Approximate performance analysis of generalized join the shortest queue routing

TL;DR

This paper develops a highly accurate approximation method for analyzing the performance of heterogeneous server systems with GJSQ routing, focusing on equilibrium distributions and job count statistics, and shows near-insensitivity to job-size distributions.

Contribution

It introduces a novel approximation approach for GJSQ systems, modeling each server as a state-dependent single queue, capturing server correlations effectively.

Findings

The approximation accurately predicts equilibrium distributions.

Performance metrics are nearly insensitive to job-size distribution.

Simulation confirms the effectiveness of the approximation method.

Abstract

In this paper we propose a highly accurate approximate performance analysis of a heterogeneous server system with a processor sharing service discipline and a general job-size distribution under a generalized join the shortest queue (GJSQ) routing protocol. The GJSQ routing protocol is a natural extension of the well-known join the shortest queue routing policy that takes into account the non-identical service rates in addition to the number of jobs at each server. The performance metrics that are of interest here are the equilibrium distribution and the mean and standard deviation of the number of jobs at each server. We show that the latter metrics are near-insensitive to the job-size distribution using simulation experiments. By applying a single queue approximation we model each server as a single server queue with a state-dependent arrival process, independent of other servers in the system, and derive the distribution of the number of jobs at the server. These state-dependent arrival rates are intended to capture the inherent correlation between servers in the original system and behave in a rather atypical way.