Sankhya: The Indian Journal of Statistics

2002, Volume 64, Series B, Pt. 1, 37--49

ANALYSIS OF THE MX/G/1 QUEUEING SYSTEM WITH VACATION TIMES

By

GAUTAM CHOUDHURY, Institute of Advanced Study in Science and Technology, Guwahati, Assam, India

SUMMARY. We consider an MX/G/1 quening system, where batches of customers are assumed to arrive the system according to a compound Poisson process. As soon as the system becomes empty, the server takes a vacation for a random length of time called vacation time to do other jobs, which is uninterruptible. After returning from that vacation, there are two possibilities viz. (i) he keeps on taking vacations till he finds at least one unit in the queue (multiple vacations) or (ii) he may take only one vacation between two successive busy periods (single vacation). The steady state behaviour of this MX/G/1 queueing system is derived by an analytic approach to study the queue size distribution at a stationary (random) as well as a departure point of time under multiple vacation policy. Also, attempts have been made to obtain the queue size distribution of a more generalized model at a departure point to cover both the cases multiple and single vacations.

AMS (1991) subject classification. Primary 60K25; secondary 60J15.

Key words and phrases. MX/G/1 queue, queue size, multiple vacation and single vacation.

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