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We study a queueing network with a single shared server that serves thequeues in a cyclic order. External customers arrive at the queues according toindependent Poisson processes. After completing service, a customer eitherleaves the system or is routed to another queue. This model is very generic andfinds many applications in computer systems, communication networks,manufacturing systems, and robotics. Special cases of the introduced networkinclude well-known polling models, tandem queues, systems with a waiting room,multi-stage models with parallel queues, and many others. A complicating factorof this model is that the internally rerouted customers do not arrive at thevarious queues according to a Poisson process, causing standard techniques tofind waiting-time distributions to fail. In this paper we develop a new methodto obtain exact expressions for the Laplace-Stieltjes transforms of thesteady-state waiting-time distributions. This method can be applied to a widevariety of models which lacked an analysis of the waiting-time distributionuntil now.

Waiting times in queueing networks with a single shared server