Sankhya: The Indian Journal of Statistics

2000, Volume 62, Series B, Pt. 2, pp. 290--302

TRANSIENT SOLUTION FOR THE NUMBER OF BUSY SERVERS FOR THE DISCRETE-TIME QUEUE GEOMX/G/$\infty$

By

M.L. CHAUDHRY, Royal Military College of Canada

SUMMARY. Using probabilistic arguments, we derive the distribution of the number of busy servers at time k for the infinite-server discrete-time queue GeomX/G/$\infty$ in which arrivals are in groups of random size X, interarrival times are independently geometrically distributed and service times are independently generally distributed. Numerical and steady-state results as well as several other distributions and properties are discussed.

AMS (1991) subject classification. primary 60K25; secondary 68M20.

Key words and phrases. Distribution, infinite-server, Markov processes, queueing.

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