AN M/G/1 QUEUE WITH BERNOULLI SCHEDULES AND COXIAN-2 SERVER VACATIONS

摘要

We study the time-dependent and the steady state behaviour of an M/G/1 queue with Bernoulli schedules and Coxian-2 server vacations. Customers arrive one by one at the system in a Poisson stream. The service time of a customer is assumed to be general (arbitrary). At each service completion epoch, the server may opt to take a vacation with probability p or else may continue to be available in the system. The vacation period of the server is assumed to have a Coxian-2 distribution. We obtain time-dependent probability generating functions for the queue size and the system size. The corresponding steady stale results including the stability condition have been derived in explicit and closed forms. Some particular cases of interest including known results of the M/G/1 queue have been derived.