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On a tandem G-network with blocking

Gómez Corral, Antonio (2002) On a tandem G-network with blocking. Advances in Applied Probability, 34 (3). pp. 626-661. ISSN 0001-8678

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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 die 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.

Item Type:Article
Uncontrolled Keywords:Markovian arrival process; Markov renewal theory; phase-type distribution; tandem queue; negative arrival
Subjects:Sciences > Mathematics > Stochastic processes
ID Code:15641
Deposited On:15 Jun 2012 08:09
Last Modified:06 Feb 2014 10:28

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