Transient behavior of a two-processor heterogeneous system with catastrophes, server failures and repairs

In this paper, the transient behavior dealing with a two-processor heterogeneous system with catastrophes, server failures and repairs is investigated, where tasks arrive according to a Poisson process and execution times are exponentially distributed. Each task requires exactly one processor for it...

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Bibliographic Details
Published inApplied mathematical modelling Vol. 38; no. 7-8; pp. 2224 - 2234
Main Author Ammar, Sherif I.
Format Journal Article
LanguageEnglish
Published Elsevier Inc 01.04.2014
Subjects
Catastrophes
Catastrophic failure analysis
Failure
Generating function
Maintenance
Mathematical analysis
Mathematical models
Multiprocessor systems
Repairing
Server failures
Servers
Tasks
Transient analysis
Catastrophes
Server failures
Generating function
Transient analysis
Multiprocessor systems
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ISSN0307-904X
DOI10.1016/j.apm.2013.10.033

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Summary:In this paper, the transient behavior dealing with a two-processor heterogeneous system with catastrophes, server failures and repairs is investigated, where tasks arrive according to a Poisson process and execution times are exponentially distributed. Each task requires exactly one processor for its execution and the scheduling policy is FCFS. For this model, the exact time dependent solutions of system size probabilities are obtained using the generating function technique. An explicit expression is also found for the time dependent mean and variance of the system size distribution .Moreover, the current system may be regarded as an extension to some previous studies such as that Dharmaraja [4]. Finally, numerical illustrations are used to discuss the system behavior.
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ISSN:0307-904X
DOI:10.1016/j.apm.2013.10.033