Busy period analysis of the state dependent M/M/1/K queue

Authors:
Ahmad Al Hanbali;Onno Boxma
Affiliations:
EURANDOM and Department of Mathematics and Computer Science, Eindhoven University of Technology, The Netherlands;EURANDOM and Department of Mathematics and Computer Science, Eindhoven University of Technology, The Netherlands
Venue:
Operations Research Letters
Year:
2010

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Queueing Systems: Theory and Applications

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Abstract

In this paper, we study the transient behavior of a state dependent M/M/1/K queue during the busy period. We derive in closed-form the joint transform of the length of the busy period, the number of customers served during the busy period, and the number of losses during the busy period. For two special cases called the threshold policy and the static policy we determine simple expressions for their joint transform.