A.S.Yashkova and S.F.Yashkov
 

Distribution of the Virtual Sojourn Time in the M/G/1 Processor Sharing Queue

 

Processor sharing queuing systems are well-known and very attractive models in applied probability and modern applications of queueing theory. This paper continues the investigations of the M/G/1 queue with Egalitarian Processor Sharing (EPS) discipline. We give, in the form of triple transforms, the time-dependent distribution of virtual sojourn time of a job, arriving at time t with the service demand (length) u in this queueing system which is empty at initial instant t=0. Further we study main important special cases as the direct consequences of our general result. We show also how extend the main theorem to the case when the M/G/1—EPS queue is modified by having K ≥0 extra permanent jobs with infinite lengths.