Loss probability in priority limited processing queueing system

Abstract

In this paper, a queueing system with a preemptive priority limited processor sharing system with some versions of the discipline is considered. The problem of lost probability is an important aspect for developing methods to improve efficiency and productivity of in modern communications system and computer networks. In the paper, the following conditions are considered. The total service rate depends on the number of jobs serviced simultaneously, and this number is limited. The service rate of simultaneously serviced jobs is the same. There are jobs of different priorities. If the maximum quantity of jobs are serviced simultaneously, and a new job arrives, then depending on the priorities of the arriving and serviced jobs, the arriving job can be lost or preempt a serviced job. Four versions of the service discipline are considered. Depending on the discipline version, an arriving job can preempt or not preempt a job of the same priority, and preempted job is lost or its service is resumed later. This paper develops an approach to compute the loss probability of a prescribed priority job for each version of the discipline.