A Single Server Queue with Gated Processor Sharing Discipline

In this paper we consider a single server queue in which arrivals occur according to a Poisson process and each customer's service time is exponentially distributed. The server works according to the gated process-sharing d discipline. In this discipline, the server provides service to a batch of at most m customers at a time. Once a batch of customers begins service, no other waiting customer can receive service until all members of the batch have completed their service. For this queue, we derive performance characteristics, such as waiting time distribution, queue length distribution etc. For this queue, it is possible to obtain the mean conditional response time for a customer whose service time is known. This conditional response time is a nonlinear function (as opposed to the linear case for the ordinary processor- sharing queue). A special case of the queue (where m = proportional to) has an interesting and unusual solution. For this special case, the size of the batch for service is a Markov chain whose steady state distribution can be explicitly written down and it is closely related to the Lambert series. Apart from the contribution to the theory of Markov chains and queues, the model may be applicable to scheduling of computer and communications systems.