The Impact of Correlation on Queueing Systems

Abstract

In unobservable or ticket queues, customers have multiple opportunities to abandon the queue. Arriving customers can balk based on the queue length or renege due to the virtual waiting time. In all the current literature, the balking and reneging distributions are considered independent. Removing this assumption, we study the impact of dependent balking and reneging on the queue length and workload processes. We will show that increasing the correlation between balking and reneging increases congestion in the queue. Furthermore, we compare characteristics of the simulated queue processes to their heavy traffic approximations and find them to be largely accurate.