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Transient behaviour of queueing networks

Published online by Cambridge University Press:  14 July 2016

P. G. Harrison
P. G. Harrison*
Affiliation:
Imperial College, London
*
∗Postal address: Department of Computing, Imperial College of Science and Technology, 180 Queen's Gate, London SW7 2BZ.
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Abstract

In most contemporary queueing network analysis, the assumption is made that a network is in a state of equilibrium. That is, the network's state space probabilities are assumed to be time independent. It is therefore important to be able to quantify precisely when this assumption is valid. Furthermore there are also situations in which it is desirable to model the transient behaviour of networks which occur in practice, such as computer and communication systems. For example, the immediate effects of component failure or instantaneous alteration of system status may be predicted.

In this paper an iterative solution is derived to the time-dependent Kolmogorov equations of queueing networks, and is shown to be convergent. From the solution, modelling of transient situations becomes possible and the time periods during which the equilibrium assumption can and should not be made may be identified; for example in terms of a time constant which is easily computed to a first-order approximation.

Keywords

MARKOV PROCESSESMODELLINGQUEUEING NETWORKSTIME-DEPENDENT SOLUTIONSTRANSIENTS
Type
Research Papers
Information
Journal of Applied Probability , Volume 18 , Issue 2 , June 1981 , pp. 482 - 490
Copyright
Copyright © Applied Probability Trust 

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References

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