Response-time Approximations for Multi-server, Multi-class Production Systems with Significant Setups

A multi-server polling model is a queueing model where many order classes share a set of identical servers and a setup time is incurred whenever a server changes class. This paper develops approximations for the waiting time distribution in a multi-server polling model with cyclic serve-to-exhaustion service. These approximations are derived using previously established heavy-traac results and the assumption of signiicant setup times. They improve as the total setup over all classes increases. In a manufacturing environment, setups are only performed if there are orders waiting. We introduce the concept of positive-queue setups for the case where setups depend on the presence of orders, in contrast to the traditional polling model with empty-queue setups. The approximation is derived both for systems with empty-queue setups and systems with positive-queue setups. This study of polling models was motivated by a production scheduling problem at Raychem Corporation. The approximation formulas are tested by simulating polling models with parameter values characteristic of the Raychem setting as well as values arising from a second manufacturing setting.