Optimal local storage policy based on stochastic intensities and its large scale behavior

TL;DR

This paper investigates the optimal local storage management policy using stochastic process tools, deriving a threshold-based policy for large-scale systems and validating its effectiveness through simulations.

Contribution

It introduces a rigorous framework for optimal local storage policies based on stochastic intensities and characterizes the large-scale limit behavior, including a threshold policy and performance estimates.

Findings

Optimal policy compares stochastic intensity to a threshold.

Asymptotic performance metrics are derived.

Optimal policy outperforms heuristic methods for regular traffic.

Abstract

In this paper, we analyze the optimal management of local memory systems, using the tools of stationary point processes. We provide a rigorous setting of the problem, building upon recent work, and characterize the optimal causal policy that maximizes the hit probability. We specialize the result for the case of renewal request processes and derive a suitable large scale limit as the catalog size N grows to infinity, when a fixed fraction c of items can be stored. We prove that in the limiting regime, the optimal policy amounts to comparing the stochastic intensity (observed hazard rate) of the process with a fixed threshold, defined by a quantile of an appropriate limit distribution, and derive asymptotic performance metrics, as well as sharp estimates for the pre-limit case. Moreover, we establish a connection with optimal timer based policies for the case of monotonic hazard rates. We also present detailed validation examples of our results, including some close form expressions for the miss probability that are compared to simulations. We also use these examples to exhibit the significant superiority of the optimal policy for the case of regular traffic patterns.