SOOCHOW JOURNAL OF MATHEMATICS

Volume 31, No. 1, pp. 21-29, January 2005




SOME ASPECTS OF AN $ M^x/G/1$ QUEUE WITH TWO

DIFFERENT VACATION PERIODS UNDER MULTIPLE

VACATION POLICY$ ^*$


BY


GAUTAM CHOUDHURY



Abstract. This paper deals with the steady state behaviour of an $ M^x/G/1$ queuing system with two different vacation periods under multiple vacation policy, where length of the first vacation is different from the rest of the vacations. We are concerned with the distribution of the queue size at busy period initiation epoch and distribution of the unfinished work. Further, we present a simple transform free method to obtain the mean waiting time for this model.

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Received November 14, 2002; revised September 2, 2004.

AMS Subject Classification. 60K25, 90B22.

Key words. $ M^x/G/1$ queue, vacation time, unfinished work, waiting time.

$ ^*$This work is being supported by Department of Atomic Energy, Govt. of India, through NBHM, Project No.:- 48/2/2001/R & DII/1211, India.