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

Ahmad Al Hanbali

Research output: Contribution to journalArticleAcademicpeer-review

12 Citations (Scopus)
53 Downloads (Pure)


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.
Original languageEnglish
Pages (from-to)221-249
JournalQueueing systems
Issue number3
Publication statusPublished - 2011


  • PH/PH/1/K queue – Phase-type distributions – Level dependent queues – Busy period – Transient analysis – Absorbing Markov chains – Matrix analytical approach
  • METIS-275144
  • IR-76968


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