Performance analysis of M/M/1 queue with working vacation, N-policy and customer impatience in transient mode

This paper deals with the Markovian queueing system with working vacation in which the server may encounter with breakdowns. The repair process does start immediately after a breakdown. During this period any new customer is allowed to join the system. Whenever the server finds nobody, the server goes for a working vacation during which the server renders service at a slower rate than the normal. Further, we considered two types of customer's impatience Balking and Reneging. We solved the system of differential equations 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 and observed the impact on different parameters.