Complete analytic and computational analyses of the discrete-time bulk-arrival infinite-server system: GIX/Geom/∞

Authors:
M. L. Chaudhry;Jin D. Kim
Affiliations:
Department of Mathematics and Computer Science, Royal Military College of Canada, P.O. Box 17000, STN Forces, Kingston, Ont., Canada K7K 7B4;Department of Industrial Engineering, Korea Advanced Institute of Science and Technology, Taejon, 305-701, South Korea
Venue:
Computers and Operations Research
Year:
2004

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Abstract

In this paper, we consider the discrete-time queueing system with bulk arrivals, generally distributed inter-batch times, geometrically distributed service times, and infinite number of servers: the GIX/Geom/∞ queue. Under the assumptions of early arrival system (EAS) and late arrival system (LAS), we derive the system size distributions at two different epochs--prearrival and random. In addition, simple relations among the binomial moments of the steady-state system-size distributions of the two systems are derived. Special cases, such as the GIX/Geom/∞ or GI/D/∞ queues, are also presented. Some numerical results are included at the end.