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On a tandem G-network with blocking

Part of: Special processes Computer system organization Operations research and management science

Published online by Cambridge University Press:  01 July 2016

A. Gómez-Corral
A. Gómez-Corral*
Affiliation:
Universidad Complutense de Madrid
*
∗ Postal address: Department of Statistics and Operations Research I, Faculty of Mathematics, Universidad Complutense de Madrid, 28040 Madrid, Spain. Email address: [email protected]
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Abstract

An important class of queueing networks is characterized by the following feature: in contrast with ordinary units, a disaster may remove all work from the network. Applications of such networks include computer networks with virus infection, migration processes with mass exodus and serial production lines with catastrophes. In this paper, we deal with a two-stage tandem queue with blocking operating under the presence of a secondary flow of disasters. The arrival flows of units and disasters are general Markovian arrival processes. Using spectral analysis, we determine the stationary distribution at departure epochs. That distribution enables us to derive the distribution of the number of units which leave the network at a disaster epoch. We calculate the stationary distribution at an arbitrary time and, finally, we give numerical results and graphs for certain probabilistic descriptors of the network.

Keywords

Markovian arrival processMarkov renewal theoryphase-type distributiontandem queuedisasternegative arrival

MSC classification

Primary: 60K25: Queueing theory
Secondary: 60K20: Applications of Markov renewal processes (reliability, queueing networks, etc.) 68M20: Performance evaluation; queueing; scheduling 90B22: Queues and service
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 34 , Issue 3 , September 2002 , pp. 626 - 661
Copyright
Copyright © Applied Probability Trust 2002 

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