Preemptive Priority Markovian Queue Subject to Server Breakdown with Imperfect Coverage and Working Vacation Interruption

This work considers a preemptive priority queueing system with vacation, where the single server may break down imperfect coverage. Various combinations of vacation models have been studied by many scholars. A common assumption in these is that will only resume its normal service rate after over. However, such speculation more limited real-world situations. Hence, this study, be interrupted if customer waits for at moment completion during vacation. The stationary probability distribution derived using generating function approach. We also develop varieties performance measures and provide simple numerical example to illustrate measures. Optimization analysis finally carried out, including cost optimization tri-object optimization.