MARKOVIAN PHASE-TYPE SINGLE WORKING VACATION QUEUE WITH BREAKDOWN AND STANDBY SERVER.

We consider a single server queueing model with three service types, each with three phases, where customers arrive according to a Poisson process and the service time of each customer follows a Hyper-Erlang distribution. This study aims to analyze the impact of interruptions, such as breakdowns, repairs, and single working vacations, on the performance of the queueing system. The standby server activates whenever the main server experiences a breakdown. Using the matrix geometric method, we examine the steady-state probability vector of the model. Our results demonstrate the impact of these interruptions on system performance measures and provide a cost analysis. Finally, we present numerical examples to illustrate the practical applications of our findings in an image compression system. [ABSTRACT FROM AUTHOR]