# Relating Polling Models with Zero and Nonzero Switchover Times

We consider a system of *N* queues served by a single server in
cyclic order. Each queue has its own distinct Poisson arrival stream and its
own distinct general service-time distribution (asymmetric queues); and each
queue has its own distinct distribution of switchover time (the time
required for the server to travel from that queue to the next). We consider
two versions of this classical polling model: In the first, which we refer
to as the zero-switchover-times model, it is assumed that all switchover
times are zero and the server stops traveling whenever the system becomes
empty. In the second, which we refer to as the nonzero-switchover-times
model, it is assumed that the sum of all switchover times in a cycle is
nonzero and the server does not stop traveling when the system is empty.
After providing a new analysis for the zero-switchover-times model, we
obtain, for a host of service disciplines, transform results that completely
characterize the relationship between the waiting times in these two,
operationally-different, polling models. These results can be used to derive
simple relations that express (all) waiting-time moments in the
nonzero-switchover-times model in terms of those in the
zero-switchover-times model. Our results, therefore, generalize
corresponding results for the expected waiting times obtained recently by
Fuhrmann (1992) and Cooper, Niu, and Srinivasan (1992).