The authors 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). They consider two versions of this classical polling model: In the first, which the authors 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 they refer to as the nonzero-switchover-times model, it is assumed that the sum of all switchover times in a cyclic 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, the authors 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. The present results, therefore, generalize corresponding results for the expected waiting times obtained recently by Fuhrmann and Cooper, Niu, and Srinivasan.
