On G / G / 1 Queues with Lifo - P Service Discipline

J. George Shanthikumar University of California Berkeley Ushio Sumita University of Rochester (Received September 25,1985: Revised March 27,1986) We consider a single server queueing system G/G/l having general interarrival times (not necessarily i.i.d), i.i.d. service times, and LIFO-P (preemptive last in first out, but not restricted to resumption) service disciplines. Furthermore a customer finding n other customers in system upon his arrival joins the system with probability pen) and immediately leaves the system with probability 1 pen), where 0 ::;'p(n)::;' 1. The relations among various ergodic probabilities of the number of customers in system are established via sample path arguments. Sufficient conditions are given for the customer average ergodic probability distribution to be geometric, thereby extending recent results of Fakinos (1981) and Yamazaki(1982, 1984).