ON A M^[X]/G/1 QUEUEING SYSTEM WITH GENERALIZED COXIAN-2 SERVICE AND OPTIONAL GENERALIZED COXIAN-2 VACATION

Abstract

We study the steady state behaviour of a batch arrival single server queue in which the first service with general service times G1 is compulsory and the second service with general service times G2 is optional. We term such a two phase service as generalized Coxian-2 service. Just after completion of a service the server may take a vacation of random length of time with general vacation times V1. After completion of the first phase of vacation the server may or may not take the second optional vacation with general vacation times V2. We term this two phase vacation as optional generalized Coxian-2 sever vacation. We obtain steady state probability generating functions for the queue size at a random epoch of time in explicit and closed forms. Some particular cases of interest including some known results have been derived.