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

In this paper, we study the transient behavior of a level dependent PH/PH/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. We differentiate between two types of losses: the over°ow 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 transform