Conditional Waiting Time Analysis in Tandem Polling Queues

Abstract

We analyze a tandem network of polling queues with two product types and two stations. We assume that external arrivals to the network follow a Poisson process, and service times at each station are exponentially distributed. For this system, we determine the mean conditional waiting time for an arriving customer using a sample path analysis approach. The approach classifies system state upon arrival into scenarios and exploits an inherent structure in the sequence of events that occur till the customer departs to obtain conditional waiting time estimates. We conduct numerical studies to show both the accuracy of our conditional waiting time estimates and their practical importance.