Storage Allocation Under Processor Sharing II: Further Asymptotic Results

TL;DR

This paper analyzes the asymptotic behavior of a processor sharing storage model with primary and secondary spaces, focusing on the joint distribution of occupied spaces under large system limits and near-critical traffic conditions.

Contribution

It extends previous work by deriving further asymptotic results for the joint distribution in large-scale and high-traffic regimes of the storage allocation model.

Findings

Asymptotic distribution for large number of primary spaces with fixed traffic

Behavior of the system as traffic intensity approaches capacity in large systems

Quantitative descriptions of storage occupancy in different asymptotic regimes

Abstract

We consider a processor sharing storage allocation model, which has m primary holding spaces and infinitely many secondary ones, and a single processor servicing the stored items (customers). All of the spaces are numbered and ordered. An arriving customer takes the lowest available space. We define the traffic intensity rho to be lambda/mu where lambda is the customers' arrival rate and mu is the service rate of the processor. We study the joint probability distribution of the numbers of occupied primary and secondary spaces. We study the problem in two asymptotic limits: (1) m -> infinity with a fixed rho <1, and (2) rho -> 1, m -> infinity with m(1-rho)= O(1).