We study cyclic polling models with exhaustive service at each queue under a variety of non-FCFS local service orders, namely Last-Come-First-Served (LCFS) with and without preemption, Random-Order-of-Service (ROS), Processor Sharing (PS), the multi-class priority scheduling with and without preemption, Shortest-Job-First (SJF) and the Shortest Remaining Processing Time (SRPT) policy. For each of these policies, we rst express the waiting-time distributions in terms of intervisit-time distributions. Next, we use these expressions to derive the asymptotic waiting-time distributions under heavy-trac assumptions, i.e., when the system tends to saturate. The results show that in all cases the asymptotic waiting-time distribution at queue i is fully characterized and of the form
Polling system, service discipline, waiting-time distribution, heavy traffic
Queueing theory (msc 60K25)
Logistics (theme 3)
CWI
Stochastics [ST]
Stochastics

Vis, P, Bekker, R, & van der Mei, R.D. (2014). Heavy-traffic limits for Polling Models with Exhaustive Service and non-FCFS Service Order Policies. Stochastics [ST]. CWI.