Approximations for the waiting time distribution in polling models with and without state-dependent setups

A polling model is a queueing model where many job classes share a single s erver and a setup time is incurred whenever the server changes class. Polli ng models are applicable to many computing, telecommunications, and manufac turing environments. The scheduling method considered in this paper is a co mmon policy known as cyclic, serve to exhaustion (CSE). Recently, Coffman, Puhalskii and Reiman (CPR) have developed a heavy-traffic approximation for the waiting time distribution in a CSE polling model. This paper presents three new approximations. Firstly, the CPR approximatio n and the traditional (non-heavy-traffic) polling model literature are comb ined to obtain a refinement of the CPR approximation. This refinement is mu ch more accurate under conditions of moderate loading. Next, an approximati on is made for the distribution of the number of jobs present in a queue up on it being polled. Lastly. the previous two approximations are combined to form an approximation for the waiting time distribution when setups are no t performed for queues containing no jobs. A simulation study is undertaken to evaluate these three approximations. (C) 2001 Elsevier Science B.V. All rights reserved.