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 server and a setup time is incurred whenever the server changes class. Polling models are applicable to many computing, telecommunications, and manufacturing environments. The scheduling method considered in this paper is a common 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 approximation and the traditional (non-heavy-traffic) polling model literature are combined to obtain a refinement of the CPR approximation. This refinement is much more accurate under conditions of moderate loading. Next, an approximation is made for the distribution of the number of jobs present in a queue upon it being polled. Lastly, the previous two approximations are combined to form an approximation for the waiting time distribution when setups are not performed for queues containing no jobs. A simulation study is undertaken to evaluate these three approximations.