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

Ahmad Hanbali (1)

1 School of Management and Governance, Department Operational Methods for Production and Logistics

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.

Mots clés: PH/PH/1/K queue; Phase-type distributions; Level dependent queues; Busy period; Transient analysis; Absorbing Markov chains; Matrix analytical approach; 60K25; 60J05; 68M20; 90B22

Domaines: Réseaux et télécommunications [cs.NI]

Ahmad Hanbali. Busy period analysis of the level dependent PH/PH/1/K queue. Queueing Systems, 2011, 67 (3), pp.221-249. ⟨10.1007/s11134-011-9213-6⟩. ⟨hal-00787342⟩