In this paper, we study the moments of the Age of Information (AoI) for both active and passive users in a random access network. In this network, active users broadcast sensing data, while passive users detect in-band radio activities from out-of-network devices, such as jammers. Collisions occur when multiple active users transmit simultaneously. Passive users can detect radio activities only when no active user transmits. Each active user’s transmission behavior follows a Markov process. We aim to minimize the weighted sum of any moments of AoI for both user types. To achieve this, we employ a second-order analysis of system behavior. Specifically, we characterize an active user’s transmission Markov process using its mean and temporal variance. We show that any moment of the AoI can be approximated by a function of these two parameters. This insight enables us to analyze and optimize the transmission Markov process for active users. We apply this strategy to two different random access models. Simulation results show that policies derived from this strategy outperform other baseline policies.

In this work, we study the tradeoff between total throughput of a network and the cumulative emitted energy experienced by one or more external nodes that are not members of the network. We formulate the linear program to determine the routing and scheduling that maximizes the fair throughput for uplink and downlink traffic subject to the energy at each external node being below a threshold. Due to the spatial reuse with simultaneous transmitters and the multi-path routing approach, the number of variables in the linear program is exponential in the number of nodes in the network, so we solve this large linear program using an iterative approach known as column generation. We present numerical results in the form of energy heatmaps generated by the optimal schedule for individual network realizations, as well as the average energy heatmap over many Monte Carlo realizations, demonstrating the impact of the external node locations. We also present throughput results as a function of the node distance and the energy threshold for the single external node case. These results characterize the tradeoff between throughput and the distance and sensed energy sensitivity level, which provides a bound with which to compare the performance of practical routing and scheduling algorithms.

We examine a simplified distributed collaborative beamforming (DCB) system with two transmitters sending data over independent channels with significant time-varying phase distortion. The transmitters sample the state of their respective channels using a periodic sounding waveform sent by the receiver and use the last sensed state along with the sample age to correct for the channel phase distortion. As the age of the last sampled channel state increases, the transmitters are correctly estimating the current state with decreasing likelihood, leading to reduced beamforming gain. However, because sensing and transmitting must occur on the same channel, the transmitters cannot both send data and sample the channel at the same time. As a result, the cost associated with channel sensing is the transmitters not sending data for some duration; this compromise is embodied by the frame-averaged expected beamforming gain. Expressions for instantaneous and averaged expected gain are developed, and an example is presented to demonstrate finding the optimal sensing period and how the optimal sensing period can change depending on the last sensed states of the channels.

This paper introduces a new theoretical framework for optimizing second-order behaviors of wireless networks. Unlike existing techniques for network utility maximization, which only consider first-order statistics, this framework models every random process by its mean and temporal variance. The inclusion of temporal variance makes this framework well-suited for modeling Markovian fading wireless channels and emerging network performance metrics such as age-of-information (AoI) and timely-throughput. Using this framework, we sharply characterize the second-order capacity region of wireless access networks. We also propose a simple scheduling policy and prove that it can achieve every interior point in the second-order capacity region. To demonstrate the utility of this framework, we apply it to an unsolved network optimization problem where some clients wish to minimize AoI while others wish to maximize timely-throughput. We show that this framework accurately characterizes AoI and timely-throughput. Moreover, it leads to a tractable scheduling policy that outperforms other existing work.

In this paper, we address the optimization problem of moments of Age of Information (AoI) for active and passive users in a random access network. In this network, active users broadcast sensing data while passive users only receive signals. Collisions occur when multiple active users transmit simultaneously, and passive users are unable to receive signals while any active user is transmitting. Each active user follows a Markov process for their transmissions. We aim to minimize the weighted sum of any moments of AoI for both active and passive users in this network. To achieve this, we employ a second-order analysis to analyze the system. Specifically, we characterize an active user’s transmission Markov process by its mean and temporal process. We show that any moment of the AoI can be expressed a function of the mean and temporal variance, which, in turn, enables us to derive the optimal transmission Markov process. Our simulation results demonstrate that this proposed strategy outperforms other baseline policies that use different active user transmission models.

This paper introduces a new theoretical framework for optimizing second-order behaviors of wireless networks. Unlike existing techniques for network utility maximization, which only consider first-order statistics, this framework models every random process by its mean and temporal variance. The inclusion of temporal variance makes this framework well-suited for modeling stateful fading wireless channels and emerging network performance metrics such as age-of-information (AoI). Using this framework, we sharply characterize the second-order capacity region of wireless access networks. We also propose a simple scheduling policy and prove that it can achieve every interior point in the second-order capacity region. To demonstrate the utility of this framework, we apply it for an important open problem: the optimization of AoI over Gilbert-Elliott channels. We show that this framework provides a very accurate characterization of AoI. Moreover, it leads to a tractable scheduling policy that outperforms other existing work.

This work studies the role of Age of Information (AoI) in the network state updating process for wireless software defined networks (SDN). The SDN routers must routinely update their knowledge of the network state, which is used as a basis for making routing and scheduling decisions. However, the network updates require communication resources, so there is a tradeoff between the frequency of updates and maximum network throughput. We assume the network state is Markovian and no new observations are received in between updates, so the AoI of the network state information impacts the ability of the network to optimize its performance. We formulate the problem as a finite-horizon Partially Observable Markov Decision Process (POMDP) for each period. For a symmetric fading model of the network, we derive the limiting performance and an upper bound. To generate policies for a range of fixed time horizons, we use Monte Carlo planning-based POMDP solvers. Simulation of these policies show that there is a finite optimal update period that maximizes network throughput. In addition, we study non-uniform update intervals, which can yield even higher throughput if the interval is chosen based on the state observed. We conclude that AoI itself is not sufficient to characterize performance, but what matters is the AoI for the specific network state information.

Age of information is often studied as a primary objective to be optimized, but for problems where age is not the primary objective, it can still have a major role that can be utilized. This work studies a two-user, single-channel cognitive radio network, where the primary user’s transmit/idle dynamics are modeled as a binary Markov chain, and the secondary user decides to either sense or transmit. Under this setup, the age of the information sensed by the secondary user has a direct impact on its performance. The secondary user aims to maximize its throughput subject to a constraint on the probability of collision experienced by the primary. Using the Markov chain model of the primary user, the secondary user decides on its transmission and sensing strategy based on the estimated evolution of the primary user transmission state. For a stationary randomized transmission policy that depends on the sensed state, we derive the secondary throughput and the collision probability. Due to the complexity of the resulting expressions, we develop an alternative formulation of the problem by recognizing that the throughput and collision probability are functions of the age of each type of sensed information. Therefore, we transform the problem by converting the randomized policy to its induced age distribution function. As a result, the age distribution-based formulation results in a linear program, which can be solved efficiently. We include numerical results and simulations, and discuss the role of the age distribution and other related qualities of the information.

Communication over an interference channel, which is fundamental and pervasive in the wireless and wireline environment, is often intended to carry information among different transmitter-receiver pairs. For applications that require time critical updates, it is desirable to maintain the freshness of the received information, which is quantified by the age metric (unlike the familiar delay metric). In this paper, we consider the case of two transmitter-receiver pairs, and address the impact of interference on information freshness by formulating a two-player “interference” game, in which each player is a transmitter desiring to maintain the freshness of the information updates it sends to its receiver. The strategy of a player is the choice of power level at which it will transmit. We then derive both Nash and Stackelberg strategies for the game. Our analysis shows that the Stackelberg strategy uses less power than the Nash strategy, and that it dominates the Nash strategy (i.e., the Stackelberg total cost function is lower than the Nash total cost function). Our obtained Nash and Stackelberg strategies are desirable user operating points in competitive situations.

We study the age of information, which is a measure of the freshness of a continually updated piece of information as observed at a remote monitor. The age of information metric has been studied for a variety of different queueing systems, and in this paper, we introduce a packet deadline as a control mechanism to study its impact on the average age of information for an M/M/1/2 queueing system. We analyze the system for the cases of a fixed deadline and a random exponential deadline and derive closed-form expressions for the average age. We also derive a closed-form expression for the optimal average deadline for the random exponential case. Our numerical results show the relationship of the age performance to that of the M/M/1/1 and M/M/1/2 systems, and we demonstrate that using a deadline can outperform both the M/M/1/1 and M/M/1/2 without deadline.

We propose a model for mobile caching in which the rate of requests for content is dependent on the popularity and the freshness of the information. We model popularity based on the history of requests and freshness based on the age of the content. We consider a discrete time (slotted) system in which new packets arrive at a limited capacity cache at discrete times. We prove that the optimal policy for choosing the set of packets to reside in a full cache when a packet arrives is to reject the one with the lowest request rate in that particular slot. Thus, there is no advantage to separately knowing the history of requests or the age of the content. Since the optimal policy depends on the profile of the request process, we also study the expected behavior of the request model. We provide a sufficient condition under which the change in the request rate goes to zero and provide some numerical examples that illustrate this behavior. We also consider a slight alteration to the model, in which only the recent history of requests is used for determining the request rate. In this case, we provide a sufficient condition for when the rate is equal to zero, which approximates the duration of requests for content.

For time critical updates, it is desirable to maintain the freshness of the received information. We address the impact of hostile interference on information freshness by formulating a non-zero-sum two-player game, in which one player is the transmitter aiming to maintain the freshness of the information updates it sends to its receiver, and the other player is the interferer aiming to prevent this. The strategy of a player is the power level transmitted by that player. We then derive the equilibria for both Nash and Stackelberg strategies. We show that both players have the same power cost at Nash equilibrium. In addition, the Stackelberg strategy dominates the Nash strategy, i.e., the Stackelberg utility function exceeds the Nash utility function.

We study the age of information, which is a recently introduced metric for measuring the freshness of a continually updated piece of information as observed at a remote monitor. The age of information metric has been studied for a variety of different queuing systems. In this work, we introduce a packet deadline as a control mechanism and study its impact on the average age of information for an M/M/1/2 queuing system. We analyze the system for a fixed deadline and derive a mathematical expression for the average age. We numerically evaluate the expression and show the relationship of the age performance to that of the M/M/1/1 and M/M/1/2 systems. We show that the system with a deadline constraint can outperform both the M/M/1/1 and M/M/1/2 without such a deadline.

We formulate the interaction between communication and hostile interference in wireless systems as a non-zero-sum two-player game. One player is the transmitter aiming to establish or maintain the communication to its receivers, and the other player is the interferer aiming to prevent or disrupt the communication. The strategy of the transmitter is a transmission power level, while the strategy of the interferer is an interfering power level. We provide closed-form equilibria for both Nash and Stackelberg models. We show that, while a Stackelberg equilibrium always exists, a Nash equilibrium exists only when the wireless channel is affected by fading. In addition, for the case of Rayleigh channel fading, we show that both players have the same power cost at Nash equilibrium.

This paper focuses on status age, which is a metric for measuring the freshness of a continually updated piece of information (i.e., status) as observed at a remote monitor. In paper, we study a system in which a sensor sends random status updates over a dynamic network to a monitor. For this system, we consider the impact of having messages take different routes through the network on the status age. First, we consider a network with plentiful resources (i.e., many nodes that can provide numerous alternate paths), so that packets need not wait in queues at each node in a multihop path. This system is modeled as a single queue with an infinite number of servers, specifically as an M/M/∞ queue. Packets routed over a dynamic network may arrive at the monitor out of order, which we account for in our analysis for the M/M/∞ model. We then consider a network with somewhat limited resources, so that packets can arrive out of order but also must wait in a queue. This is modeled as a single queue with two servers, specifically an M/M/2 queue. We present the exact approach to computing the analytical status age, and we provide an approximation that is shown to be close to the simulated age. We also compare both models with M/M/1, which corresponds to severely limited network resources, and we demonstrate the tradeoff between the status age and the unnecessary network resource consumption.

We study the minimum latency broadcast scheduling problem, in which a single source has a quantity of data that must be transmitted to all other nodes in a multi-hop network in minimum time. Aside from the obvious application to classical communications, this problem also relates to some more general problems in the field of network science. Previous approaches to scheduling have assumed a simplistic collision model of interference, while others have studied the more realistic physical model of total received interference power. Existing suboptimal approaches for transmitting the data typically assume a collision-free, fixed-rate, single packet transmission. In this work, we devise an optimal approach for broadcast under a physical interference model with fixed-rate, single packet transmission by converting it to a shortest path problem for an unweighted, undirected graph. Since this optimal approach does not scale well, we also consider a suboptimal layered approach which separates the routing and scheduling functions, but relaxes the fixed-rate, single packet assumption. This goes beyond the signal-to-interference-plus-noise (SINR) threshold model to allow for rate adaptation as a function of SINR. We include improvements on previous routing approaches, and we formulate a linear programming approach to the variable-rate scheduling for broadcast. Simulations show that in some special cases, this variable-rate layered approach can even outperform the optimal fixed-rate, single packet approach.

We consider a wireless network consisting of source-destination pairs, in which each source is required to transmit a given bit volume to its destination. The goal is for all the sources to transmit the given bit volumes, under a time constraint, so that the total transmission energy is minimized. Our approach is the joint optimization of link scheduling and power control for minimum energy. We show that TDMA scheduling is appropriate for this goal, in the sense that TDMA is asymptotically optimal when the time constraint approaches infinity. When the time constraint is strictly bounded, we show that TDMA is also optimal for the case of equal channel gains.

We investigate the performance of a status monitoring system, in which a sensor sends random status updates over a network to a remote monitor. Specifically, we analyze the status age metric, which characterizes how old the information at the monitor is from the last received status update. The system on which we focus is a single queue with 2 servers (specifically, an M/M/2). In a dynamic network, different status packets may take different routes to the monitor, which allows for the possibility of packets arriving out of order. In the case of the status monitoring system, only the latest status is useful. Studying a system with 2 servers allows for the possibility of packets to arrive out-of-order while still having to queue. We present the exact approach to computing the analytical status age, and we provide an approximation that matches very closely with the simulated age. We also compare with the M/M/∞ and M/M/1, and we demonstrate the tradeoff between status age and network resource consumption.

We study the energy-efficient transmission problem for a time-varying interference channel. Assume that each source transmits in each time slot according to a transmission probability, which is a continuous value between 0 and 1. Our goal is to determine the values of the transmission probabilities and the transmission power levels so that the network energy efficiency is maximized. We show that the energy efficiency is maximized when the transmission probabilities are either 0 or 1. We also show that simultaneous transmissions reduce energy efficiency. We then address the impact of the accuracy and timeliness of channel state information (CSI) on energy efficiency. The following cases are considered: perfect CSI, erroneous CSI, delayed CSI, and unknown CSI.

This paper addresses fundamental issues in a shared channel where the users have different priority levels. In particular, we study a two-user cognitive shared channel consisting of a primary (higher-priority) and a secondary user, operating in the cognitive underlay fashion, but in a novel way where interference suffered by the primary user is compensated by requiring the secondary user to cooperatively relay some of the primary's packets. We start by analyzing the case of no node cooperation, where nodes transmit their own packets to their respective destinations. We then extend the analysis to a system in which the secondary node acts as a relay for the primary user, in addition to serving its own packets. Specifically, in the cognitive cooperation case, the secondary node forwards those packets to the primary destination that it receives successfully from the primary source. In such cognitive shared channels, a tradeoff arises in terms of activating the secondary along with the primary so that both transmissions may be successful, but with a lower probability, compared to the case of the secondary node staying idle when the primary user transmits. Results show the benefits of relaying for both the primary as well as the secondary nodes in terms of the stable-throughput region.

We evaluate the throughput that can be achieved under BER constraints by combined use of transmission scheduling and multiuser detection. A schedule is a rule that specifies which subset of users is allowed to simultaneously transmit in a time slot. These subsets of overlapping transmissions, which can vary in different time slots of the transmission frame, are decoded by receivers equipped with multiuser detection. The goal is to find the largest such subsets under the requirement that each transmission satisfies a BER constraint. The joint problem of scheduling and multiuser-detection is highly complex in general. However, for certain class of multiuser detectors, the problem has efficient and optimal solution. By constructing transmission schedules that directly reflect the performance and exploit the capability of the multiuser detection receivers, as expected, multiuser detection-based scheduling significantly outperforms other methods such as TDMA and the conventional single-user detection-based scheduling.

In this work, we investigate the queue stability of a two-user cognitive radio system with multicast traffic. We study the impact of network-level cooperation, in which one of the nodes can relay the packets of the other user that are not received at the destinations. Under this approach, if a packet transmitted by the primary user is not successfully received by the destination set but is captured by the secondary source, then the secondary user assumes responsibility for completing the transmission of the packet; therefore, the primary releases it from its queue, enabling it to process the next packet. We demonstrate that the stability region of this cooperative approach is larger than that of the noncooperative approach, which translates into a benefit for both users of this multicast system. Our system model allows for the possibility of multipacket reception, and the optimal transmission strategies for different levels of multipacket reception capability are observed in our numerical results.

We consider the system where a source randomly generates status update messages and transmits them via a network cloud to the intended destination. These update message can take different times to traverse the network, which we model as exponential service times, and may result in packets reaching the destination out of order, rendering some of the earlier transmissions obsolete. We analyze the status update age for such a system, and show that it tracks well with simulation results.

The underwater acoustic channel is characterized by a path loss that is dependent on both the distance and the frequency of communication. Given this dependence, it has been previously demonstrated that for a given communication distance, there is an optimal operating frequency, where conditions for signal propagation and noise are most favorable. In this work, we consider extending this optimal frequency concept to scenarios in which the frequencies that can be employed by the system are constrained. Such constraints are important considerations for practical system design. The first problem we study is to find a single frequency that minimizes the energy over a number of links of varying lengths. An approximate model for this frequency is proposed that is very close to the true optimal. We then generalize this problem to finding the best frequency band, within which the frequency can be tuned for different link lengths. We demonstrate how our model is applied to a 2-D network scenario. We simulate random node placement for such a network, and we observe that the optimal frequencies are very close to the proposed model.

In applications involving networks of sensor-equipped autonomous vehicles, it is crucial to have an energy-efficient communication protocol due to the limited on-board batteries. Unlike traditional sensor networks, vehicle sensor networks typically consist of only a small number of nodes. We exploit this fact in our protocol design by optimizing specifically for these mobile small-scale networks. Our proposed solution, ConverSS, is a hybrid MAC/routing protocol that is energy-efficient for vehicle sensor networks. We have evaluated the protocol through simulation in ns-2 and verified its operation in a testbed network deployment. The results show that ConverSS is robust to real-world link impairments and that it outperforms common layered solutions by as much as a factor of 10.

Vehicle-based networks need energy-efficient communication to extend the battery lifetime, which subsequently extends the mission time of the node. We observe that these kinds of networks operate under different assumptions than traditional static sensor networks. The main difference is that these a