Waiting time distribution in a class of discrete-time cyclic service multi-queue systems

A new approximate method is developed for finding the waiting and sojourn time distributions in a class of multi-queue systems served in cyclic order at discrete intervals. An immediate application for such a model is in communication networks where a number of different traffic sources compete to access a group of transmission channels operating under a time-slotted sharing policy. This system maps naturally onto a model in which the inter-visit time has a probability mass function of phase-type. We derive a set of matrix equations with easily tractable iterative procedures for their solution and controllable accuracy in their numerical evaluation. We then validate the analytical model against simulation and discuss the validity of the assumptions. This methodology can be extended to several other polling strategies.