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We consider the problem of real-time remote monitoring of a two-state Markov process, where a sensor observes the state of the source and makes a decision on whether to transmit the status updates over an unreliable channel or not. We introduce a modified randomized stationary sampling and transmission policy where the decision to perform sampling occurs probabilistically depending on the current state of the source and whether the system was in a sync state during the previous time slot or not. We then propose two new performance metrics, coined the Version Innovation Age (VIA) and the Age of Incorrect Version (AoIV) and analyze their performance under the modified randomized stationary and other state-of-the-art sampling and transmission policies. Specifically, we derive closed-form expressions for the distribution and the average of VIA, AoIV, and Age of Incorrect Information (AoII) under these policies. Furthermore, we formulate and solve three constrained optimization problems. The first optimization problem aims to minimize the average VIA subject to constraints on the time-averaged sampling cost and time-averaged reconstruction error. In the second and third problems, the objective is to minimize the average AoIV and AoII, respectively, while considering a constraint on the time-averaged sampling cost. Finally, we compare the performance of various sampling and transmission policies and identify the conditions under which each policy outperforms the others in optimizing the proposed metrics., Comment: arXiv admin note: substantial text overlap with arXiv:2401.17691

The Age of Incorrect Information (AoII) is studied within the context of remote monitoring a Markov source using variable-length stop-feedback (VLSF) coding. Leveraging recent results on the non-asymptotic channel coding rate, we consider sources with small cardinality, where feedback is non-instantaneous as the transmitted information and feedback message have comparable lengths. We focus on the feedback sequence, i.e. the times of feedback transmissions, and derive AoII-optimal and delay-optimal feedback sequences. Our results showcase the impact of the feedback sequence on the AoII, revealing that a lower average delay does not necessarily correspond to a lower average AoII. We discuss the implications of our findings and suggest directions for coding scheme design.

In this paper, we propose two new performance metrics, coined the Version Innovation Age (VIA) and the Age of Incorrect Version (AoIV) for real-time monitoring of a two-state Markov process over an unreliable channel. We analyze their performance under the change-aware, semantics-aware, and randomized stationary sampling and transmission policies. We derive closed-form expressions for the distribution and the average of VIA, AoIV, and AoII for these policies. We then formulate and solve an optimization problem to minimize the average VIA, subject to constraints on the time-averaged sampling cost and time-averaged reconstruction error. Finally, we compare the performance of various sampling and transmission policies and identify the conditions under which each policy outperforms the others in optimizing the proposed metrics.

In this paper, we introduce two metrics, namely, age of actuation (AoA) and age of actuated information (AoAI), within a discrete-time system model 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 use Markov Chain analysis to model the system's evolution. Furthermore, we employ three-dimensional Markov Chain analysis to characterize the stationary distributions for AoA and AoAI and calculate their average values. Our findings from the analysis, validated by simulations, show that while AoAI consistently decreases with increased data and energy packet arrival rates, AoA presents a more complex behavior, with potential increases under conditions of limited data or energy resources. These metrics go towards the semantics of information and goal-oriented communications since they consider the timeliness of utilizing the information to perform an action.

In this paper, we investigate a model relevant to semantics-aware goal-oriented communications, and we propose a new metric that incorporates the utilization of information in addition to its timelines. Specifically, 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 to achieve a goal. We focus on a wireless power transfer (WPT) model, where the receiver receives energy from a dedicated power transmitter and occasionally from the data transmitter when they share a common channel. We analyze the Age of Information (AoI) and propose a new metric, the \textit{Age 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 \textit{Probability of Missing Actuation (PoMA)}; this metric becomes relevant also \textit{to quantify 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., Comment: Submitted for possible Journal publication. arXiv admin note: text overlap with arXiv:2303.00507

We consider a time slotted communication network with a base station (BS) and a user. At each time slot a fresh update packet arrives at the BS with probability $p>0$. When the BS transmits an update packet for the first time, it goes through with a success probability of $q_1$. In all subsequent re-transmissions, the packet goes through with a success probability of $q_2$ where $q_2>q_1$, due to the accumulation of observations at the receiver used to decode the packet. When the packet goes through the first time, the age of the user drops to 1, while when the packet goes through in subsequent transmissions, the age of the user drops to the age of the packet since its generation. Thus, when the BS is in the process of re-transmitting an old packet, if it receives a new packet, it has to decide whether to re-transmit the old packet with higher probability of successful transmission but resulting in higher age, or to transmit the new packet which will result in a lower age upon successful reception but this will happen with lower probability. In this paper, we provide an optimal algorithm to solve this problem.

The Age of Incorrect Information (AoII) is a recently proposed metric for real-time remote monitoring systems. In particular, AoII measures the time the information at the monitor is incorrect, weighted by the magnitude of this incorrectness, thereby combining the notions of freshness and distortion. This paper addresses the definition of an AoII-optimal transmission policy in a discrete-time communication scheme with a resource constraint and a hybrid automatic repeat request (HARQ) protocol. Considering an $N$-ary symmetric Markov source, the problem is formulated as an infinite-horizon average-cost constrained Markov decision process (CMDP). The source model is characterized by the cardinality of the state space and the probability of staying at the same state. Interestingly, it is proved that under some conditions, the optimal transmission policy is to never transmit. This reveals that there exists a region of the source dynamics where communication is inadequate in reducing the AoII. Elsewhere, there exists an optimal transmission policy, which is a randomized mixture of two discrete threshold-based policies that randomize at one state. The optimal threshold and the randomization component are derived analytically. Numerical results illustrate the impact of source dynamics, channel conditions, and resource constraints on the average AoII., Comment: 16 pages, 12 figures. This work has been submitted to the IEEE for possible publication

In this paper, we study a model relevant to semantics-aware goal-oriented communications. More specifically, observations from an external process are transmitted through status updates to a battery-powered receiver. From these updates, the receiver is informed about the status of the process and if there is sufficient energy, uses them to perform an actuation to achieve a goal. We consider a wireless power transfer model where the destination receives energy from a dedicated power transmitter and occasionally from the data transmitter. We provide the analysis for the Age of Information (AoI). Furthermore, we propose a new metric, namely the \textit{Age of Actuation (AoA) which is relevant when the receiver utilizes the status updates to perform actions in a timely manner}. We analytically characterize the AoA and we show that is a more general metric than AoI. We provide the optimization problems for both metrics, and we numerically evaluate our analytical results., Comment: IEEE INFOCOM Workshop of Age of Information 2023

We consider a transmitter-receiver pair in a slotted-time system. The transmitter observes a dynamic source and sends updates to a remote receiver through an error-free communication channel that suffers a random delay. We consider two cases. In the first case, the update is guaranteed to be delivered within a certain number of time slots. In the second case, the update is immediately discarded once the transmission time exceeds a predetermined value. The receiver estimates the state of the dynamic source using the received updates. In this paper, we adopt the Age of Incorrect Information (AoII) as the performance metric and investigate the problem of optimizing the transmitter's action in each time slot to minimize AoII. We first characterize the optimization problem using the Markov decision process and investigate the performance of the threshold policy, under which the transmitter transmits updates only when the transmission is allowed and the AoII exceeds the threshold $\tau$. By delving into the characteristics of the system evolution, we precisely compute the expected AoII achieved by the threshold policy using the Markov chain. Then, we prove that the optimal policy exists and provide a computable relative value iteration algorithm to estimate the optimal policy. Furthermore, by leveraging the policy improvement theorem, we theoretically prove that, under an easily verifiable condition, the optimal policy is the threshold policy with $\tau=1$. Finally, numerical results are presented to highlight the performance of the optimal policy., Comment: This work is a merger of arXiv:2203.02979 and arXiv:2207.02926. This paper is the extension of arXiv:2212.14381

We consider a time slotted communication system consisting of a base station (BS) and a user. At each time slot an update packet arrives at the BS with probability $p$, and the BS successfully transmits the update packet with probability $q$ over an erasure channel. We assume that the BS has a unit size buffer where it can store an update packet upon paying a storage cost $c$. There is a trade-off between the age of information and the storage cost. We formulate this trade-off as a Markov decision process and find an optimal switching type storage policy.

We consider a time slotted communication network consisting of a base station (BS), an adversary, $N$ users and $N_s$ communication channels. Both the BS and the adversary have average power constraints and the probability of successful transmission of an update packet depends on the transmission power of the BS and the blocking power of the adversary. We provide a universal lower bound for the average age for this communication network. We prove that the uniform scheduling algorithm with any feasible transmission power choosing policy is $4$ optimal; and the max-age user choosing policy is $2$ optimal. In the second part of the paper, we consider the setting where the BS chooses a transmission policy and the adversary chooses a blocking policy from the set of randomized stationary policies. We show that the Nash equilibrium point may or may not exist for this communication network. We find special cases where the Nash equilibrium always exists.

This paper investigates the Age of Incorrect Information (AoII) in a communication system whose channel suffers a random delay. We consider a slotted-time system where a transmitter observes a dynamic source and decides when to send updates to a remote receiver through the communication channel. The threshold policy, under which the transmitter initiates transmission only when the AoII exceeds the threshold, governs the transmitter's decision. In this paper, we analyze and calculate the performance of the threshold policy in terms of the achieved AoII. Using the Markov chain to characterize the system evolution, the expected AoII can be obtained precisely by solving a system of linear equations whose size is finite and depends on the threshold. We also give closed-form expressions of the expected AoII under two particular thresholds. Finally, calculation results show that there are better strategies than the transmitter constantly transmitting new updates., Comment: This work is a merger of parts of arXiv:2203.02979 and arXiv:2207.02926

We study the problem of optimizing the decisions of a preemptively capable transmitter to minimize the Age of Incorrect Information (AoII) when the communication channel has a random delay. We consider a slotted-time system where a transmitter observes a Markovian source and makes decisions based on the system status. In each time slot, the transmitter decides whether to preempt or skip when the channel is busy. When the channel is idle, the transmitter decides whether to send a new update. A remote receiver estimates the state of the Markovian source based on the update it receives. We consider a generic transmission delay and assume that the transmission delay is independent and identically distributed for each update. This paper aims to optimize the transmitter's decision in each time slot to minimize the AoII with generic time penalty functions. To this end, we first use the Markov decision process to formulate the optimization problem and derive the analytical expressions of the expected AoIIs achieved by two canonical preemptive policies. Then, we prove the existence of the optimal policy and provide a feasible value iteration algorithm to approximate the optimal policy. However, the value iteration algorithm will be computationally expensive if we want considerable confidence in the approximation. Therefore, we analyze the system characteristics under two canonical delay distributions and theoretically obtain the corresponding optimal policies using the policy improvement theorem. Finally, numerical results are presented to illustrate the performance improvements brought about by the preemption capability.

We consider a slotted-time system with a transmitter-receiver pair. In the system, a transmitter observes a dynamic source and sends updates to a remote receiver through a communication channel. We assume that the channel is error-free but suffers a random delay. Moreover, when an update has been transmitted for too long, the transmission will be terminated immediately, and the update will be discarded. We assume the maximum transmission time is predetermined and is not controlled by the transmitter. The receiver will maintain estimates of the current state of the dynamic source using the received updates. In this paper, we adopt the Age of Incorrect Information (AoII) as the performance metric and investigate the problem of optimizing the transmitter's action in each time slot to minimize AoII. We first characterize the optimization problem using Markov Decision Process and evaluate the performance of some canonical transmission policies. Then, by leveraging the policy improvement theorem, we prove that, under a simple and easy-to-verify condition, the optimal policy for the transmitter is the one that initiates a transmission whenever the channel is idle and AoII is not zero. Lastly, we take the case where the transmission time is geometrically distributed as an example. For this example, we verify the condition numerically and provide numerical results that highlight the performance of the optimal policy., Comment: This paper has been withdrawn by the authors. This paper has been superseded by arXiv:2301.06150 (merged from arXiv:2203.02979 and arXiv:2207.02926)

This paper investigates the problem of minimizing the Age of Incorrect Information (AoII) when the communication channel has a random delay. We consider a slotted-time system where a transmitter observes a dynamic source and decides when to send updates to a remote receiver through a channel with random delay. The receiver maintains estimates of the state of the dynamic source based on the received updates. In this paper, we adopt AoII as the performance metric and investigate the problem of optimizing the transmitter's action in each time slot to minimize AoII. We first characterize the considered problem using Markov Decision Process (MDP). Then, leveraging the policy improvement theorem and under an easy-to-verify condition, we prove that the optimal decision for the transmitter is to initiate a transmission whenever the channel is idle and AoII is not zero. The results apply to generic delay distribution. Lastly, we verify the condition numerically and provide the numerical results that highlight the performance of the optimal policy., Comment: This paper has been withdrawn by the authors. This paper has been superseded by arXiv:2301.06150 (merged from arXiv:2203.02979 and arXiv:2207.02926)

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., Comment: Accepted in IEEE TCOM

In this paper, we analyze status update systems modeled through the Stochastic Hybrid Systems (SHSs) tool. Contrary to previous works, we allow the system's transition dynamics to be polynomial functions of the Age of Information (AoI). This dependence allows us to encapsulate many applications and opens the door for more sophisticated systems to be studied. However, this same dependence on the AoI engenders technical and analytical difficulties that we address in this paper. Specifically, we first showcase several characteristics of the age processes modeled through the SHSs tool. Then, we provide a framework to establish the Lagrange stability and positive recurrence of these processes. Building on this, we provide an approach to compute the m-th moment of the age processes. Interestingly, this technique allows us to approximate the average age by solving a simple set of linear equations. Equipped with this approach, we also provide a sequential convex approximation method to optimize the average age by calibrating the parameters of the system. Finally, we consider an age-dependent CSMA environment where the backoff duration depends on the instantaneous age. By leveraging our analysis, we contrast its performance to the age-blind CSMA and showcase the age performance gain provided by the former.

In this work, we consider the problem of jointly minimizing the average cost of sampling and transmitting status updates by users over a wireless channel subject to average Age of Information (AoI) constraints. Errors in the transmission may occur and a scheduling policy has to decide if the users sample a new packet or attempt for retransmission of the packet sampled previously. The cost consists of both sampling and transmission costs. The sampling of a new packet after a failure imposes an additional cost on the system. We formulate a stochastic optimization problem with the average cost in the objective under average AoI constraints. To solve this problem, we propose three scheduling policies; a) a dynamic policy, that is centralized and requires full knowledge of the state of the system, b) two stationary randomized policies that require no knowledge of the state of the system. We utilize tools from Lyapunov optimization theory in order to provide the dynamic policy, and we prove that its solution is arbitrary close to the optimal one. In order to provide the randomized policies, we model the system by utilizing Discrete Time Markov Chain (DTMC). We provide closed-form and approximated expressions for the average AoI and its distribution, for each randomized policy. Simulation results show the importance of providing the option to transmit an old packet in order to minimize the total average cost., Comment: 30 pages, submitted on a journal

We present our vision for a departure from the established way of architecting and assessing communication networks, by incorporating the semantics of information for communications and control in networked systems. We define semantics of information, not as the meaning of the messages, but as their significance, possibly within a real time constraint, relative to the purpose of the data exchange. We argue that research efforts must focus on laying the theoretical foundations of a redesign of the entire process of information generation, transmission and usage in unison by developing: advanced semantic metrics for communications and control systems; an optimal sampling theory combining signal sparsity and semantics, for real-time prediction, reconstruction and control under communication constraints and delays; semantic compressed sensing techniques for decision making and inference directly in the compressed domain; semantic-aware data generation, channel coding, feedback, multiple and random access schemes that reduce the volume of data and the energy consumption, increasing the number of supportable devices., Comment: 10 pages, 5 figures, 1 table, 1500 words

Age of Incorrect Information (AoII) is a newly introduced performance metric that considers communication goals. Therefore, comparing with traditional performance metrics and the recently introduced metric - Age of Information (AoI), AoII achieves better performance in many real-life applications. However, the fundamental nature of AoII has been elusive so far. In this paper, we consider the AoII in a system where a transmitter sends updates about a multi-state Markovian source to a remote receiver through an unreliable channel. The communication goal is to minimize AoII subject to a power constraint. We cast the problem into a Constrained Markov Decision Process (CMDP) and prove that the optimal policy is a mixture of two deterministic threshold policies. Afterward, by leveraging the notion of Relative Value Iteration (RVI) and the structural properties of threshold policy, we propose an efficient algorithm to find the threshold policies as well as the mixing coefficient. Lastly, numerical results are laid out to highlight the performance of AoII-optimal policy.

In this paper, we introduce the Age of Incorrect Information (AoII) as an enabler for semantics-empowered communication, a newly advocated communication paradigm centered around data's role and its usefulness to the communication's goal. First, we shed light on how the traditional communication paradigm, with its role-blind approach to data, is vulnerable to performance bottlenecks. Next, we highlight the shortcomings of several proposed performance measures destined to deal with the traditional communication paradigm's limitations, namely the Age of Information (AoI) and the error-based metrics. We also show how the AoII addresses these shortcomings and captures more meaningfully the purpose of data. Afterward, we consider the problem of minimizing the average AoII in a transmitter-receiver pair scenario. We prove that the optimal transmission strategy is a randomized threshold policy, and we propose an algorithm that finds the optimal parameters. Furthermore, we provide a theoretical comparison between the AoII framework and the standard error-based metrics counterpart. Interestingly, we show that the AoII-optimal policy is also error-optimal for the adopted information source model. Concurrently, the converse is not necessarily true. Finally, we implement our policy in various applications, and we showcase its performance advantages compared to both the error-optimal and the AoI-optimal policies.

Future wireless networks will be characterized by heterogeneous traffic requirements. Such requirements can be low-latency or minimum-throughput. Therefore, the network has to adjust to different needs. Usually, users with low-latency requirements have to deliver their demand within a specific time frame, i.e., before a deadline, and they co-exist with throughput oriented users. In addition, the users are mobile and they share the same wireless channel. Therefore, they have to adjust their power transmission to achieve reliable communication. However, due to the limited power budget of wireless mobile devices, a power-efficient scheduling scheme is required by the network. In this work, we cast a stochastic network optimization problem for minimizing the packet drop rate while guaranteeing a minimum throughput and taking into account the limited-power capabilities of the users. We apply tools from Lyapunov optimization theory in order to provide an algorithm, named Dynamic Power Control (DPC) algorithm, that solves the formulated problem in realtime. It is proved that the DPC algorithm gives a solution arbitrarily close to the optimal one. Simulation results show that our algorithm outperforms the baseline Largest-Debt-First (LDF) algorithm for short deadlines and multiple users., Comment: Submitted in a journal

In this work, we combine the two notions of timely delivery of information in order to study their interplay; namely, deadline-constrained packet delivery due to latency constraints and freshness of information at the destination. 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. For this simple, yet meaningful setup, 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., Comment: Submitted to ITW

We consider the problem of minimizing the time average cost of sampling and transmitting status updates by users over a wireless channel subject to average Age of Information constraints (AoI). Errors in the transmission may occur and the scheduling algorithm has to decide if the users sample a new packet or attempt for retransmission of the packet sampled previously. The cost consists of both sampling and transmission costs. The sampling of a new packet after a failure imposes an additional cost in the system. We formulate a stochastic optimization problem with time average cost in the objective under time average AoI constraints. To solve this problem, we apply tools from Lyapunov optimization theory and develop a dynamic algorithm that takes decisions in a slot-by-slot basis. The algorithm decides if a user: a) samples a new packet, b) transmits the old one, c) remains silent. We provide optimality guarantees of the algorithm and study its performance in terms of time average cost and AoI through simulation results., Comment: Accepted in IEEE INFOCOM Workshops

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 paper, we consider a transmission scheduling problem, in which several streams of status update packets with diverse priority levels are sent through a shared channel to their destinations. We introduce a notion of Lexicographic age optimality, or simply lex-age-optimality, to evaluate the performance of multi-class status update policies. In particular, a lex-age-optimal scheduling policy first minimizes the Age of Information (AoI) metrics for high-priority streams, and then, within the set of optimal policies for high-priority streams, achieves the minimum AoI metrics for low-priority streams. We propose a new scheduling policy named Preemptive Priority, Maximum Age First, Last-Generated, First-Served (PP-MAF-LGFS), and prove that the PP-MAF-LGFS scheduling policy is lex-age-optimal. This result holds (i) for minimizing any time-dependent, symmetric, and non-decreasing age penalty function; (ii) for minimizing any non-decreasing functional of the stochastic process formed by the age penalty function; and (iii) for the cases where different priority classes have distinct arrival traffic patterns, age penalty functions, and age penalty functionals. For example, the PP-MAF-LGFS scheduling policy is lex-age-optimal for minimizing the mean peak age of a high-priority stream and the time-average age of a low-priority stream. Numerical results are provided to illustrate our theoretical findings.

In this paper, we consider the average age minimization problem where a central entity schedules M users among the N available users for transmission over unreliable channels. It is well-known that obtaining the optimal policy, in this case, is out of reach. Accordingly, the Whittle's index policy has been suggested in earlier works as a heuristic for this problem. However, the analysis of its performance remained elusive. In the sequel, we overcome these difficulties and provide rigorous results on its asymptotic optimality in the many-users regime. Specifically, we first establish its optimality in the neighborhood of a specific system's state. Next, we extend our proof to the global case under a recurrence assumption, which we verify numerically. These findings showcase that the Whittle's index policy has analytically provable optimality in the many-users regime for the AoI minimization problem. Finally, numerical results that showcase its performance and corroborate our theoretical findings are presented.

In this paper, we introduce a new performance metric in the framework of status updates that we will refer to as the Age of Incorrect Information (AoII). This new metric deals with the shortcomings of both the Age of Information (AoI) and the conventional error penalty functions as it neatly extends the notion of fresh updates to that of fresh "informative" updates. The word informative in this context refers to updates that bring new and correct information to the monitor side. After properly motivating the new metric, and with the aim of minimizing its average, we formulate a Markov Decision Process (MDP) in a transmitter-receiver pair scenario where packets are sent over an unreliable channel. We show that a simple "always update" policy minimizes the aforementioned average penalty along with the average age and prediction error. We then tackle the general, and more realistic case, where the transmitter cannot surpass a specific power budget. The problem is formulated as a Constrained Markov Decision Process (CMDP) for which we provide a Lagrangian approach to solve. After characterizing the optimal transmission policy of the Lagrangian problem, we provide a rigorous mathematical proof to showcase that a mixture of two Lagrange policies is optimal for the CMDP in question. Equipped with this, we provide a low complexity algorithm that finds the AoII-optimal operating point of the system in the constrained scenario. Lastly, simulation results are laid out to showcase the performance of the proposed policy and highlight the differences with the AoI framework.

For the emerging Internet of Things (IoT), one of the most critical problems is the real-time reconstruction of signals from a set of aged measurements. During the reconstruction, distortion occurs between the observed signal and the reconstructed signal due to sampling and transmission. In this paper, we focus on minimizing the average distortion defined as the 1-norm of the difference of the two signals under the scenario that a Poisson counting process is reconstructed in real-time on a remote monitor. Especially, we consider the reconstruction under uniform sampling policy and two non-uniform sampling policies, i.e., the threshold-based policy and the zero-wait policy. For each of the policy, we derive the closed-form expression of the average distortion by dividing the overall distortion area into polygons and analyzing their structures. It turns out that the polygons are built up by sub-polygons that account for distortions caused by sampling and transmission. The closed-form expressions of the average distortion help us find the optimal sampling parameters that achieve the minimum distortion. Simulation results are provided to validate our conclusion.

In this paper, we consider N information streams sharing a common service facility. The streams are supposed to have different priorities based on their sensitivity. A higher priority stream will always preempt the service of a lower priority packet. By leveraging the notion of Stochastic Hybrid Systems (SHS), we investigate the Age of Information (AoI) in the case where each stream has its own waiting room; when preempted by a higher priority stream, the packet is stored in the waiting room for future resume. Interestingly, it will be shown that a "no waiting room" scenario, and consequently discarding preempted packets, is better in terms of average AoI in some cases. The exact cases where this happen are discussed and numerical results that corroborate the theoretical findings and highlight this trade-off are provided., Comment: arXiv admin note: text overlap with arXiv:1901.00481

In this paper, we examine the potentials of Non- Orthogonal Multiple Access (NOMA), currently rivaling Orthogonal Multiple Access (OMA) in 3rd Generation Partnership Project (3GPP) standardization for future 5G networks Machine Type Communications (MTC), in the framework of minimizing the average Age of Information (AoI). By leveraging the notion of Stochastic Hybrid Systems (SHS), we find the total average AoI of the network in simple NOMA and conventional OMA environments. Armed with this, we provide a comparison between the two schemes in terms of average AoI. Interestingly, it will be shown that even when NOMA achieves better spectral efficiency in comparison to OMA, this does not necessarily translates into a lower average AoI in the network.

In this paper, we investigate a network of N interfering links contending for the channel to send their data by employing the well-known Carrier Sense Multiple Access (CSMA) scheme. By leveraging the notion of stochastic hybrid systems, we find a closed form of the total average age of the network in this setting. Armed with this expression, we formulate the optimization problem of minimizing the total average age of the network by calibrating the back-off time of each link. By analyzing its structure, the optimization problem is then converted to an equivalent convex problem that can be solved efficiently to find the optimal back-off time of each link. Insights on the interaction between the links is provided and numerical implementations of our optimized CSMA scheme in an IEEE 802.11 environment is presented to highlight its performance. We also show that, although optimized, the standard CSMA scheme still lacks behind other distributed schemes in terms of average age in some special cases. These results suggest the necessity to find new distributed schemes to further minimize the average age of any general network.

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. 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., Comment: arXiv admin note: substantial text overlap with arXiv:1701.06927

We consider a system consisting of $N$ source nodes communicating with a common receiver. Each source node has a buffer of infinite capacity to store incoming bursty traffic in the form of status updates transmitted in packets, which should maintain the status information at the receiver fresh. Packets waiting for transmission can be discarded to avoid wasting network resources for the transmission of stale information. We investigate the age of information (AoI) performance of the system under scheduled and random access. Moreover, we present analysis of the AoI with and without packet management at the transmission queue of the source nodes, where as packet management we consider the capability to replace unserved packets at the queue whenever newer ones arrive. Finally, we provide simulation results that illustrate the impact of the network operating parameters on the age performance of the different access protocols.

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.

This paper is motivated by the observation that the average queueing delay can be decreased by sacrificing power efficiency in wireless communications. In this sense, we naturally wonder what is the minimum queueing delay when the available power is limited and how to achieve the minimum queueing delay. To answer these two questions in the scenario where randomly arriving packets are transmitted over multi-state wireless fading channel, a probabilistic cross-layer scheduling policy is proposed in this paper, and characterized by a constrained Markov Decision Process (MDP). Using the steady-state probability of the underlying Markov chain, we are able to derive the mathematical expressions of the concerned metrics, namely, the average queueing delay and the average power consumption. To describe the delay-power tradeoff, we formulate a non-linear programming problem, which, however, is very challenging to solve. By analyzing its structure, this optimization problem can be converted into an equivalent Linear Programming (LP) problem via variable substitution, which allows us to derive the optimal delay-power tradeoff as well as the optimal scheduling policy. The optimal scheduling policy turns out to be dual-threshold-based, which means transmission decisions should be made based on the optimal thresholds imposed on the queue length and the channel state.

We study the problem of \emph{jamming} in multiple independent \emph{Gaussian channels} as a zero-sum game. We show that in the unique Nash equilibrium of the game the best-response strategy of the transmitter is the \emph{waterfilling} to the sum of the jamming and the noise power in each channel and the best-response strategy of the jammer is the \emph{waterfilling} only to the noise power.

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 fulfils both timeliness and throughput requirements.

In this paper, we examine a system where status updates are generated by a source and are forwarded in a First-Come-First-Served (FCFS) manner to the monitor. We consider the case where the server has other tasks to fulfill, a simple example being relaying the packets of another stream. Due to the server's necessity to go on vacations, the age process of the stream of interest becomes complicated to evaluate. By leveraging specific queuing theory tools, we provide a closed form of the average age for both streams which enables us to optimize the generation rate of packets belonging to each stream to achieve the minimum possible average age. The tools used can be further adopted to provide insights on more general multi-hop scenarios. Numerical results are provided to corroborate the theoretical findings and highlight the interaction between the two streams., Comment: 7 figures

Carrier Sense Multiple Access (CSMA) is widely used as a Medium Access Control (MAC) in wireless networks due to its simplicity and distributed nature. This motivated researchers to find CSMA schemes that achieve throughput optimality. In 2008, it has been shown that a simple CSMA-type algorithm is able to achieve optimality in terms of throughput and has been given the name "adaptive" CSMA. Lately, new technologies emerged where prolonged battery life is crucial such as environment and industrial monitoring. This inspired the foundation of new CSMA based MAC schemes where links are allowed to transition into sleep mode to reduce the power consumption. However, throughput optimality of these schemes was not established. This paper therefore aims to find a new CSMA scheme that combines both throughput optimality and energy efficiency by adapting to the throughput and power consumption needs of each link. This is done by controlling operational parameters such as back-off and sleeping timers with the aim of optimizing a certain objective function. The resulting CSMA scheme is characterized by being asynchronous, completely distributed and being able to adapt to different power consumption profiles required by each link while still ensuring throughput optimality. The performance gain in terms of energy efficiency compared to the conventional adaptive CSMA scheme is demonstrated through computer simulations.

In this paper, we revisit the stability region of a cellular time division duplex (TDD) network. We characterize the queuing stability region of a network model that consists of two types of communications: (i) users communicating with the base station and (ii) users communicating with each other by passing through the base station. When a communication passes through the base station (BS) then a packet cannot be delivered to the destination UE until it is first received by the BS queue from the source UE. Due to the relaying functionality at the BS level, a coupling is created between the queues of the source users and the BS queues. In addition, contrarily to the majority of the existing works where an ON/OFF model of transmission is considered, we assume a link adaptation model (i.e. multiple rate model) where the bit rate of a link depends on its radio conditions. The coupling between the queues as well as the multiple rate model are the main challenges that highly increase the complexity of the stability region characterization. In this paper, we propose a simple approach that permits to overcome these challenges and to provide a full characterization of the exact stability region as a convex polytope with a finite number of vertices. An approximated model is proposed for reducing the computational complexity of the exact stability region. For the multi-user scenario, a trade-off is established between the complexity and the preciseness of the approximated stability region compared to the exact one. Furthermore, numerical results are presented to corroborate our claims., Comment: 55 pages one column document, 12 figures

In this work, we study the benefit of partial relay cooperation. We consider a two-node system consisting of one source and one relay node transmitting information to a common destination. The source and the relay have external traffic and in addition, the relay is equipped with a flow controller to regulate the incoming traffic from the source node. The cooperation is performed at the network level. A collision channel with erasures is considered. We provide an exact characterization of the stability region of the system and we also prove that the system with partial cooperation is always better or at least equal to the system without the flow controller., Comment: Submitted for journal publication. arXiv admin note: text overlap with arXiv:1502.01134

This paper considers the problem of power control in Massive MIMO systems taking into account the pilot contamination issue and the arrivals and departures of users in the network. Contrary to most of existing work in MIMO systems that focuses on the physical layer with fixed number of users, we consider in this work that the users arrive dynamically and leave the network once they are served. We provide a power control strategy, having a polynomial complexity, and prove that this policy stabilizes the network whenever possible. We then provide a distributed implementation of the power control policy requiring low information exchange between the BSs and show that it achieves the same stability region as the centralized policy., Comment: conference paper, submitted

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 the minimization of the average CoUD.

This paper characterizes the performance of interference alignment (IA) technique taking into account the dynamic traffic pattern and the probing/feedback cost. We consider a time-division duplex (TDD) system where transmitters acquire their channel state information (CSI) by decoding the pilot sequences sent by the receivers. Since global CSI knowledge is required for IA, the transmitters have also to exchange their estimated CSIs over a backhaul of limited capacity (i.e. imperfect case). Under this setting, we characterize in this paper the stability region of the system under both the imperfect and perfect (i.e. unlimited backhaul) cases, then we examine the gap between these two resulting regions. Further, under each case, we provide a centralized probing algorithm (policy) that achieves the max stability region. These stability regions and scheduling policies are given for the symmetric system where all the path loss coefficients are equal to each other, as well as for the general system. For the symmetric system, we compare the stability region of IA with the one achieved by a time division multiple access (TDMA) system where each transmitter applies a simple singular value decomposition technique (SVD). We then propose a scheduling policy that consists in switching between these two techniques, leading the system, under some conditions, to achieve a bigger stability region. Under the general system, the adopted scheduling policy is of a high computational complexity for moderate number of pairs, consequently we propose an approximate policy that has a reduced complexity but that achieves only a fraction of the system stability region. A characterization of this fraction is provided., Comment: 66 pages, 13 figures, 1 table, submitted to IEEE Transactions on Information Theory

In this paper we consider the two-user broadcast channel and we characterize its stable throughout 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 consider 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., Comment: Submitted for journal publication

We consider a communication system in which status updates arrive at a source node, and should be transmitted through a network to the intended destination node. The status updates are samples of a random process under observation, transmitted as packets, which also contain the time stamp to identify when the sample was generated. The age of the information available to the destination node is the time elapsed since the last received update was generated. In this paper, we model the source-destination link using queuing theory, and we assume that the time it takes to successfully transmit a packet to the destination is an exponentially distributed service time. We analyze the age of information in the case that the source node has the capability to manage the arriving samples, possibly discarding packets in order to avoid wasting network resources with the transmission of stale information. In addition to characterizing the average age, we propose a new metric, called peak age, which provides information about the maximum value of the age, achieved immediately before receiving an update., Comment: 20 pages, 7 figures

In this paper, the impact of energy constraints on a two-hop network with a source, a relay and a destination under random medium access is studied. A collision channel with erasures is considered, and the source and the relay nodes have energy harvesting capabilities and an unlimited battery to store the harvested energy. Additionally, the source and the relay node have external traffic arrivals and the relay forwards a fraction of the source node's traffic to the destination; the cooperation is performed at the network level. An inner and an outer bound of the stability region for a given transmission probability vector are obtained. Then, the closure of the inner and the outer bound is obtained separately and they turn out to be identical. This work is not only a step in connecting information theory and networking, by studying the maximum stable throughput region metric but also it taps the relatively unexplored and important domain of energy harvesting and assesses the effect of that on this important measure., Comment: 20 pages, 4 figures