Efficient and Timely Memory Access

TL;DR

The paper addresses memory sampling in status updating systems, formulating an MDP to minimize the average client-age plus memory-sampling cost. It proves that the optimal policy is stationary and deterministic with a threshold on memory-age, derives an explicit optimal threshold $Y_0^*$ and the corresponding average cost $g$, and provides a lower bound that captures the influence of the sampling cost $c$ and update probability $p$. Through discounted-cost analysis and relative-value methods, it characterizes the optimal policy structure and confirms existence of a stationary average-cost optimal policy, supported by numerical evaluation. The results offer practical guidance for designing sampling strategies in shared-memory status updating systems, balancing timely updates against sampling overhead.

Abstract

This paper investigates the optimization of memory sampling in status updating systems, where source updates are published in shared memory, and reader process samples the memory for source updates by paying a sampling cost. We formulate a discrete-time decision problem to find a sampling policy that minimizes average cost comprising age at the client and the cost incurred due to sampling. We establish that an optimal policy is a stationary and deterministic threshold-type policy, and subsequently derive optimal threshold and the corresponding optimal average cost.

Figures (4)

• Figure 1: A writer updates memory based on the update received from source. A client requests the Reader process to read the source updates from the memory. The source update publication in the memory generates age process $x(t)$, and the update sampling by the Reader generates age process $y(t)$ at the client input.
• Figure 2: Plot of average cost $g_0(Y_0)$ as a function of threshold $Y_0$ with sampling cost $c=80$. Here, $\circ$ is the true optimal cost $g_0(Y_0^*)$, and $\times$ is the approximate optimal average cost $g_0(\tilde{Y}_0^*)$.
• Figure 3: Plot of optimal threshold $Y_0^*$ as a function of probability $p$ of source update publication in a slot, with a fixed sampling cost $c$.
• Figure 4: Comparison of optimal average cost $g$ and the corresponding lower bound (LB) as a function of probability $p$ of source update publication in a slot, with a fixed sampling cost $c$.

Theorems & Definitions (18)

• Proposition 1
• Proposition 2
• Proposition 3
• Proposition 4
• Proposition 5
• Proposition 6
• Lemma 1
• Theorem 1
• proof
• Lemma 2