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 GEOM^{X}/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
Geom^{X}/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.