block-fading wireless channels so that served monitors can timely fulfill their goals. A truncated error control scheme is derived, which allows transmitters to drop or retransmit undelivered packets based on their significance. Then, we formulate the timely source encoding optimization problem and analytically derive the optimal codeword lengths assigned to the admitted packets which maximize a weighted sum of semantic utility functions for all pairs of communicating sensors and monitors. Our analytical and numerical results provide the optimal design parameters for different arrival rates and highlight the improvement in timely status update delivery using the proposed semantic filtering, source coding, and error control schemes.

Timely status updating is the premise of emerging interaction-based applications in the Internet of Things (IoT). Using redundant devices to update the status of interest is a promising method to improve the timeliness of information. However, parallel status updating leads to out-of-order arrivals at the monitor, significantly challenging timeliness analysis. This work studies the Age of Information (AoI) of a multi-queue status update system where multiple devices monitor the same physical process. Specifically, two systems are considered: theBasic System, which only has type-1 devices that are ad hoc devices located close to the source, and theHybrid System, which contains additional type-2 devices that are infrastructure-based devices located in fixed points compared to theBasic System. Using the Stochastic Hybrid Systems (SHS) framework, a mathematical model that combines discrete and continuous dynamics, we derive the expressions of the average AoI of the considered two systems in closed form. Numerical results verify the accuracy of the analysis. It is shown that when the number and parameters of the type-1 devices/type-2 devices are fixed, the logarithm of average AoI will linearly decrease with the logarithm of the total arrival rate of type-2 devices or that of the number of type-1 devices under specific condition. It has also been demonstrated that the proposed systems can significantly outperform the FCFS M/M/Nstatus update system.

In this work, we study the real-time tracking and reconstruction of an information source with the purpose of actuation. A device monitors the state of the information source and transmits status updates to a receiver over a wireless erasure channel. We consider two models for the source, namely anN-state Markov chain and anN-state Birth-Death Markov process. We investigate several joint sampling and transmission policies, including a semantics-aware one, and we study their performance for a set of metrics. Specifically, we investigate the real-time reconstruction error and its variance, the cost of actuation error, the consecutive error, and the cost of memory error. These metrics capture different characteristics of the system performance, such as the impact of erroneous actions and the timing of errors. In addition, we propose a randomized stationary sampling and transmission policy and we derive closed-form expressions for the aforementioned metrics. We then formulate two optimization problems. The first optimization problem aims to minimize the time-averaged reconstruction error subject to time-averaged sampling cost constraint. Then, we compare the optimal randomized stationary policy with uniform, change-aware, and semantics-aware sampling policies. Our results show that in the scenario of constrained sampling generation, the optimal randomized stationary policy outperforms all other sampling policies when the source is rapidly evolving. Otherwise, the semantics-aware policy performs the best. The objective of the second optimization problem is to obtain an optimal sampling policy that minimizes the average consecutive error with a constraint on the time-averaged sampling cost. Based on this, we propose await-then-generatesampling policy which is simple to implement.

Many real-time applications of the Internet of Things (IoT) need to deal with correlated information generated by multiple sensors. The design of efficient status update strategies that minimize the Age of Correlated Information (AoCI) is a key factor. In this paper, we consider an IoT network consisting of sensors equipped with the energy harvesting (EH) capability. We optimize the average AoCI at the data fusion center (DFC) by appropriately managing the energy harvested by sensors, whose true battery states are unobservable during the decision-making process. Particularly, we first formulate the dynamic status update procedure as a partially observable Markov decision process (POMDP), where the environmental dynamics are unknown to the DFC. In order to address the challenges arising from the causality of energy usage, unknown environmental dynamics, unobservability of sensors' true battery states, and large-scale discrete action space, we devise a deep reinforcement learning (DRL)-based dynamic status update algorithm. The algorithm leverages the advantages of the soft actor-critic and long short-term memory techniques. Meanwhile, it incorporates our proposed action decomposition and mapping mechanism. Extensive simulations are conducted to validate the effectiveness of our proposed algorithm by comparing it with available DRL algorithms for POMDPs.

We optimize the Age of Information (AoI) in mobile networks using the age-threshold slotted ALOHA (TSA) protocol. The network comprises multiple source-destination pairs, where each source sends a sequence of status update packets to its destination over a shared spectrum. The TSA protocol stipulates that a source node must remain silent until its AoI reaches a predefined threshold, after which the node accesses the radio channel with a certain probability. Using stochastic geometry tools, we derive analytical expressions for the transmission success probability, mean peak AoI, and time-average AoI. Subsequently, we obtain closed-form expressions for the optimal update rate and age threshold that minimize the mean peak and time-average AoI, respectively. In addition, we establish a scaling law for the mean peak AoI and time-average AoI in mobile networks, revealing that the optimal mean peak AoI and time-average AoI increase linearly with the deployment density. Notably, the growth rate of time-average AoI under TSA is half of that under SA. When considering the optimal mean peak AoI, the TSA protocol exhibits comparable performance to the traditional slotted ALOHA protocol. These findings conclusively affirm the advantage of TSA in reducing higher-order AoI, particularly in densely deployed networks.

In this work, we consider mixed traffic with time-sensitive users; a deadline-constrained user, and an AoI-oriented user. To develop an efficient scheduling policy, we cast a novel optimization problem formulation for minimizing the average AoI while satisfying the timely throughput constraints. The optimization problem is a Constrained Markov Decision Process (CMDP). We relax the constrained problem to an unconstrained Markov Decision Process (MDP) problem by utilizing Lyapunov optimization theory. The unconstrained problem is solved for each frame by applying backward dynamic programming. Simulation results show that the timely throughput constraints are satisfied while minimizing the average AoI. Also, simulation results show the convergence of the algorithm for different values of the weighted factor and the trade-off between the AoI and the timely throughput.

Emerging interaction-based Internet of Things (IoT) applications have stringent demand for timeliness, imposing critical challenges to the design of status update system. Using redundant devices to update the status of the same process is a promising way to improve timeliness, but this approach can result in out of order update arrivals, making it difficult to analyze timeliness. To that end, the present paper conducts a theoretical study toward the Age of Information (AoI) of a multi-queue status update system where multiple sensors observe one physical process and update a common monitor. Based on the stochastic hybrid systems method, the average AoI of the considered system is derived in closed form. The theoretical results are consistent with the simulation results, verifying the correctness of the theoretical analysis. It is shown that the logarithm of the average AoI is linearly decreasing with the logarithm of the number of sensors.

We propose a frame slotted ALOHA (FSA)-based protocol for source nodes to update status information toward their intended destinations in a random access network. We evaluate the effect of such a protocol on the network’s timeliness performance using the Age of Information (AoI) metric. Specifically, we leverage tools from stochastic geometry to model the geographical positions of the source-destination pairs and capture the entanglement amongst the nodes’ spatial-temporal attributes through the interference they caused to each other. We derive closed-form expressions for the average AoI over a typical transmission link. Our analysis shows that in densely deployed networks, the FSA-based status updating protocol can significantly decrease the average AoI. Furthermore, under the same updating frequency, converting a slotted ALOHA protocol into an FSA-based one always leads to a reduction in the average AoI.

This paper considers a communication system where a source sends time-sensitive information to its destination. We assume that both arrival and service processes of the messages are memoryless and the source has a single server with no buffer. Besides, we consider that the service is interrupted by an independent random process, which we model using an OnOff process. For this setup, we study the age of information for two queueing disciplines: 1) non-preemptive, where the messages arriving while the server is occupied are discarded, and 2) preemptive, where the in-service messages are replaced with newly arriving messages in the Off states. For these disciplines, we derive closed-form expressions for the mean peak age and mean age.

Goal-oriented communication is a promising approach to tailor the network resource management algorithms to the needs of particular applications, thus enhancing the efficiency of resource utilization and boosting the application performance. In the context of distributed cyber-physical systems and networked control systems, the design of a control-aware transport layer (TL) represents a realistic approach for goaloriented communications since it can be integrated into generic control setups without making assumptions on particular hardware or network technologies and deliver enhanced end-to-end performance. This demo showcases the application performance of different TL schemes used for communication between the sensors and the controllers monitoring and actuating inverted pendulums, i.e., multi-dimensional plants. The nodes of the control loops are realized with Zolertia Re-Mote devices, and multiple control loops communicate over the shared wireless network using IEEE 802.15.4 standard. We use the demonstration testbed to compare the performance of conventional, state-of-the-art, and novel goal-oriented TL schemes by observing the emulated dynamics of inverted pendulums.

In Wireless Networked Control Systems (WNCSs), the feedback control loops are closed over a wireless communication network. The proliferation of WNCSs requires efficient network resource management mechanisms since the control performance is significantly affected by the impairments caused by network limitations. In conventional communication networks, the amount of transmitted data is one of the key performance indicators. In contrast, in WNCSs, the efficiency of the network is measured by its ability to facilitate control applications, and the data transmission rate should be limited to avoid network congestion. In this work, we consider an experimental setup where multiple control loops share a wireless communication network. Our testbed comprises up to five control loops that include Zolertia Re-Mote devices implementing IEEE 802.15.4 standard. We propose a novel relevance- and network-aware transport layer (TL) scheme for WNCSs. The proposed scheme admits the most important measurements for the control process into the network while considering current network conditions. Moreover, we propose a mechanism for the scheme parameters adaptation in dynamic scenarios with unknown network statistics. Unlike the conventional TL mechanisms failing to provide adequate control performance due to either congestion in the network or inefficient utilization of available resources, our method prevents network congestion while keeping the control performance high. We argue that relevance- and network-awareness are critical components of network protocol design to avoid control performance degradation in practice.

We develop a theoretical framework to study the training of federated learning models with partial gradients via over-the-air computing. The system consists of an edge server and multiple clients, aiming to collaboratively minimize a global loss function. The clients conduct local training and upload the intermediate parameters (e.g. the gradients) by analog transmissions. Specifically, each client modulates the entries of its local gradient onto a set of common orthogonal waveforms and sends out the signal simultaneously to the edge server; owing to the limited number of orthogonal waveforms, only a subset of the parameters can be selected for uploading during each round of communication. On the server side, it passes the received analog signal to a bank of match filters and obtains a noisy partial gradient vector. The server then uses this partial gradient to update the global parameter and feeds the new model back to all the clients for another round of local training. We derive the convergence rate of such a model training algorithm. We also conduct experiments to investigate the effects of different masking schemes on the convergence performance. The findings advance the understanding of over-the-air federated learning and provide useful insights for system designs.

This work studies the average Age of Information (AoI) of a remote monitoring system in which two sensors observe the same physical process and update the status to a common monitor using orthogonal channels. While using redundant devices to update the status of a process can improve the information timeliness at the monitor, the out-of-order arrivals of updates impose a challenge to the AoI analysis. We first model the system as two parallel M/M/1/1 queues. By leveraging tools from stochastic hybrid systems, we obtain analytically the average AoI of the system. In particular, when the arrival or service rates are the same for the two sensors, the average AoI is given in closed form. Our analysis reveals that the average AoI of the considered system is reduced by 16.44% compared to the single-sensor system when the arrival and service rates are equal to 1. Numerical results show that the considered system outperforms the M/M/2 system in average AoI at high arrival rates.

In this work, we investigate the dynamic power management problem in a two-user secure broadcast channel scenario where the information at the source is kept in two separate queues, one for confidential and one for non-confidential information. The intended receiver of the confidential information transmits a jamming signal to prevent the other receiver from successfully decoding the confidential information. The decoding strategies used at the receivers include successive decoding (SD) and treating interference as noise (TIN). An autonomous agent, located at the source, decides on the power that will be used for the transmission of confidential information. We formulate the transmission power decision problem as a Markov Decision Process (MDP) and utilize the Deep Deterministic Policy Gradient (DDPG) algorithm for the agent to learn approximately optimal policies. We demonstrate that SD yields better rewards than TIN at the legitimate receiver. Additionally, we contrast the DDPG algorithm with three baseline power control policies and show that the former performs better than the latter.

In this work, we consider a real-time loT monitoring system in which an energy harvesting sensor with a finite-size battery measures a physical process and transmits the status updates to an aggregator. The aggregator, equipped with caching capabilities, can serve the external requests of a destination network with either a stored update or a fresh update from the sensor. We assume that the destination network act as a gossiping network in which the update packets are forwarded among the nodes in a randomized setting. We utilize the Markov Decision Process framework to model and optimize the network's average Version Age of Information (AoI) and obtain the optimal policy at the aggregator. The structure of the optimal policy is analytically demonstrated and numerically verified. Numerical results highlight the effect of the system parameters on the average Version AoI. The simulations reveal the superior performance of the optimal policy compared to a set of baseline policies.

We consider a source node deployed in a real-time monitoring application that needs to sample a stochastic process and convey its state timely and accurately to a destination over a wireless ON/OFF channel. The source can either process a raw sample to determine its current state and transmit that information or transmit the raw sample and let the destination determine the state. The source is subjected to an average cost constraint, and it cannot sample, process, and transmit at all the time instants due to the associated costs. When the destination does not receive information, it uses the previous information as an estimate of the current state, which, if it matches the actual state at the source, the distortion is considered to be zero. The objective is to minimize average expected distortion subject to constraints on the average expected age of information (AoI) of states of interest and costs incurred by the source, where the AoI of a state increases if no status update is received, else drops to unity. We derive a stationary randomized policy (SRP) to solve the formulated problem, for which we obtain the expression for the expected AoI under the SRP using a lumpability argument on the two-dimensional discrete-time Markov chain formed using AoI and instantaneous distortion as states. We extensively study the impact of the system parameters on the average distortion under the SRP and draw significant conclusions.

We investigate the performance of a random access network consisting of source-destination dipoles. The source nodes transmit information packets to their destinations over a shared spectrum. All the transmitters in this network adhere to an age threshold slotted ALOHA (TSA) protocol: every source node remains silent until the age of information (AoI) reaches a threshold, after which the source accesses the radio channel with a certain probability. We derive a tight approximation for the signal-to-interference-plus-noise ratio (SINR) meta distribution and verify its accuracy through simulations. We also obtain analytical expressions for the average AoI. Our analysis reveals that when the network is densely deployed, employing TSA significantly decreases the average AoI. The update rate and age threshold must be jointly optimized to fully exploit the potential of the TSA protocol.

We consider a random access network consisting of source-destination pairs. Each source node generates status updates and transmits this information to its intended destination over a shared spectrum. The goal is to minimize the network-wide Age of Information (AoI). We develop a frame slotted ALOHA (FSA)-based policy for generating and transmitting status updates, where the frame size of each source node is adjusted according to its local environment. The proposed policy is of low complexity and can be implemented in a distributed manner. Additionally, it significantly improves the network AoI performance by (a) equalizing the update generation intervals at each source and (b) reducing interference across the network. Furthermore, we derive an analytical expression for the average network AoI attained for that policy. We evaluate the performance of the proposed scheme through simulations, which demonstrate that the locally adaptive FSA policy achieves a remarkable gain in terms of AoI compared to the slotted ALOHA counterpart, confirming the effectiveness of the proposed method.

We propose a frame slotted ALOHA (FSA)-based protocol for a random access network where sources transmit status updates to their intended destinations. We evaluate the effect of such a protocol on the network’s timeliness performance using the Age of Information (AoI) metric. Specifically, we leverage tools from stochastic geometry to model the spatial positions of the source-destination pairs and capture the entanglement amongst the nodes’ spatial-temporal attributes through the interference they caused to each other. We derive analytical expressions for the average and variance of AoI over a typical transmission link in Poisson bipolar and cellular networks, respectively. Our analysis shows that in densely deployed networks, the FSA-based status updating protocol can significantly decrease the average AoI and in addition, stabilizes the age performance by substantially reducing the variance of AoI. Furthermore, under the same updating frequency, converting a slotted ALOHA protocol into an FSA-based one always leads to a reduction in the average AoI. Moreover, implementing FSA in conjunction with power control can further benefit the AoI performance, although the particular values of framesize and power control factor must be adequately tuned to achieve the optimal gain.

In 5G and beyond communication systems, the notion of latency gets great momentum in wireless connectivity as a metric for serving real-time communications requirements. However, in many applications, research has pointed out that latency could be inefficient to handle applications with data freshness requirements. Recently, Age of Information (AoI) metric, which can capture the freshness of the data, has attracted a lot of attention. In this work, we consider mixed traffic with time-sensitive users; a deadline-constrained user, and an AoI-oriented user. To develop an efficient scheduling policy, we cast a novel optimization problem formulation for minimizing the average AoI while satisfying the timely throughput constraints. The formulated problem is cast as a Constrained Markov Decision Process (CMDP). We relax the constrained problem to an unconstrained Markov Decision Process (MDP) problem by utilizing the Lyapunov optimization theory and it can be proved that it is solved per frame by applying backward dynamic programming algorithms with optimality guarantees. In addition, we provide a low-complexity algorithm guaranteeing that the timely-throughput constraint is satisfied. Simulation results show that the timely throughput constraints are satisfied while minimizing the average AoI. Simulation results show the convergence of the algorithms for different values of the weighted factor and the trade-off between the AoI and the timely throughput.

We study the average Age of Information (AoI) and peak AoI (PAoI) of a dual-queue status update system that monitors a common stochastic process through two independent channels. Although the double queue parallel transmission is instrumental in reducing AoI, the out of order of data arrivals also imposes a significant challenge to the performance analysis. We consider two settings: the M-M system where the service time of two servers is exponentially distributed; the M-D system in which the service time of one server is exponentially distributed and that of the other is deterministic. For the two dual-queue systems, closed-form expressions of average AoI and PAoI are derived by resorting to the graphic method and state flow graph analysis method. Our analysis reveals that when the two servers have the same service rate, compared with the single-queue system with an exponentially distributed service time, the average PAoI and the average AoI of the M-M system decrease by 33.3% and 37.5%, respectively, and those of the M-D system decrease by 27.7% and 39.7%, respectively. Numerical results show that the two dual-queue systems also outperform the M/M/2 single queue dual-server system with optimized arrival rate in terms of average AoI and PAoI.

We study a multiuser system in which an information source provides status updates to two monitors with heterogeneous goals. Semantic filtering is first performed to select the most useful realizations for each monitor. Packets are then encoded and sent so that each monitor can timely fulfill its goal. In this regard, some realizations are important for both monitors, while every other realization is informative for only one monitor. We determine the optimal real codeword lengths assigned to the selected packet arrivals in the sense of maximizing a weighted sum of semantics-aware utility functions for the two monitors. Our analytical and numerical results provide the optimal design parameters for different arrival rates and highlight the improvement in timely status update delivery using semantic filtering and source coding.

We study the average age of information (AoI) and peak AoI (PAoI) of a dual-queue status update system that monitors a common stochastic process. We capture the state transition characteristics of the considered system by establishing a Markov chain. Using the state flow graph analysis method, we derive closed-form expressions of the average peak age of information (PAoI) and the average age of information (AoI) for the dual-queue update system. The numerical results show that compared with the single-queue update system, the average PAoI of the dual-queue update system is reduced by 33.5% and the average AoI dropped by 37.5%.

Recently, short packet communications gained significant attention due to the advancements in finite blocklength information theory. However, performance of short packet communications over interference-limited scenarios under channel uncertainty have remained largely unexplored. This work investigates the performance of treating interference as noise and joint decoding schemes in two-user Gaussian Z-interference channel under finite blocklength coding regime. The average error and throughput of the two-user Z-interference channel are characterized for different schemes in a Rayleigh fading scenario. However, the average throughput does not take account of the bursty nature of the data arrivals at the users. Thus, we consider the stability region as a metric, and it is characterized using the probability of successful decoding at the receivers. The average error developed for the different interference mitigation techniques under the finite blocklength coding help to obtain the stability region. A main takeaway message is that even for the weak interference regime, the joint decoding scheme can perform better than the treating interference as noise scheme for low rates.

We consider a resource-constrained IoT network, where users make on-demand requests to a cache-enabled edge node to send status updates about various random processes, each monitored by an energy harvesting sensor. The edge node serves users’ requests by either commanding the corresponding sensor to send a fresh status update or retrieving the most recently received measurement from the cache. We aim to find a control policy at the edge node to minimize the average age of information (AoI) of the received measurements upon requests, i.e., average on-demand AoI, subject to per-slot transmission and energy constraints. We develop a low-complexity algorithm – termed relax-then-truncate – and prove that it is asymptotically optimal as the number of sensors goes to infinity. Numerical results assess the performance of the proposed method.

In this work we address a problem of active fault detection in an IoT scenario, whereby a monitor probes a remote device in order to detect faults and acquire fresh information. However, probing can have a significant impact on the IoT network’s energy and communication resources. To address this problem we utilize Age of Information as a measure of the freshness of information at the monitor and adopt a semantics-aware communication approach between the monitor and the remote device. In semantics-aware communications, the processes of generating and transmitting information are treated jointly in order to consider the importance of information and the purpose of communication. We formulate the problem as a Partially Observable Markov Decision Process and propose a computationally efficient stochastic approximation algorithm to approximate the optimal policy. Finally, we present numerical results that exhibit the advantage of our approach compared to a conventional delay-based probing policy.

With the advent of 5G technology, the notion oflatencygot a prominent role in wireless connectivity, serving as a proxy term for addressing the requirements for real-time communication. As wireless systems evolve toward 6G, the ambition to immerse the digital into physical reality will increase. Besides making the real-time requirements more stringent, this immersion will bring the notions of time, simultaneity, presence, and causality to a new level of complexity. A growing body of research points out that latency is insufficient to parameterize all real-time requirements. Notably, one such requirement that received significant attention is information freshness, defined through the Age of Information (AoI) and its derivatives. In general, the metrics derived from a conventional black-box approach to communication network design are not representative of new distributed paradigms, such as sensing, learning, or distributed consensus. The objective of this article is to investigate the general notion of timing in wireless communication systems and networks, and its relation to effective information generation, processing, transmission, and reconstruction at the senders and receivers. We establish a general statistical framework oftimingrequirements in wireless communication systems, which subsumes both latency and AoI. The framework is made by associating a timing component with the two basic statistical operations: decision and estimation. We first use the framework to present a representative sample of the existing works that deal with timing in wireless communication. Next, it is shown how the framework can be used with different communication models of increasing complexity, starting from the basic Shannon one-way communication model and arriving at communication models for consensus, distributed learning, and inference. Overall, this article fills an important gap in the literature by providing a systematic treatment of various timing measures in wireless communication and sets the basis for design and optimization for the next-generation real-time systems.

Intelligent reflecting surface (IRS) and device-to-device (D2D) communication are two promising technologies for improving transmission reliability between transceivers in communication systems. In this paper, we consider the design of reliable communication between the access point (AP) and actuators for a downlink multiuser multiple-input single-output (MISO) system in the industrial IoT (IIoT) scenario. We propose a two-stage protocol combining IRS with D2D communication so that all actuators can successfully receive the message from AP within a given delay. The superiority of the protocol is that the communication reliability between AP and actuators is doubly augmented by the IRS-aided first-stage transmission and the second-stage D2D transmission. A joint optimization problem of active and passive beamforming is formulated, which aims to maximize the number of actuators with successful decoding. We study the joint beamforming problem for cases where the channel state information (CSI) is perfect and imperfect. For each case, we develop efficient algorithms that include convergence and complexity analysis. Simulation results demonstrate the necessity and role of IRS with a well-optimized reflection matrix, and the D2D network in promoting reliable communication. Moreover, the proposed protocol can enable reliable communication even in the presence of stringent latency requirements and CSI estimation errors.

We consider a resource-constrained IoT network, where multiple users make on-demand requests to a cache-enabled edge node to send status updates about various random processes, each monitored by an energy harvesting sensor. The edge node serves users’ requests by deciding whether to command the corresponding sensor to send a fresh status update or retrieve the most recently received measurement from the cache. Our objective is to find the best actions of the edge node to minimize the average age of information (AoI) of the received measurements upon request, i.e., average on-demand AoI, subject to per-slot transmission and energy constraints. First, we derive a Markov decision process model and propose an iterative algorithm that obtains an optimal policy. Then, we develop an asymptotically optimal low-complexity algorithm – termed relax-then-truncate – and prove that it is optimal as the number of sensors goes to infinity. Simulation results illustrate that the proposed relax-then-truncate approach significantly reduces the average on-demand AoI compared to a request-aware greedy policy and a weighted AoI policy, and also depict that it performs close to the optimal solution even for moderate numbers of sensors.

We consider a status update system where multiple sensors communicate timely information about various random processes to a sink. The sensors share orthogonal sub-channels to transmit such information in the form of status update packets. A central controller can control the sampling actions of the sensors to trade-off between the transmit power consumption and information freshness which is quantified by the Age of Information (AoI). We jointly optimize the sampling action of each sensor, the transmit power allocation, and the sub-channel assignment to minimize the average total transmit power of all sensors, subject to a maximum average AoI constraint for each sensor. To solve the problem, we develop a dynamic control algorithm using the Lyapunov drift-plus-penalty method and provide optimality analysis of the algorithm. According to the Lyapunov drift-plus-penalty method, to solve the main problem, we need to solve an optimization problem in each time slot which is a mixed integer non-convex optimization problem. We propose a low-complexity sub-optimal solution for this per-slot optimization problem that provides near-optimal performance and we evaluate the computational complexity of the solution. Numerical results illustrate the performance of the proposed dynamic control algorithm and the performance of the sub-optimal solution for the per-slot optimization problem versus the different parameters of the system. The results show that the proposed dynamic control algorithm achieves more than$60~\%$saving in the average total transmit power compared to a baseline policy.

In this paper, we consider a cellular-based Internet of things (IoT) network consisting of IoT devices that can communicate directly with each other in a device-to-device (D2D) fashion as well as send real-time status updates about some underlying physical processes observed by them. We assume that such real-time applications are supported by cellular networks where cellular base stations (BSs) collect status updates over time from a subset of the IoT devices in their vicinity. We characterize two performance metrics: i) the network throughput which quantifies the performance of D2D communications, and ii) the Age of Information which quantifies the performance of the real-time IoT-enabled applications. Concrete analytical results are derived using stochastic geometry by modeling the locations of IoT devices as a bipolar Poisson Point Process (PPP) and that of the BSs as another Independent PPP. Our results provide useful design guidelines on the efficient deployment of future IoT networks that will jointly support D2D communications and several cellular network-enabled real-time applications.

This paper considers the joint optimization of trajectory and beamforming of a wirelessly connected robot using intelligent reflective surface (IRS)-assisted millimeter-wave (mm-wave) communications. The goal is to minimize the motion energy consumption subject to time and communication quality of service (QoS) constraints. This is a fundamental problem for industry 4.0, where robots may have to maximize their battery autonomy and communication efficiency. In such scenarios, IRSs and mm-waves can dramatically increase the spectrum efficiency of wireless communications providing high data rates and reliability for new industrial applications.We present a solution to the optimization problem that exploits mm-wave channel characteristics to decouple beamforming and trajectory optimizations. Then, the latter is solved by a successive-convex optimization (SCO) algorithm. The algorithm takes into account the obstacles’ positions and a radio map and provides solutions that avoid collisions and satisfy the QoS constraint. Moreover, we prove that the algorithm converges to a solution satisfying the Karush-Kuhn-Tucker (KKT) conditions.

A typical Internet-of-Things (IoT) system consists of three major layers: 1) sensing; 2) communication; and 3) application (i.e., actuation and control) layers. The co-design of these layers has been studied for over two decades, dating back to the concept of communication, computing, and control, i.e., 3C, convergence in the 1990s. Nowadays, with the emergence of wireless-networked machine-type applications, such as connected autonomous driving and factory automation, this co-design is more urgently desired than ever to meet the stringent quality-of-service requirements thereof. To realize this goal, the 5G wireless network of today has mainly focused on the communication part and strived to reliably achieve low air-interface communication delay, i.e., ultra-reliable and low-latency communications (uRLLC). However, more and more wireless communications in IoT are based on status updates instead of general content delivery. The current uRLLC design is insufficient to characterize the status update quality, and thus is unable to optimize for timely status update with constrained wireless resources. Therefore, the performance of computing and control in IoT networks that rely highly on wireless communications is suboptimal.

In this work, we investigate information freshness in a status update communication system consisting of a source-destination link. Initially, we study the properties of a sample path of the age of information (AoI) process at the destination. We obtain a general formula of the stationary distribution of the AoI, under the assumption of ergodicity. We relate this result to a discrete time queueing system and provide a general expression of the generating function of AoI in relation with the system time and the peak age of information (PAoI) metric. Furthermore, we consider three different single-server system models and we obtain closed-form expressions of the generating functions and the stationary distributions of the AoI and the PAoI. The first model is a first-come-first-served (FCFS) queue, the second model is a preemptive last-come-first-served (LCFS) queue, and the last model is a bufferless system with packet dropping. We build upon these results to provide a methodology for analyzing general non-linear age functions for this type of systems, using representations of functions as power series.

In this work, we consider a random access Internet of Things IoT wireless network assisted by two aggregators collecting information from two disjoint groups of sensors. The nodes and the aggregators are transmitting in a random access manner under slotted time, the aggregators perform network-level cooperation for the data collection. The aggregators are equipped with queues to store data packets that are transmitted by the network nodes and relaying them to the destination node. We characterize the throughput performance of the IoT network and we obtain the stability conditions for the queues at the aggregators. We apply the theory of boundary value problems to analyze the delay performance. Our results show that the presence of the aggregators provides significant gains in the IoT network performance, in addition, we provide useful insights regarding the scalability of the IoT network.

This paper studies the interplay between device-to-device (D2D) communications and real-time monitoring systems in a cellular-based Internet of Things (IoT) network. In particular, besides the possibility that the IoT devices communicate directly with each other in a D2D fashion, we consider that they frequently send time-sensitive information/status updates (about some underlying physical processes observed by them) to their nearest cellular base stations (BSs). Specifically, we model the locations of the IoT devices as a bipolar Poisson Point Process (PPP) and that of the BSs as another independent PPP. For this setup, we characterize the performance of D2D communications using the average network throughput metric whereas the performance of the real-time applications is quantified by the Age of Information (AoI) metric. The IoT devices are considered to employ a distance-proportional fractional power control scheme while sending status updates to their serving BSs. Hence, depending upon the maximum transmission power available, the IoT devices located within a certain distance from the BSs can only send status updates. This association strategy, in turn, forms theJohnson-Mehl (JM)tessellation, such that the IoT devices located in theJM cellsare allowed to send status updates. The average network throughput is obtained by deriving the mean success probability for the D2D links. On the other hand, the temporal mean AoI of a given status update link can be treated as a random variable over space since its success delivery rate is a function of the interference field seen from its receiver. Thus, in order to capture the spatial disparity in the AoI performance, we characterize the spatial moments of the temporal mean AoI. In particular, we obtain these spatial moments by deriving the moments of both the conditional success probability and the conditional scheduling probability for status update links. Our results provide useful design guidelines on the efficient deployment of future massive IoT networks that will jointly support D2D communications and several cellular network-enabled real-time applications.

The term Tactile Internet broadly refers to a communication network that is capable of delivering control, touch, and sensing/actuation information in real-time. The Tactile Internet is currently a topic of interest for various standardization bodies. The emerging IEEE P1918.1 standards working group is focusing on defining a framework for the Tactile Internet. The main objective of this work is to present the IEEE P1918.1 reference architecture framework for the Tactile Internet. The paper provides an indepth survey of various architectural aspects including the key entities, the interfaces, the functional capabilities, and the protocol stack. A case study has been presented as a manifestation of the architecture. Performance evaluation demonstrates the impact of functional capabilities and the underlying enablers on user-level utility pertaining to a generic Tactile Internet application.

We study a discrete-time wireless network that serves both cacheable and non-cacheable traffic with assistance of a relay node with storage capabilities for both types of traffic. We investigate how allocating the storage capacity to cacheable and non-cacheable traffic affects the network throughput. Our numerical results provide useful insights by varying not only the allocation of cacheable to non-cacheable storage but also the rate by which non-cacheable content is transmitted, the rate by which cacheable content is requested, as well as different popularity distributions of the cached files.

This paper considers a status update communication system consisting of a source-destination link with timeliness requirements. First, we study the properties of a sample path of the age of information (AoI) process at the destination. Under the assumption of ergodicity, we obtain a general formula of the stationary distribution of the AoI. We relate this result to a discrete time queueing system and provide a general expression of the generating function of AoI in relation with the system time and the peak age of information (PAoI). Furthermore, we consider the first-come-first-served (FCFS) Geo/Geo/1 queue and we obtain closed-form expressions of the generating functions and the stationary distributions of the AoI and the PAoI. We built upon these results to provide a methodology for analyzing general non-linear age functions for this type of systems.

Multi-connectivity is emerging as a promising solution to provide reliable communications and seamless connectivity for the millimeter-wave frequency range. Due to the blockage sensitivity at such high frequencies, connectivity with multiple cells can drastically increase the network performance in terms of throughput and reliability. However, an inefficient link scheduling, i.e., over and under-provisioning of connections, can lead either to high interference and energy consumption or to unsatisfied user's quality of service (QoS) requirements. In this work, we present a learning-based solution that is able to learn and then to predict the optimal link scheduling to satisfy users' QoS requirements while avoiding communication interruptions. Moreover, we compare the proposed approach with two base line methods and the genie-aided link scheduling that assumes perfect channel knowledge. We show that the learning-based solution approaches the optimum and outperforms the base line methods.

In this work, we combine the two notions of timely delivery of information to study their interplay; namely, deadline-constrained packet delivery due to latency constraints and freshness of information. More specifically, we consider a two-user multiple access setup with random-access, in which user 1 is a wireless device with a queue and has external bursty traffic which is deadline-constrained, while user 2 monitors a sensor and transmits status updates to the destination. We provide analytical expressions for the throughput and drop probability of user 1, and an analytical expression for the average Age of Information (AoI) of user 2 monitoring the sensor. The relations reveal that there is a trade-off between the average AoI of user 2 and the drop rate of user 1: the lower the average AoI, the higher the drop rate, and vice versa. Simulations corroborate the validity of our theoretical results.

A large body of applications that involve monitoring, decision making, and forecasting require timely status updates for their efficient operation. Age of Information (AoI) is a newly proposed metric that effectively captures this requirement. Recent research on the subject has derived AoI optimal policies for the generation of status updates and AoI optimal packet queueing disciplines. Unlike previous research, we focus on low-end devices that typically support monitoring applications in the context of the Internet of Things. We acknowledge that these devices host a diverse set of applications some of which are AoI sensitive while others are not. Furthermore, due to their limited computational resources, they typically utilize a simple first-in-first-out (FIFO) queueing discipline. We consider the problem of optimally controlling the status update generation process for a system with a source-destination pair that communicates via a wireless link, whereby the source node is composed of a FIFO queue and serves two applications, one that is AoI sensitive and one that is not. We formulate this problem as a dynamic programming problem and utilize the framework of Markov decision processes to derive the optimal policy for the generation of status update packets. Due to the lack of comparable methods in the literature, we compare the derived optimal policies against baseline policies such as the zero-wait policy. Results indicate that the baseline policy fails to capture the complex system dynamics that determine the relationship between the frequency of status update generation and the resulting queueing delay and thus perform poorly. To the best of our knowledge, the derived optimal policy does not exhibit a simple structure; thus, we utilized the baseline policies, whose operation is intuitive, to gain insight into the inner workings of the optimal policy.

In this paper, we study a real-time monitoring system in which multiple source nodes are responsible for sending update packets to a common destination node in order to maintain the freshness of information at the destination. Since it may not always be feasible to replace or recharge batteries in all source nodes, we consider that the nodes are powered through wireless energy transfer (WET) by the destination. For this system setup, we investigate the optimal online sampling policy (referred to as the age-optimal policy) that jointly optimizes WET and scheduling of update packet transmissions with the objective of minimizing the long-term average weighted sum of Age of Information (AoI) values for different physical processes (observed by the source nodes) at the destination node, referred to as the sum-AoI. To solve this optimization problem, we first model this setup as an average cost Markov decision process (MDP) with finite state and action spaces. Due to the extreme curse of dimensionality in the state space of the formulated MDP, classical reinforcement learning algorithms are no longer applicable to our problem even for reasonable-scale settings. Motivated by this, we propose a deep reinforcement learning (DRL) algorithm that can learn the age-optimal policy in a computationally-efficient manner. We further characterize the structural properties of the age-optimal policy analytically, and demonstrate that it has a threshold-based structure with respect to the AoI values for different processes. We extend our analysis to characterize the structural properties of the policy that maximizes average throughput for our system setup, referred to as the throughput-optimal policy. Afterwards, we analytically demonstrate that the structures of the age-optimal and throughput-optimal policies are different. We also numerically demonstrate these structures as well as the impact of system design parameters on the optimal achievable average weighted sum-AoI.

We consider a status update communication system consisting of a source-destination link. A stochastic process is observed at the source, where samples are extracted at random time instances, and delivered to the destination, thus, providing status updates for the source. In this paper, we expand the concept of information ageing by introducing the cost of update delay (CoUD) metric to characterize the cost of having stale information at the destination. The CoUD captures the freshness of the information at the destination and can be used to reflect the information structure of the source. Moreover, we introduce the value of information of update (VoIU) metric that captures the reduction of CoUD upon reception of an update. Using the CoUD, its by-product metric called peak cost of update delay (PCoUD), and the VoIU, we evaluate the performance of an M/M/1 system in various settings that consider exact expressions and bounds. The optimal server utilization policy is to minimize the time average CoUD and maximize the time average VoIU. Our results indicate that the performance of CoUD differs depending on the cost assigned per time unit, however the optimal policy remains the same for linear ageing and varies for non-linear ageing. When it comes to the VoIU the performance difference appears only when the cost increases non-linearly with time. The study illustrates the importance of the newly introduced variants of age, furthermore supported in the case of VoIU by its tractability.

In this paper, we study a real-time Internet of Things (IoT)-enabled monitoring system in which a source node (e.g., IoTdevice or an aggregator located near a group of IoT devices) is responsible for maintaining the freshness of information status at a destination node by sending update packets. Since it may not always be feasible to replace or recharge batteries in all IoT devices, we consider that the source node is powered by wireless energy transfer (WET) by the destination. For this system setup, we investigate the optimal online sampling policy that minimizes the long-term average Age-of-Information (AoI), referred to as the age-optimal policy. The age- optimal policy determines whether each slot should be allocated for WET or update packet transmission while considering the dynamics of battery level, AoI, and channel state information (CSI). To solve this optimization problem, we model this setup as an average cost Markov Decision Process (MDP). After analytically establishing the monotonicity property of the value function associated with the MDP, the age-optimal policy is proven to be a thresholdbased policy with respect to each of the system state variables. We extend our analysis to characterize the structural properties of the policy that maximizes average throughput for our system setup, referred to as the throughput-optimal policy. Afterwards, we analytically demonstrate that the structures of the ageoptimal and throughput-optimal policies are different. We also numerically demonstrate these structures as well as the impact of system design parameters on the optimal achievable average AoI.

In this work, we derive optimal status update generation policies for a wireless source node that has a single queue which serves two applications, one that is Age of Information (AoI) sensitive and one that is not. Additionally, the AoI-sensitive application sets a strict upper bound on the AoI. The latter constraint is satisfied by utilizing an ultra-reliable low-latency communication link. We formulate a dynamic programming problem and utilize the framework of Markov Decision Processes to derive optimal policies for the generation of status update packets. We compare the derived optimal policies against baseline policies. Results indicate that existing status update policies fail to capture the effect of AoI insensitive traffic on queueing delay and AoI and thus perform suboptimally.

We investigate the effect of bursty traffic in an LTE and Wi-Fi aggregation (LWA)-enabled network, where part of the LTE traffic is offloaded to Wi-Fi access points (APs) to boost the performance of LTE networks. A Wi-Fi AP maintains two queues containing data intended for the LWA-mode user and the native Wi-Fi user, and it is allowed to serve them simultaneously by using superposition coding (SC). With respect to the existing works on LWA, the novelty of our study consists of a random access protocol allowing the Wi-Fi AP to serve the native WiFi user with probabilities that depend on the queue size of the LWA-mode data. We analyze the throughput of the native Wi-Fi network, accounting for different transmitting probabilities of the queues, the traffic flow splitting between LTE and Wi-Fi, and the operating mode of the LWA user with both LTE and Wi-Fi interfaces. Our results provide fundamental insights in the throughput behavior of such aggregated systems, which are essential for further investigation in larger topologies.

In this work, we consider a relay assisted adaptive queue-aware cooperative random access wireless network with multipacket (MPR) reception capabilities. The network consists of N sources transmitting packets to a common destination node with the aid of two relay nodes equipped with queues. The relays assist the sources by forwarding the packets that failed to reach the destination, by using a queue-based transmission control mechanism. Moreover, the relays have also their own traffic. We investigate the stability conditions and the throughput performance of the network for the full MPR channel model. Moreover, we derive expressions for the average queueing delay with the aid of the theory of boundary value problems for the asymmetric two-user network. We evaluate numerically the presented theoretical analysis.

We consider a system consisting of a source-destination communication link. At the transmitter of the source there is a buffer that stores packets containing status information. These randomly generated packets should keep the destination timely updated and they can be discarded to avoid wasting network resources for the transmission of stale information. In this setup, we provide an analysis of the age of information (AoI) and peak age of information (PAoI) performance of the system, with and without packet management at the transmission queue of the source node. The analysis indicates the potential performance gains obtained with the use of packet management.

In this work, we evaluate a wireless system in which we distinguish between cacheable and non-cacheable traffic. More specifically, we consider a general system in which a wireless user with limited cache storage requests cacheable content from a data center that can be directly accessed through a base station. The user can be assisted by a pair of wireless helpers that exchange non-cacheable content. Packets arrive at the queue of the source helper in bursts. Each helper has its own caches to assist the user's requests for cacheable content. Files not available from the helpers are transmitted by the base station. We analyze the system throughput and the delay experienced by the user and show how they are affected by the packet arrival rate at the source helper, the availability of caching helpers, the caches' parameters, and the user's request rate by means of numerical results.

The IEEE “Tactile Internet” (TI) Standards working group (WG), designated the numbering IEEE 1918.1, undertakes pioneering work on the development of standards for the TI. This paper describes the WG, its intentions, and its developing baseline standard and the associated reasoning behind that and touches on a further standard already initiated under its scope: IEEE 1918.1.1 on “Haptic Codecs for the TI.” IEEE 1918.1 and its baseline standard aim to set the framework and act as the foundations for the TI, thereby also serving as a basis for further standards developed on TI within the WG. This paper discusses the aspects of the framework such as its created TI architecture, including the elements, functions, interfaces, and other considerations therein, as well as the novel aspects and differentiating factors compared with, e.g., 5G Ultra-Reliable Low-Latency Communication, where it is noted that the TI will likely operate as an overlay on other networks or combinations of networks. Key foundations of the WG and its baseline standard are also highlighted, including the intended use cases and associated requirements that the standard must serve, and the TI's fundamental definition and assumptions as understood by the WG, among other aspects.

Relaying techniques for millimeter-wave wireless networks represent a powerful solution for improving the transmission performance. In this paper, we quantify the benefits in terms of delay and throughput for a random-access multi-user millimeter-wave wireless network, assisted by a full-duplex network cooperative relay. The relay is equipped with a queue for which we analyze the performance characteristics (e.g., arrival rate, service rate, average size, and stability condition). Moreover, we study two possible transmission schemes: fully directional and broadcast. In the former, the source nodes transmit a packet either to the relay or to the destination by using narrow beams, whereas, in the latter, the nodes transmit both the destination and the relay in the same timeslot by using a wider beam but with lower beamforming gain. In our analysis, we also consider the beam alignment phase that occurs every time, a transmitter node changes the destination node. We show the duration of how the beam is aligned, as well as position and a number of transmitting nodes, significantly affect the network performance. In addition, we discuss the impact of beam alignment errors and imperfect self-interference cancellation technique at the relay for full-duplex communications. Moreover, we illustrate the optimal transmission scheme (i.e., broadcast or fully directional) for several system parameters and show that a fully directional transmission is not always beneficial, but in some scenarios, broadcasting and relaying can improve the performance in terms of throughput and delay.

The next generation of mobile networks, namely 5G, together with the Internet of Things (IoT) come with a large number of delay sensitive services. To meet their requirements, cloud services are migrating to the edge of the networks to reduce latency. The notion of fog computing, where the edge plays an active role in the execution of services, comes to meet the needs for the stringent requirements. Thus, it becomes of a high importance to address the problem of mapping services' demands to infrastructure resources supply. This work addresses it taking into account the randomness of resource availability in a fog infrastructure. We introduce an integer optimization formulation to minimize the total cost under a guarantee of service execution despite the uncertainty of resources availability. Our results illustrate the effect of various system parameters, such as the diversity of the infrastructure server set, the availability of different infrastructure servers in the set, and the probability of service completion required by each service.

Wireless devices need to adapt their transmission power according to the fluctuating wireless channel in order to meet constraints of delay sensitive applications. In this paper, we consider delay sensitivity in the form of strict packet deadlines arriving in a transmission queue. Packets missing the deadline while in the queue are dropped from the system. We aim at minimizing the packet drop rate under average power constraints. We utilize tools from Lyapunov optimization to find an approximate solution by selecting power allocation. We evaluate the performance of the proposed algorithm and show that it achieves the same performance in terms of packet drop rate with that of the Earliest Deadline First (EDF) when the available power is sufficient. However, our algorithm outperforms EDF regarding the trade-off between packet drop rate and average power consumption.

We consider a cognitive shared access scheme consisting of a high priority primary node and a low priority network with N secondary nodes accessing the spectrum. Assuming bursty traffic at the primary node, saturated queues at the secondary nodes, and multipacket reception capabilities at the receivers, we derive analytical expressions of the time average age of information of the primary node and the throughput of the secondary nodes. We formulate two optimization problems, the first aiming to minimize the time average age of information of the primary node subject to an aggregate secondary throughput requirement. The second problem aims to maximize the aggregate secondary throughput of the network subject to a maximum time average staleness constraint. Our results provide guidelines for the design of a multiple access system with multipacket reception capabilities that fulfills both timeliness and throughput requirements.

In this work, we consider an adaptive two-user random access scheme with multipacket reception (MPR) capabilities. A user adapts its transmission characteristics based on the status of the other user. The users have external random traffic stored in their queues. We derive the stable throughput region of the system and the convexity conditions of this region. We derive analytically the queueing delay by formulating and solving a Riemann-Hilbert boundary value problem. Finally, we evaluate numerically the presented theoretical results.

Quality of service (QoS) provisioning in next-generation mobile communications systems entails a deep under-standing of the delay performance. The delay in wireless networks is strongly affected by the traffic arrival process and the service process, which in turn depends on the medium access protocol and the signal-to-interference-plus-noise ratio (SINR) distribution. In this work, we characterize the conditional distribution of the service process given the point process in Poisson bipolar networks. We then provide an upper bound on the delay violation probability combining tools from stochastic network calculus and stochastic geometry. Furthermore, we analyze the delay performance under statistical queueing constraints using the effective capacity formulation. The impact of QoS requirements, network geometry and link distance on the delay performance is identified. Our results provide useful insights for guaranteeing stringent delay requirements in large wireless networks.

Multi-connectivity is emerging as promising solution to provide reliable communications and seamless connectivity at the millimeter-wave frequency range. Due to the obstacles that cause frequent interruptions at such high frequency range, connectivity to multiple cells can drastically increase the network performance in terms of throughput and reliability by coordination among the network elements. In this paper, we propose an algorithm for the link scheduling optimization that maximizes the network throughput for multi-connectivity in millimeter-wave cellular networks. The considered approach exploits a centralized architecture, fast link switching, proactive context preparation and data forwarding between millimeter-wave access points and the users. The proposed algorithm is able to numerically approach the global optimum and to quantify the potential gain of multi-connectivity in millimeter-wave cellular networks.

In this paper, we consider the two-user broadcast channel and we characterize its stable throughput region. We start the analysis by providing the stability region for the general case without any specific considerations on transmission and reception mechanisms. We also provide conditions for the stable throughput region to be convex. Subsequently, we study the case where the transmitter uses superposition coding and we consider two special cases for the receivers. The first one is when both receivers treat interference as noise. The second is when the user with a better channel uses successive decoding and the other receiver treats interference as noise.

In this paper, we study the stability region of the two-user broadcast channel (BC) with bursty data arrivals and security constraints. It is assumed that one of the receivers has a secrecy constraint, i.e., its packets need to be kept secret from the other receiver, which is defined based on signal to interference noise ratio. The receiver with secrecy constraint has full-duplex capability to send a jamming signal for improving its service rate. The stability region of the two-user BC with secrecy constraint is characterized for the general decoding case. Then, assuming two different decoding schemes, the respective stability regions are derived. The full-duplex operation of receiver results in self-interference, and the effect of imperfect self-interference cancelation on the stability region is also investigated. The stability region of the BC with a secrecy constraint, where the receivers do not have full duplex capability can be obtained as a special case of the results derived in this paper. In addition, the paper considers the problem of maximizing the saturated throughput of the queue for which there is no secrecy constraint under minimum service guarantees for the other queue. The results provide new insights on the effect of the secrecy constraint on the stability region of the BC. It is found that the stability region with secrecy constraint is sensitive to the degree of self-interference cancelation.

In this paper, we analyze a shared access network with a fixed primary node and randomly distributed secondary nodes whose spatial distribution follows a poisson point process. The secondary nodes use a random access protocol allowing them to access the channel with probabilities that depend on the queue size of the primary node. Assuming a system with multipacket reception receivers, having bursty packet arrivals at the primary and saturated traffic at the secondary nodes, our protocol can be tuned to alleviate congestion at the primary. We analyze the throughput of the secondary network and the primary average delay, as well as the impact of the secondary node access probability and transmit power. We formulate an optimization problem to maximize the throughput of the secondary network under delay constraints for the primary node; in the case of no congestion control, the optimal access probability can be provided in closed form. Our numerical results illustrate the effect of network operating parameters on the performance of the proposed priority-based shared access protocol.

In this paper, we consider a two-user and a three-user slotted ALOHA network with multi-packet reception (MPR) capabilities and a queue-aware transmission control. In this setting, the nodes can adapt their transmission probabilities and their transmission parameters based on the status of the other nodes. Each user has external bursty arrivals that are stored in their infinite capacity queues. We focus on the fundamental problem of characterizing the stable throughput region, as well as of investigating the queueing delay. For the two- and the three-user cases, we obtain the exact stability region, whereas in the former case, we also provide the conditions under which the stability region is a convex set. We perform a detailed mathematical analysis to study the queueing delay in the two-user case by formulating two boundary value problems, the solution of which provides the generating function of the joint stationary probability distribution of the queue size at user nodes. Furthermore, for the two-user symmetric case with MPR, we obtain a lower and an upper bound for the average delay without the need of solving a boundary value problem. In addition, we provide a closed form expression for the gap between the lower and the upper bound. The bounds as it is seen in the numerical results appear to be tight. Explicit expressions for the average delay are obtained for the symmetrical model with capture effect. We also provide a closed form expression for the optimal transmission probability that minimizes the average delay in the symmetric capture case. Finally, we evaluate numerically the presented theoretical results.

Long Term Evolution (LTE)-Wireless Local Area Network (WLAN) Path Aggregation (LWPA) based on Multipath Transmission Control Protocol (MPTCP) has been under standardization procedure as a promising and cost-efficient solution to boost Downlink (DL) data rate and handle the rapidly increasing data traffic. This paper aims at providing tractable analysis for the DL performance evaluation of large-scale LWPA networks with the help of tools from stochastic geometry. We consider a simple yet practical model to determine under which conditions a native WLAN Access Point (AP) will work under LWPA mode to help increasing the received data rate. Using stochastic spatial models for the distribution of WLAN APs and LTE Base Stations (BSs), we analyze the density of active LWPA-mode WiFi APs in the considered network model, which further leads to closed-form expressions on the DL data rate and area spectral efficiency (ASE) improvement. Our numerical results illustrate the impact of different network parameters on the performance of LWPA networks, which can be useful for further performance optimization.

We consider a real-time status update system consisting of a source-destination network. A stochastic process is observed at the source, and samples, so called status updates, are extracted at random time instances, and delivered to the destination. In this paper, we expand the concept of information ageing by introducing the Cost of Update Delay (CoUD) metric to characterize the cost of having stale information at the destination. We introduce the Value of Information of Update (VoIU) metric that captures the reduction of CoUD upon reception of an update. The importance of the VoIU metric lies on its tractability which enables an alternative performance criterion in status update systems.

The emerging vision of smart cities necessitates the use of Internet of Things (IoT) network devices to implement sustainable solutions that will improve the operations of urban areas. A massive amount of smart cities services may demand allocation of computational resources, such as processing power or storage, that IoT devices offer. Within this context, we present an IoT network device comprising interfaces with one specific computational resource available. The efficient utilization of available IoT resources would improve the Quality of Service (QoS) of the IoT network that serves the smart city. All resource allocations must be completed within a given scheduling window and every service is parametrized by a pricing weight function to indicate its tolerance to be served at the beginning of the scheduling window. We propose a mathematical optimization formulation to minimize the total cost of allocating all demands within the scheduling window considering the tolerance level of each service at the same time. Moreover, we prove that the problem is computationally hard and we provide numerical results to gain insight into the impact of different pricing weight functions on the allocations' distribution within the scheduling window.

The rapid growth in the number and variety of connected devices requires 5G wireless systems to cope with a very heterogeneous traffic mix. As a consequence, the use of a fixed transmission time interval (TTI) during transmission is not necessarily the most efficacious method when heterogeneous traffic types need to be simultaneously serviced. This work analyzes the benefits of scheduling based on exploiting scalable TTI, where the channel assignment and the TTI duration are adapted to the deadlines and requirements of different services. We formulate an optimization problem by taking individual service requirements into consideration. We then prove that the optimization problem is NP-hard and provide a heuristic algorithm, which provides an effective solution to the problem. Numerical results show that our proposed algorithm is capable of finding near-optimal solutions to meet the latency requirements of mission critical communication services, while providing a good throughput performance for mobile broadband services.

In this work, the stability region of the broadcast channel (BC) is explored, where the receiver, for which the packets need to be kept secret from the other receiver has full-duplex (FD) capability. The effect of self-interference on the stability region has also been investigated. In particular, the stability region is characterized under two types of decoding schemes: (a) both the receivers perform treating interference as noise and (b) receiver with full-duplex capability performs successive decoding and other receiver treats interference as noise. As a by product of the analysis, the stability region of the BC with secrecy constraint where the receivers do not have FD capability can be obtained as a special case of the results derived in this paper. It is found that if the self-interference cancelation at the full-duplex receiver is not efficient, then the gain obtained in secure throughput due to transmission of the jamming signal by the FD receiver can diminish. In particular, it is found that the stability region with secrecy constraint is sensitive to the coefficient of self-interference cancelation under certain cases.

In this paper, we characterize the stability region of the two-user broadcast channel. First, we obtain the stability region in the general case. Second, we consider the particular case where each receiver treats the interfering signal as noise, as well as the case in which the packets are transmitted using superposition coding and successive decoding is employed at the strong receiver.

In this paper, we analyze a shared access network with one primary device and randomly distributed smart objects with secondary priority. Assuming random traffic at the primary device and saturated queues at the smart objects with secondary priority, an access protocol is employed to adjust the random access probabilities of the smart objects depending on the congestion level of the primary. We characterize the maximum throughput of the secondary network with respect to delay constraints on the primary. Our results highlight the impact of system design parameters on the delay and throughput behavior of the shared access network with massive number of connected objects.

Internet-of-Things (IoT) devices can be equipped with multiple heterogeneous network interfaces. An overwhelmingly large amount of services may demand some or all of these interfaces' available resources. Herein, we present a precise mathematical formulation of assigning services to interfaces with heterogeneous resources in one or more rounds. For reasonable instance sizes, the presented formulation produces optimal solutions for this computationally hard problem. We prove the NP-completeness of the problem and develop two algorithms to approximate the optimal solution for big instance sizes. The first algorithm allocates the most demanding service requirements first, considering the average cost of interfaces' resources. The second one calculates the demanding resource shares and allocates the most demanding of them first by choosing randomly among equally demanding shares. Finally, we provide simulation results giving insight into services splitting over different interfaces for both cases.

We consider a system of multiple sources generating status update packets, which need to be sent by a single transmitter to a destination over a network. In the model we study, the packet generation time may vary at each source, and the packets go through the network with a random delay. Each update carries a time stamp of its generation, allowing the destination to calculate for each source the so called Age of Information, which measures the timeliness of each status update arriving. Considering that queuing delay can unnecessarily increase the age of a critical status update, we propose here a queue management technique, in which we maintain a queue with only the latest status packet of each source, overwriting any previously queued update from that source. This simple technique drastically limits the need for buffering and can be applied in systems where the history of source status is not relevant. We show that this scheme results in significantly less transmissions compared to the standard M/M/1 queue model. Furthermore, the proposed technique reduces the per source age of information, especially in settings not using queue management with high status update generation rates.

In this work, we investigate the operation of energy efficient relay nodes assisting the transmission of packets from a number of users to a destination node. We study the impact of switching randomly a fraction of the relays on and off to the aggregate throughput, the average queue size and delay per packet of systems with relays transmitting in either Full- or Half-Duplex mode and under different channel transmissions characteristics. Furthermore, we prove analytically and illustrate via simulation means how these network metrics are affected.

With the densification of nodes in cellular networks, free space optic (FSO) connections are becoming an appealing low cost and high rate alternative to copper and fiber backhaul solutions for wireless communication systems. To ensure a reliable cellular backhaul, provisions for redundant disjoint paths between the nodes must be made in the design phase. This paper aims at finding a cost-effective solution to upgrade the cellular backhaul with pre-deployed optical fibers using FSO links and mirror components. Since the quality of the FSO links depends on several factors, such as transmission distance, power, and weather conditions, we adopt an elaborate formulation to calculate link reliability. We present a novel integer linear programming model to approach optimal FSO backhaul design, guaranteeing $K$-disjoint paths connecting each node pair. Next, we derive a column generation method to a path-oriented mathematical formulation. Applying the method in a sequential manner enables high computational scalability. We use realistic scenarios to demonstrate that our approaches efficiently provide optimal or near-optimal solutions, and thereby allow for accurately dealing with the trade-off between cost and reliability.

The effect of full-duplex cooperative relaying in a random access multiuser network is investigated here. First, we model the self-interference incurred due to full-duplex operation, assuming multi-packet reception capabilities for both the relay and the destination node. Traffic at the source nodes is considered saturated and the cooperative relay, which does not have packets of its own, stores a source packet that it receives successfully in its queue when the transmission to the destination has failed. We obtain analytical expressions for key performance metrics at the relay, such as arrival and service rates, stability conditions, and average queue length, as functions of the transmission probabilities, the self interference coefficient, and the links' outage probabilities. Furthermore, we study the impact of the relay node and the self-interference coefficient on the per-user and aggregate throughput, and the average delay per packet. We show that perfect self-interference cancelation plays a crucial role when the SINR threshold is small, since it may result to worse performance in throughput and delay comparing with the half-duplex case. This is because perfect self-interference cancelation can cause an unstable queue at the relay under some conditions.

Managing interference is a major technical challenge in large wireless networks. Distributed cooperation techniques, such as Interference Alignment (IA), exploit the available spatial degrees of freedom of the interference channel holding promise of enhanced spectral efficiency. Most prior results, however, consider isolated network settings, neglecting the interference from nodes that are not participating in the cooperation scheme. This paper analyzes the performance of IA in the presence of uncoordinated interference from a heterogeneous network. Specifically, we analyze perfect downlink IA in a fixed-size cell, where the interfering nodes are distributed according to a spatial point process, and compare it with a non-cooperative MIMO scheme. Furthermore, the performance gains by using a guard zone between the IA cluster and the interference field are evaluated and design guidelines for the necessary isolation distance from out-of-cluster interferers are provided.

In this paper, we investigate the impact of the deployment of a second relay node in a cooperative communication scheme. The relay nodes relay packets from a number of users to a destination node. We assume that the two relays do not have packets of their own and the users have saturated queues and random access to the medium with slotted time. We obtain analytical expressions for the arrival and service rates of the queues of the two relays and the stability conditions. We also study a model of the system, in which the users are divided into two clusters, and show its advantages in terms of aggregate and per user throughput. We quantify the above, analytically and through simulations, for different number of users and we indicate the conditions under which the deployment of a second relay in the system provides significant advantages.

The stable throughput region of the two-user interference channel is investigated here. First, the stability region for the general case is characterized. Second, we study the cases where the receivers treat interference as noise or perform successive interference cancelation. Finally, we provide conditions for the convexity/concavity of the stability region and for which a certain interference management strategy leads to broader stability region.

In this paper we study the impact of a relay node in a two-user network. We assume a random access collision channel model with erasures. In particular we obtain an inner and an outer bound for the stability region.

In this paper, we evaluate the benefits of using one user of a two-user random access system to relay traffic of the other user.

In this work we examine the operation of a node relaying packets from a number of users to a destination node. We assume multi-packet reception capabilities for the relay and the destination node and that the relay node can transmit and receive at the same time, so the problem of self interference arises. The relay does not have packets of its own and the traffic at the source nodes are assumed saturated. The relay node stores a source packet that it receives successfully in its queue when the transmission to the destination node has failed. We obtain analytical expressions for the characteristics of the relay's queue (such as arrival and service rate), the stability condition and the average length of the queue as functions of the probabilities of transmissions, the self interference coefficient and the outage probabilities of the links. We study the impact of the relay node and the self interference coefficient on the throughput per user-source as well as the aggregate throughput.

This paper considers the scenario in which a set of nodes share a common channel. Some nodes have a rechargeable battery and the others are plugged to a reliable power supply and, thus, have no energy limitations. We consider two source-destination pairs and apply the concept of cognitive radio communication in sharing the common channel. Specifically, we give high-priority to the energy-constrained source-destination pair, i.e., primary pair, and low-priority to the pair which is free from such constraint, i.e., secondary pair. In contrast to the traditional notion of cognitive radio, in which the secondary transmitter is required to relinquish the channel as soon as the primary is detected, the secondary transmitter not only utilizes the idle slots of primary pair but also transmits along with the primary transmitter with probability p. This is possible because we consider the general multipacket reception model. Given the requirement on the primary pair's throughput, the probability p is chosen to maximize the secondary pair's throughput. To this end, we obtain two-dimensional maximum stable throughput region which describes the theoretical limit on rates that we can push into the network while maintaining the queues in the network to be stable. The result is obtained for both cases in which the capacity of the battery at the primary node is infinite and also finite.

In this work, we study the impact of a relay node to a network with a finite number of users-sources and a destination node. We assume that the users have saturated queues and the relay node does not have packets of its own; we have random access of the medium and the time is slotted. The relay node stores a source packet that it receives successfully in its queue when the transmission to the destination node has failed. The relay and the destination nodes have multi-packet reception capabilities. We obtain analytical equations for the characteristics of the relay's queue such as average queue length, stability conditions etc. We also study the throughput per user and the aggregate throughput for the network.

In this paper, we examine the operation of a node relaying packets from a number of users to a destination node. We assume that the relay does not have packets of its own, the traffic from the users is saturated and we have random access of the medium with slotted time. We study the impact of the relay node on the throughput per user and the aggregate throughput for the group of users. We obtain analytical expressions for the arrival and service rate of the queue of the relay, the stability conditions and the average length of the queue. We quantify the above, analytically and through simulations, for different numbers of users and different transmission characteristics of the users and the relay and give the conditions under which there are significant advantages from the deployment of the relay.

In this paper we investigate the performance that can be achieved by exploiting path diversity through multipath forwarding together with redundancy through linear network coding, in wireless mesh networks with directional links. A key contribution of the paper is to capture the tradeoff between packet delay and throughput achieved by combining multipath forwarding and network coding, and compare this tradeoff with that of simple multipath routing where different flows follow different paths, the transmission of multiple copies of packets over multiple paths, and single path routing. The analytical framework considers the case of end-to-end retransmission for achieving reliability, and is generalized for an arbitrary number of paths and hops. We also derive the minimum and maximum number of coded packets that are needed at the receiver to retrieve all packets sent by the sender; this can be used to obtain a lower and upper bound for the delay in the case of linear network coding with multipath forwarding.

The alphabet size of a network code is a crucial parameter for the existence of a code in a network topology. In this paper we present a method to compute the alphabet size of a linear network code for an one-source acyclic directed graph using only the outgoing edges from the source. In addition we show a method to reduce the alphabet size for a class of combination networks.