On the relationships among queue lengths at arrival, departure, and random epochs in the discrete-time queue with D-BMAP arrivals

Authors:
Nam K. Kim;Seok H. Chang;Kyung C. Chae
Affiliations:
Department of Industrial Engineering, Korea Advanced Institute of Science and Technology, Daejon 305-701, South Korea;Department of Industrial Engineering, Korea Advanced Institute of Science and Technology, Daejon 305-701, South Korea;Department of Industrial Engineering, Korea Advanced Institute of Science and Technology, Daejon 305-701, South Korea
Venue:
Operations Research Letters
Year:
2002

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Abstract

We consider finite- and infinite-capacity queues with discrete-time batch Markovian arrival processes (D-BMAP) under the assumption of the Late Arrival System with Delayed Access as well as the Early Arrival System. Using simple arguments such as the balance equation, ''rate in=rate out'', we derive relationships among the stationary queue lengths at arrival, at departure, and at random epochs. Such relationships hold for a broad class of discrete-time queues with D-BMAP arrivals.