On a vacation queue with two parallel severs each equipped with a stand-by

Abstract

The paper studies an M/M/2 queueing system in which each server is equipped with a stand-by. The stand-by are employed only during the vacation períods of main severs. The vacation periods of the two severs are aasumed to be independent with an identical exponential distribution. The time dependent results giving probability generating functions for the number in the system under various states have been obtained and in a particular case a known result has been derived at. The corresponding steady state results are also derived.