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Markov-modulated single-server queueing systems

Part of: Markov processes Special processes

Published online by Cambridge University Press:  14 July 2016

N. U. Prabhu  and
L. C Tang
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Abstract

We consider single-server queueing systems that are modulated by a discrete-time Markov chain on a countable state space. The underlying stochastic process is a Markov random walk (MRW) whose increments can be expressed as differences between service times and interarrival times. We derive the joint distributions of the waiting and idle times in the presence of the modulating Markov chain. Our approach is based on properties of the ladder sets associated with this MRW and its time-reversed counterpart. The special case of a Markov-modulated M/M/1 queueing system is then analysed and results analogous to the classical case are obtained.

Keywords

MARKOV-MODULATED QUEUEING SYSTEMMARKOV RANDOM WALKSWAITING TIMEIDLE TIMETIMEREVERSIBILITY

MSC classification

Primary: 60J20: Applications of Markov chains and discrete-time Markov processes on general state spaces (social mobility, learning theory, industrial processes, etc.)
Secondary: 60K25: Queueing theory
Type
Part 3 Queueing Theory
Information
Journal of Applied Probability , Volume 31 , Issue A , 1994 , pp. 169 - 184
Copyright
Copyright © Applied Probability Trust 1994 

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