Sojourn time distributions in the queue defined by a general QBD process

Authors:
Toshihisa Ozawa
Affiliations:
Department of Business Administration, Komazawa University, Tokyo, Japan 154-8525
Venue:
Queueing Systems: Theory and Applications
Year:
2006

Citing 0
Cited 3

Queues where customers of one queue act as servers of the other queue

Queueing Systems: Theory and Applications
A matrix geometric representation for the queue length distribution of multitype semi-Markovian queues

Performance Evaluation
Asymptotics for the sojourn time distribution in the queue defined by a general QBD process with a countable phase space

Queueing Systems: Theory and Applications

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Abstract

We consider a general QBD process as defining a FIFO queue and obtain the stationary distribution of the sojourn time of a customer in that queue as a matrix exponential distribution, which is identical to a phase-type distribution under a certain condition. Since QBD processes include many queueing models where the arrival and service process are dependent, these results form a substantial generalization of analogous results reported in the literature for queues such as the PH/PH/c queue. We also discuss asymptotic properties of the sojourn time distribution through its matrix exponential form.