Optimal Policies for Age and Distortion in a Discrete-Time Model

Abstract

We study a discrete-time model where each packet has a cost of not being sent -this cost might depend on the packet content.We study the tradeoff between the age and the cost where the sender is confined to packet-based strategies. The optimal tradeoff is found by an appropriate formulation of the problem as a Markov Decision Process (MDP). We show that the optimal tradeoff can be attained with finite-memory policies and we devise an efficient policy iteration algorithm to find these optimal policies. We further study a related problem where the transmitted packets are subject to erasures. We show that the optimal policies for our problem are also optimal for this new setup. Allowing coding across packets significantly extends the packet-based strategies.We show that when the packet payloads are small, the performance can be improved by coding.

Age-Optimal Causal Labeling of Memoryless Processes

“…The condition in (6) implies that if we alter s (K) (m, n) to l, the policy does not improve if C+ph(n+1, 0)+qh(0, n+1) ≥ ph(m+n+1, 0)+qh(m, n+1). Some calculation reveals that this condition is equivalent to (10) -at the bottom of this page.…”

“…In this case, one may ask (i) what and (ii) when to send with an aim to optimize AoI? Studying the first question may need classification of data according to their importance, which might be based on a distortion metric [4]- [6]; or one may resort to packet management techniques [7] in the absence of such metrics. The second question is addressed for example in [8]- [10], and in [11]- [16] when the throughput is limited due to energy constraints.…”

“…The second question is addressed for example in [8]- [10], and in [11]- [16] when the throughput is limited due to energy constraints. All of these studies assume a priori knowledge of the network dynamics, e.g., the data is known to be conveyed through a single-server queue [4], [5], or through a Multiple Access Channel [6], etc. In this work, we assume that the sender is oblivious of the network dynamics except the limit on the output data rate.…”

Timely updates in MEC-assisted status update systems: Joint task generation and computation offloading scheme

“…It is well known that age of information (AoI) [1] is considered to capture the core notion of timeliness, and it has been widely used in communication systems. Related works include [2]- [10]. The optimal sampling policy for generateat-will sources have been investigated in [2] and [3] without involving coding.…”

“…Furthermore, the tradeoff between freshness and distortion is considered in [9] from the remote estimation perspective. In [10], an age-distortion tradeoff has been discussed, where the distortion quantifies the importance of data.…”