Introduction to shape stability for a storage model

TL;DR

This paper introduces a new concept called shape stability for a storage model on multiple nodes, demonstrating conditions under which the system remains stable using simple local policies.

Contribution

It proposes a novel shape stability framework for storage models and identifies local policies that ensure positive recurrence of the system.

Findings

Conditions for stability under natural assumptions on arrival rates

Simple local policies can guarantee shape stability

The model's multidimensional process is positive recurrent under these policies

Abstract

We consider a new idea for a storage model on n nodes, namely stability of shape. These nodes support K neighborhoods S_i \subset {1, ..., n} and items arrive at the S_i as independent Poisson streams with rates lambda_i, i=1, ...,K. Upon arrival at S_i an item is stored at node j \in S_i where j is determined by some policy. Under natural conditions on the lambda_i we exhibit simple local policies such that the multidimensional process describing the evolution of the number of items at each node is positive recurrent (stable) in shape.