We consider a spectrum sharing problem where two users attempt to communicate over N channels. The Primary User (PU) has prioritized transmissions and its occupancy on each channel over time can be modeled as a Markov chain. The Secondary User (SU) needs to determine which channels are free at each time-slot and attempt opportunistic transmissions. The goal of the SU is to maximize its own throughput, while simultaneously minimizing collisions with the PU, and satisfying spectrum access constraints. To solve this problem, we first decouple the multiple-channel problem into N single-channel problems. For each decoupled problem, we prove that there exists an optimal threshold policy that depends on the last observed PU occupancy and the freshness of this occupancy information. Second, we establish the indexability of the decoupled problems by analyzing the structure of the optimal threshold policy. Using this structure, we derive a Whittle index-based scheduling policy that allocates SU transmissions using the Age of Information (AoI) of accessed channels. We also extend our insights to PU occupancy models that are correlated across channels and incorporate learning of unknown Markov transition matrices into our policies. Finally, we provide detailed numerical simulations that demonstrate the performance gains of our approach.

Remote tracking systems play a critical role in applications such as IoT, monitoring, surveillance and healthcare. In such systems, maintaining both real-time state awareness (for online decision making) and accurate reconstruction of historical trajectories (for offline post-processing) are essential. While the Age of Information (AoI) metric has been extensively studied as a measure of freshness, it does not capture the accuracy with which past trajectories can be reconstructed. In this work, we investigate reconstruction error as a complementary metric to AoI, addressing the trade-off between timely updates and historical accuracy. Specifically, we consider three policies, each prioritizing different aspects of information management: Keep-Old, Keep-Fresh, and our proposed Inter-arrival-Aware dropping policy. We compare these policies in terms of impact on both AoI and reconstruction error in a remote tracking system with a finite buffer. Through theoretical analysis and numerical simulations of queueing behavior, we demonstrate that while the Keep-Fresh policy minimizes AoI, it does not necessarily minimize reconstruction accuracy. In contrast, our proposed Inter-arrival-Aware dropping policy dynamically adjusts packet retention decisions based on generation times, achieving a balance between AoI and reconstruction error. Our results provide key insights into the design of efficient update policies for resource-constrained IoT networks.

We investigate a real-time remote inference system where multiple correlated sources transmit observations over a communication channel to a receiver. The receiver utilizes these observations to infer multiple time-varying targets. Due to limited communication resources, the delivered observations may not be fresh. To quantify data freshness, we employ the Age of Information (AoI) metric. To minimize the inference error, we aim to design a signal-agnostic scheduling policy that leverages AoI without requiring knowledge of the actual target values or the source observations. This scheduling problem is a restless multi-armed bandit (RMAB) problem with a non-separable penalty function. Unlike traditional RMABs, the correlation among sources introduces a unique challenge: the penalty function of each source depends on the AoI of other correlated sources, preventing the problem from decomposing into multiple independent Markov Decision Processes (MDPs), a key step in applying traditional RMAB solutions. To address this, we propose a novel approach that approximates the penalty function for each source and establishes an analytical bound on the approximation error. We then develop scheduling policies for two scenarios: (i) full knowledge of the penalty functions and (ii) no knowledge of the penalty functions. For the case of known penalty functions, we present an upper bound on the optimality gap that highlights the impact of the correlation parameter and the system size. For the case of unknown penalty functions and signal distributions, we develop an online learning approach that utilizes bandit feedback to learn an online Maximum Gain First policy. Simulation results demonstrate the effectiveness of our proposed policies in minimizing inference error and achieving scalability in the number of sources.

We consider a setting where multiple correlated sources send real-time observations over a wireless communication channel to a receiver. The receiver uses the delivered observations to infer multiple time-varying targets. Due to limited communication resources, these observations may not always be fresh. To quantify data timeliness, we utilize the Age of Information (AoI) metric. Our goal is to minimize realtime inference error by developing signal-agnostic scheduling policies that leverage AoI without requiring knowledge of the actual target values or the specific source observations. For the two-source case, we obtain an optimal cyclic policy with low computational complexity. For more than two-sources, we establish an information-theoretic lower bound on inference error. Building upon this lower bound, we approximate the scheduling problem and propose an approximate Whittle index policy that is asymptotically optimal as the number of sources increases and the correlation among sources decreases. Our scheduling policies hold for arbitrary target and source processes and loss functions. Finally, we conduct simulations of a network of cameras with overlapping field of views tracking multiple mobile objects to demonstrate the effectiveness of our policies.

Modern sensing and monitoring applications typically consist of sources transmitting updates of different sizes, ranging from a few bytes (position, temperature, etc.) to multiple megabytes (images, video frames, LIDAR point scans, etc.). Existing approaches to wireless scheduling for information freshness typically ignore this mix of large and small updates, leading to suboptimal performance. In this paper, we consider a single-hop wireless broadcast network with sources transmitting updates of different sizes to a base station over unreliable links. Some sources send large updates spanning many time slots while others send small updates spanning only a few time slots. Due to medium access constraints, only one source can transmit to the base station at any given time, thus requiring careful design of scheduling policies that takes the sizes of updates into account. First, we derive a lower bound on the achievable Age of Information (AoI) by any transmission scheduling policy. Second, we develop optimal randomized policies that consider both switching and no-switching during the transmission of large updates. Third, we introduce a novel Lyapunov function and associated analysis to propose an AoI-based Max-Weight policy that has provable constant factor optimality guarantees. Finally, we evaluate and compare the performance of our proposed scheduling policies through simulations, which show that our Max-Weight policy achieves near-optimal AoI performance.

Cooperative localization leverages noisy inter-node distance measurements and exchanged wireless messages to estimate node positions in a wireless network. In communicationconstrained environments, however, transmitting large messages becomes problematic. In this paper, we propose an approach for communication-efficient cooperative localization that addresses two main challenges. First, cooperative localization often needs to be performed over wireless networks with loopy graph topologies. Second is the need for designing an algorithm that has low localization error while simultaneously requiring a much lower communication overhead. Existing methods fall short of addressing these two challenges concurrently. To achieve this, we propose a vector quantized message passing neural network (VQ-MPNN) for cooperative localization. Through end-to-end neural network training, VQ-MPNN enables the co-design of node localization and message compression. Specifically, VQMPNN treats prior node positions and distance measurements as node and edge features, respectively, which are encoded as node and edge states using a graph neural network. To find an efficient representation for the node state, we construct a vector quantized codebook for all node states such that instead of sending long messages, each node only needs to transmit a codeword index. Numerical evaluations demonstrates that our proposed VQ-MPNN approach can deliver localization errors that are similar to existing approaches while reducing the overall communication overhead by an order of magnitude.

We study the design of scheduling policies to minimize the monitoring error of a collection of correlated sources, where only one source can be observed at any given time. We model correlated sources as a discrete-time Wiener process, where the increments are multivariate normal random variables, with a general covariance matrix that captures the correlation structure between the sources. Under a Kalman filter-based optimal estimation framework, we show that the performance of all scheduling policies oblivious to instantaneous error can be lower and upper bounded by the weighted sum of Age of Information (AoI) across the sources for appropriately chosen weights. We use this insight to design scheduling policies that are only a constant factor away from optimality, and make the rather surprising observation that AoI-based scheduling that ignores correlation is sufficient to obtain performance guarantees. We also derive scaling results showing that the optimal error scales roughly as the square of the system's dimensionality, even with correlation. Finally, we provide simulation results to verify our claims.

We study the design of scheduling policies to minimize monitoring error for a collection of correlated sources, where only one source can be observed at any given time. We model correlated sources as a discrete-time Wiener process, where the increments are multivariate normal random variables, with a general covariance matrix that captures the correlation structure between the sources. Under a Kalman filter based optimal estimation framework, we show that the performance of all scheduling policies oblivious to instantaneous error, can be lower and upper bounded by the weighted sum of Age of Information (AoI) across the sources for appropriately chosen weights. We use this insight to design scheduling policies that are only a constant factor away from optimality, and make the rather surprising observation that AoI-based scheduling that ignores correlation is sufficient to obtain performance guarantees. We also derive scaling results that show that the optimal error scales roughly as the square of the dimensionality of the system, even in the presence of correlation. Finally, we provide simulation results to verify our claims.

We develop a simple model for the timely monitoring of correlated sources over a wireless network. Using this model, we study how to optimize weighted-sum average Age of Information (AoI) in the presence of correlation. First, we discuss how to find optimal stationary randomized policies and show that they are at-most a factor of two away from optimal policies in general. Then, we develop a Lyapunov drift-based max-weight policy that performs better than randomized policies in practice and show that it is also at-most a factor of two away from optimal. Next, we derive scaling results that show how AoI improves in large networks in the presence of correlation. We also show that for stationary randomized policies, the expression for average AoI is robust to the way in which the correlation structure is modeled. Finally, for the setting where correlation parameters are unknown and time-varying, we develop a heuristic policy that adapts its scheduling decisions by learning the correlation parameters in an online manner. We also provide numerical simulations to support our theoretical results.

We consider a setting where multiple active sources send real-time updates over a single-hop wireless broadcast network to a monitoring station. Our goal is to design a scheduling policy that minimizes the time-average of general non-decreasing cost functions of Age of Information. We use a Whittle index based approach to find low complexity scheduling policies that have good performance. We prove that for a system with two sources, having possibly different cost functions and reliable channels, the Whittle index policy is exactly optimal. We derive structural properties of an optimal policy, that suggest that the performance of the Whittle index policy may be close to optimal in general. These results might also be of independent interest in the study of restless multi-armed bandit problems with similar underlying structure. We further establish that minimizing monitoring error for linear time-invariant systems and symmetric Markov chains is equivalent to minimizing appropriately chosen monotone functions of Age of Information. Finally, we provide simulations comparing the Whittle index policy with optimal scheduling policies found using dynamic programming, which support our results.

We consider the design of distributed scheduling algorithms that minimize age of information in single-hop wireless networks. The centralized max-weight policy is known to be nearly optimal in this setting; hence, our goal is to design a distributed CSMA scheme that can mimic its performance. To that end, we propose a distributed protocol called Fresh-CSMA and show that in an idealized setting, Fresh-CSMA can match the scheduling decisions of the max-weight policy with high probability in each frame, and also match the theoretical performance guarantees of the max-weight policy over the entire time horizon. We then consider a more realistic setting and study the impact of protocol parameters on the probability of collisions and the overhead caused by the distributed nature of the protocol. Finally, we provide simulations that support our theoretical results and show that the performance gap between the ideal and realistic versions of Fresh-CSMA is small.

We consider the problem of minimizing age of information in multihop wireless networks and propose three classes of policies to solve the problem - stationary randomized, age difference, and age debt. For the unicast setting with fixed routes between each source-destination pair, we first develop a procedure to find age optimal Stationary Randomized policies. These policies are easy to implement and allow us to derive closed-form expression for average AoI. Next, for the same unicast setting, we develop a class of heuristic policies, called Age Difference, based on the idea that if neighboring nodes try to reduce their age differential then all nodes will have fresher updates. This approach is useful in practice since it relies only on the local age differential between nodes to make scheduling decisions. Finally, we propose the class of policies called Age Debt, which can handle 1) non-linear AoI cost functions; 2) unicast, multicast and broadcast flows; and 3) no fixed routes specified per flow beforehand. Here, we convert AoI optimization problems into equivalent network stability problems and use Lyapunov drift to find scheduling and routing schemes that stabilize the network. We also provide numerical results comparing our proposed classes of policies with the best known scheduling and routing schemes available in the literature for a wide variety of network settings.

We develop a simple model for the timely monitoring of correlated sources over a wireless network. Using this model, we study how to optimize weighted-sum average Age of Information (AoI) in the presence of correlation. First, we discuss how to find optimal stationary randomized policies and show that they are at-most a factor of two away from optimal policies in general. Then, we develop a Lyapunov drift-based max-weight policy that performs better than randomized policies in practice and show that it is also at-most a factor of two away from optimal. Next, we derive scaling results that show how AoI improves in large networks in the presence of correlation. We also show that for stationary randomized policies, the expression for average AoI is robust to the way in which the correlation structure is modeled. Finally, for the setting where correlation parameters are unknown and time-varying, we develop a heuristic policy that adapts its scheduling decisions by learning the correlation parameters in an online manner. We also provide numerical simulations to support our theoretical results.

We consider systems that require timely monitoring of sources over a communication network, where the cost of delayed information is unknown, time-varying and possibly adversarial. For the single source monitoring problem, we design algorithms that achieve sublinear regret compared to the best fixed policy in hindsight. For the multiple source scheduling problem, we design a new online learning algorithm called Follow the Perturbed Whittle Leader and show that it has low regret compared to the best fixed scheduling policy in hindsight, while remaining computationally feasible. The algorithm and its regret analysis are novel and of independent interest to the study of online restless multi-armed bandit problems. We further design algorithms that achieve sublinear regret compared to the best dynamic policy when the environment is slowly varying. Finally, we apply our algorithms to a mobility tracking problem. We consider non-stationary and adversarial mobility models and illustrate the performance benefit of using our online learning algorithms compared to an oblivious scheduling policy.

We investigate the problem of co-designing computation and communication in a multi-agent system (e.g., a sensor network or a multi-robot team). We consider the realistic setting where each agent acquires sensor data and is capable of local processing before sending updates to a base station, which is in charge of making decisions or monitoring phenomena of interest in real time. Longer processing at an agent leads to more informative updates but also larger delays, giving rise to a delay-accuracy trade-off in choosing the right amount of local processing at each agent. We assume that the available communication resources are limited due to interference, bandwidth, and power constraints. Thus, a scheduling policy needs to be designed to suitably share the communication channel among the agents. To that end, we develop a general formulation to jointly optimize the local processing at the agents and the scheduling of transmissions. Our novel formulation leverages the notion of Age of Information to quantify the freshness of data and capture the delays caused by computation and communication. We develop efficient resource allocation algorithms using the Whittle index approach and demonstrate our proposed algorithms in two practical applications: multi-agent occupancy grid mapping in time-varying environments, and ride sharing in autonomous vehicle networks. Our experiments show that the proposed codesign approach leads to a substantial performance improvement (18 – 82% in our tests).

We consider the problem of timely exchange of updates between a central station and a set of ground terminals$V$, via a mobile agent that traverses across the ground terminals along a mobility graph$G = (V, E)$. We design the trajectory of the mobile agent to minimize average-peak and average age of information (AoI), two recently proposed metrics for measuring timeliness of information. We consider randomized trajectories, in which the mobile agent travels from terminal$i$to terminal$j$with probability$P_{i,j}$. For the information gathering problem, we show that a randomized trajectory is average-peak age optimal and factor-$8\mathcal {H}$average age optimal, where$\mathcal {H}$is the mixing time of the randomized trajectory on the mobility graph$G$. We also show that the average age minimization problem is NP-hard. For the information dissemination problem, we prove that the same randomized trajectory is factor-$O(\mathcal {H})$average-peak and average age optimal. Moreover, we propose an age-based trajectory, which utilizes information about current age at terminals, and show that it is factor-2 average age optimal in a symmetric setting.

In this work, we consider a system with multiple sensors, each measuring a different time-varying signal. The sensors report their measurements to a central monitoring station via multiple orthogonal communication channels. An important performance metric in such systems is the age of information at the monitoring station, defined as the amount of time that has elapsed since the recent most update from each sensor. We propose two scheduling policies and prove their optimality with respect to this metric. Another key objective in such systems is to minimize the energy consumption of the sensors. Motivated by this, we propose energy- efficient variants of the two scheduling policies and show that close to optimal performance can be achieved with significant reductions in the energy consumption of the sensors. We provide numerical results to validate our theoretical guarantees.