A class of equivalent idle-time-order-based routing policies for heterogeneous multi-server systems

TL;DR

This paper demonstrates that a broad class of idle-time-order-based routing policies in heterogeneous multi-server systems lead to identical steady state behavior, effectively simplifying the analysis by equating them to random routing.

Contribution

It introduces a class of idle-time-order-based routing policies and proves their steady state equivalence to random routing in heterogeneous multi-server systems.

Findings

All policies in the class result in the same steady state.

These policies are equivalent to the naive Random routing policy.

The result simplifies analysis of heterogeneous server systems.

Abstract

We consider an M/M/N/K/FCFS system (N>0, K>=N), where the servers operate at (possibly) heterogeneous service rates. In this situation, the steady state behavior depends on the routing policy that is used to select which idle server serves the next job in queue. We define a class of idle-time-order-based policies (including, for example, Longest Idle Server First (LISF)) and show that all policies in this class result in the same steady state behavior. In particular, they are all equivalent to the naive Random routing policy.