RELATING POLLING MODELS WITH ZERO AND NONZERO SWITCHOVER TIMES

We consider a system of N queues served by a single server in cyclic o rder. Each queue has its own distinct Poisson arrival stream and its o wn 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). W e consider two versions of this classical polling model: In the first, which we refer to as the zero-switchover-times model, it is assumed t hat all switchover times are zero and the server Stops traveling whene ver 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 swit chover times in a cycle is nonzero and the server does not stop travel ing when the system is empty. After providing a new analysis for the z ero-switchover-times model, we, obtain, for a host of service discipli nes, transform results that completely characterize the relationship b etween the waiting times in these two, operationally-different, pollin g models. These results can be used to derive simple relations that ex press (all) waiting-time moments in the nonzero-switchover-times model in terms of those in the zero-switchover-times model. Our results, th erefore, generalize corresponding results for the expected waiting tim es obtained recently by Fuhrmann [Queueing Systems 11 (1992) 109-120] and Cooper, Niu, and Srinivasan [to appear in Oper. Res.].