Optimal Local Storage Policy Based on Stochastic Intensities and Its Large-Scale Behavior

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, and we characterize the optimal causal policy that maximizes the stationary hit probability. We then analyze a special case where the request processes come from a scale family and derive a suitable large-scale limit as the catalog size $N\to \infty$ when a fixed fraction c of items can be stored. In this limiting regime, the optimal policy amounts to comparing the stochastic intensity of the process with a fixed threshold, which is defined by a quantile of an appropriate limit distribution. We derive asymptotic performance metrics as well as sharp estimates for the prelimit case. Moreover, we establish a connection with optimal timer-based policies for renewal traffic and monotone hazard rates. We also present detailed validation examples of our results, including some closed-form expressions for the miss probability that are compared with simulations. We also use these examples to exhibit the significant superiority of the optimal policy for the case of regular traffic patterns.

Funding: This research was partially supported by the U.S. Air Force Office of Scientific Research [Grant FA9550-23-1-0350].