Transient Analysis of Differentiated Breakdown Model

The single server queueing system is investigated. When the system is idle or while serving a customer, it fails at random. System failure is classified into two types: hard failure and soft failure. Hard failure usually necessitates the repairman's physical presence and takes a long time. Soft...

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Bibliographic Details
Published inApplied mathematics and computation Vol. 417; p. 126779
Main Author Janani, B.
Format Journal Article
LanguageEnglish
Published Elsevier Inc 15.03.2022
Subjects
Differentiated random vacation
Hard failure
Repair
Soft failure
Transient state probabilities
Transient state probabilities
Differentiated random vacation
Hard failure
Repair
Soft failure
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Summary:The single server queueing system is investigated. When the system is idle or while serving a customer, it fails at random. System failure is classified into two types: hard failure and soft failure. Hard failure usually necessitates the repairman's physical presence and takes a long time. Soft failure, on the other hand, takes less time because the system can be restored to operation by simply rebooting it. When the system is being repaired, the server is forced to take a vacation and the repair process begins immediately. The model's transient state probabilities are derived and using the final value theorem of the Laplace transform, steady state probabilities are derived from transient state probabilities. Finally, numerical illustrations are provided to demonstrate the system's behaviour as the parameters' values are varied.
ISSN:0096-3003
1873-5649
DOI:10.1016/j.amc.2021.126779