# 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 in some cyclic production systems (that is, reduction in switchover
times can increase waiting times in some polling models). We present,
for polling models with exhaustive and gated
service disciplines, some explicit formulas that provide additional insight
and characterization of this anomaly. More specifically, we show that, for
both of these models, 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 the 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 explicit formula for the expected waiting time.