Waiting times in queueing networks with a single shared server

We study a queueing network with a single shared server that serves the queues in a cyclic order. External customers arrive at the queues according to independent Poisson processes. After completing service, a customer either leaves the system or is routed to another queue. This model is very generic and finds many applications in computer systems, communication networks, manufacturing systems, and robotics. Special cases of the introduced network include well-known polling models, tandem queues, systems with a waiting room, multi-stage models with parallel queues, and many others. The present research develops a novel unifying framework to find the waiting time distribution, which can be applied to a wide variety of models which lacked an analysis of the waiting time distribution until now. That is, we derive the waiting time distributions for stable systems as well as various asymptotic results (heavy traffic, light traffic, and infinite switch-over times) for systems with general renewal arrival processes. By interpolating between these asymptotic regimes, we develop simple closed-form approximations for the waiting time distribution for arbitrary loads. Keywords: queueing network, waiting times, heavy traffic, light traffic, approximation