# An approximation for the mean response time for shortest queue routing with general interarrival and service times

## Abstract

In this paper we derive an approximation for the mean respone time of a multiple queue system in which shortest queue routing is used. We assume there are K identical queues with infinite capacity. Interarrival and service times are generally distributed, and an arriving job is routed to a queue of minimal length. Our approximation is a simple closed form equation that requires only the mean and coefficient of variation of job's interarrival and service times. The approximation is extensively compared to simulated values for values of K ≤ 8, and has small relative errors, typically less than 5%, for systems where the coefficient of variation of interarrival and serivce times are both ≤ 1. For the system consisting of Poisson arrivals and exponential service times, we extend the approximation so that the error is less than one half of one percent for K ≤ 8. © 1993.