Advances in Applied Probability

On a tandem G-network with blocking

A. Gómez-Corral

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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.

Article information

Source
Adv. in Appl. Probab. Volume 34, Number 3 (2002), 626-661.

Dates
First available in Project Euclid: 3 October 2002

Permanent link to this document
http://projecteuclid.org/euclid.aap/1033662169

Digital Object Identifier
doi:10.1239/aap/1033662169

Zentralblatt MATH identifier
1020.60084

Mathematical Reviews number (MathSciNet)
MR1929601

Subjects
Primary: 60K25: Queueing theory [See also 68M20, 90B22]
Secondary: 60K20: Applications of Markov renewal processes (reliability, queueing networks, etc.) [See also 90Bxx] 68M20: Performance evaluation; queueing; scheduling [See also 60K25, 90Bxx] 90B22: Queues and service [See also 60K25, 68M20]

Keywords
Markovian arrival process Markov renewal theory phase-type distribution tandem queue disaster negative arrival

Citation

Gómez-Corral, A. On a tandem G-network with blocking. Adv. in Appl. Probab. 34 (2002), no. 3, 626--661. doi:10.1239/aap/1033662169. http://projecteuclid.org/euclid.aap/1033662169.


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