Setups in Polling Models: Does it Make Sense to Set Up if No Work is
Waiting?
We compare two versions of a symmetric two-queue polling model
with switchover times and setup times. The SI version has
State-Independent setups, according to which the server sets up
at the polled queue whether or not work is waiting there; and the
SD version has State-Dependent setups, according to which the
server sets up only when work is waiting at the polled queue. Naive
intuition would lead one to believe that the SD version should
perform better than the SI version. We characterize the difference
in the expected waiting times in these two versions, and we uncover
some surprising facts. In particular, we show that, regardless of
the server utilization or the service-time distribution, the SD
version performs (i) the same as, (ii) worse than, or (iii) better
than its SI counterpart if the switchover and setup times
are, respectively, (i) both constants, (ii) variable
(i.e., nondeterministic) and constant, or (iii) constant and
variable. Only (iii) is consistent with naive intuition.