Abstract
This paper presents the transient behaviour of a finite Markovian queueing system with vacation in which the server may face problem of breakdowns while in service. The repair process does start immediately after a breakdown which immediately resumes the service. During this period any new customer is allowed to join the system. Whenever the server finds nobody, the server goes for a vacation and resumes service after N customers are accumulated. Meanwhile it triggers pre-service called start-up. Further, we considered two types of repair facilities for the broken-down server with an optional probability. The server first provides essential service to all customers and second optional service will be provided with a probability of “p”. The customer may renege in first phase of service. We adopted Runge-Kutta Method to find Transient state probabilities and computed various performance indices like expected length of system, the mean waiting time etc. We then performed the sensitivity analysis to explore the effect of different parameters.
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