WHEN DOES FORCED IDLE TIME IMPROVE PERFORMANCE IN POLLING MODELS

Sarkar and Zangwill (1991) showed by numerical examples that reduction in setup times can, surprisingly, actually increase work in process i n some cyclic production systems (that is, reduction in switchover tim es can increase waiting times in some polling models). We present, for polling models with exhaustive and gated service disciplines, some ex plicit formulas that provide additional insight and characterization o f this anomaly. More specifically, we show that, for both of these mod els, there exist simple formulas that define for each queue a critical value z of the mean total setup time z per cycle such that, if z < z , then the expected waiting time at that queue will be minimized if t he server is forced to idle for a constant length of time z - z every cycle; also, for the symmetric polling model, we give a simple explic it formula for the expected waiting time and the critical value z tha t minimizes it.