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.
We consider a class of restless multi-armed bandit problems (RMBP) that arises in dynamic multichannel access, user/server scheduling, and optimal activation in multi-agent systems. For this class of RMBP, we establish the indexability and obtain Whittle's index in closed-form for both discounted and average reward criteria. These results lead to a direct implementation of Whittle's index policy with remarkably low complexity. When these Markov chains are stochastically identical, we show that Whittle's index policy is optimal under certain conditions. Furthermore, it has a semi-universal stru…
This paper examines the average age minimization problem where only a fraction of the network users can transmit simultaneously over unreliable channels. Finding the optimal scheduling scheme, in this case, is known to be challenging. Accordingly, the Whittle's index policy was proposed in the literature as a low-complexity heuristic to the problem. Although simple to implement, characterizing this policy's performance is recognized to be a notoriously tricky task. In the sequel, we provide a new mathematical approach to establish its optimality in the many-users regime for specific network se…
We design a new scheduling policy to minimize the general non-decreasing cost function of age of information (AoI) in a multiuser system. In this system, the base station stochastically generates time-sensitive packets and transmits them to corresponding user equipments via an unreliable channel. We first formulate the transmission scheduling problem as an average cost constrained Markov decision process problem. Through introducing the service charge, we derive the closed-form expression for the Whittle index, based on which we design the scheduling policy. Using numerical results, we demonst…
Age of information is a new concept that characterizes the freshness of information at end devices. This paper studies the age of information from a scheduling perspective. We consider a wireless broadcast network where a base-station updates many users on stochastic information arrivals. Suppose that only one user can be updated for each time. In this context, we aim at developing a transmission scheduling algorithm for minimizing the long-run average age. To develop a low-complexity transmission scheduling algorithm, we apply the Whittle's framework for restless bandits. We successfully deri…
We investigate the coexistence of task-oriented and data-oriented communications in a IoT system that shares a group of channels, and study the scheduling problem to jointly optimize the weighted age of incorrect information (AoII) and throughput, which are the performance metrics of the two types of communications, respectively. This problem is formulated as a Markov decision problem, which is difficult to solve due to the large discrete action space and the time-varying action constraints induced by the stochastic availability of channels. By exploiting the intrinsic properties of this probl…
The age of Incorrect Information (AoII) has been introduced recently to address the shortcomings of the standard Age of information metric (AoI) in real-time monitoring applications. In this paper, we consider the problem of monitoring the states of remote sources that evolve according to a Markovian Process. A central scheduler selects at each time slot which sources should send their updates in such a way to minimize the Mean Age of Incorrect Information (MAoII). The difficulty of the problem lies in the fact that the scheduler cannot know the states of the sources before receiving the updat…
We consider a wireless broadcast network with a base station sending time-sensitive information to a number of clients through unreliable channels. The Age of Information (AoI), namely the amount of time that elapsed since the most recently delivered packet was generated, captures the freshness of the information. We formulate a discrete-time decision problem to find a transmission scheduling policy that minimizes the expected weighted sum AoI of the clients in the network. We first show that in symmetric networks a Greedy policy, which transmits the packet with highest current age, is optimal…
We propose a variant of the Age of Information (AoI) metric called Channel-Aware Age of Information (CA-AoI). Unlike AoI, CA-AoI takes into account the channel conditions between the source and the intended destination to compute the "age" of the recent most update received by the destination. This new metric ensures that the resource allocation is not heavily tilted towards the sources with poor channel conditions. We design scheduling policies for multi-sensor systems in which sensors report their measurements to a central monitoring station via a shared unreliable communication channel with…
Age of information is a new network performance metric that captures the freshness of information at end-users. This paper studies the age of information from a scheduling perspective. To that end, we consider a wireless broadcast network where a base-station (BS) is updating many users on random information arrivals under a transmission capacity constraint. For the offline case when the arrival statistics are known to the BS, we develop a structural MDP scheduling algorithm and an index scheduling algorithm, leveraging Markov decision process (MDP) techniques and the Whittle's methodology for…
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-priori…
In this paper, we investigate scheduling policies that minimize the age of information in single-hop queueing systems. We propose a Last-Generated, First-Serve (LGFS) scheduling policy, in which the packet with the earliest generation time is processed with the highest priority. If the service times are i.i.d. exponentially distributed, the preemptive LGFS policy is proven to be age-optimal in a stochastic ordering sense. If the service times are i.i.d. and satisfy a New-Better-than-Used (NBU) distributional property, the non-preemptive LGFS policy is shown to be within a constant gap from the…
In a heterogeneous unreliable multiaccess network, wherein terminals share a common wireless channel with distinctive error probabilities, existing works have showed that a persistent round-robin (RR-P) scheduling policy (i.e., greedy policy) can be arbitrarily worse than the optimum in terms of Age of Information (AoI) under standard Automatic Repeat reQuest (ARQ), and one must resort to Whittle's index approach for optimal AoI. In this paper, practical Hybrid ARQ (HARQ) schemes which are widely-used in today's wireless networks are considered. We show that RR-P is very close to optimum with …
In the multiuser downlink, power allocation for linear precoders that minimize the sum of mean squared errors under a sum power constraint is a non-convex problem. Many existing algorithms solve an equivalent convex problem in the virtual uplink and apply a transformation based on uplink-downlink duality to find a downlink solution. In this letter, we analyze the optimality criteria for the power allocation subproblem in the virtual uplink, and demonstrate that the optimal solution leads to identical power allocations in the downlink and virtual uplink. We thus extend the known duality results…
In network communications, information transmission often encounters wiretapping attacks. Secure network coding is introduced to prevent information from being leaked to adversaries. The investigation of performance bounds on the numbers of source symbols and random symbols are two fundamental research problems. For an important case that each wiretap-set with cardinality not larger than $r$, Cai and Yeung proposed a coding scheme, which is optimal in the senses of maximizing the number of source symbols and at the same time minimizing the number of random symbols. In this letter, we further s…
The problem of minimizing convex functionals of probability distributions is solved under the assumption that the density of every distribution is bounded from above and below. A system of sufficient and necessary first-order optimality conditions as well as a bound on the optimality gap of feasible candidate solutions are derived. Based on these results, two numerical algorithms are proposed that iteratively solve the system of optimality conditions on a grid of discrete points. Both algorithms use a block coordinate descent strategy and terminate once the optimality gap falls below the desir…
Age-of-Information (AoI) is a recently proposed metric for quantifying the freshness of information from the UE's perspective in a communication network. Recently, Kadota et al. [1] have proposed an index-type approximately optimal scheduling policy for minimizing the average-AoI metric for a downlink transmission problem. For delay-sensitive applications, including real-time control of a cyber-physical system, or scheduling URLLC traffic in 5G, it is essential to have a more stringent uniform control on AoI across all users. In this paper, we derive an exactly optimal scheduling policy for th…
Set partitioning is a key component of many algorithms in machine learning, signal processing, and communications. In general, the problem of finding a partition that minimizes a given impurity (loss function) is NP-hard. As such, there exists a wealth of literature on approximate algorithms and theoretical analyses of the partitioning problem under different settings. In this paper, we formulate and solve a variant of the partition problem called the minimum impurity partition under constraint (MIPUC). MIPUC finds an optimal partition that minimizes a given loss function under a given concave…
