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Abstract
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.
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