Busy period analysis of the level dependent PH/PH/1/K queue

Authors:
Ahmad Hanbali
Affiliations:
School of Management and Governance, Department Operational Methods for Production and Logistics, University of Twente, AE Enschede, The Netherlands 7500
Venue:
Queueing Systems: Theory and Applications
Year:
2011

Citing 3
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Abstract

In this paper, we study the transient behavior of a level dependent single server queuing system with a waiting room of finite size during the busy period. The focus is on the level dependent PH/PH/1/K queue. 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. We differentiate between two types of losses: the overflow losses that are due to a full queue and the losses due to an admission controller. For the M/PH/1/K, M/PH/1/K under a threshold policy, and PH/M/1/K queues, we determine simple expressions for their joint transforms.