Analysis of single server repairable queueing system with many kinds of service, single working vacation and standby server

We consider a single server queueing model in which the customers arrive according to a Markovian Arrival Process (MAP). We modeled this queueing system with many kinds of service where the customers can choose any kind from the server. Each kind of service follows Phase-type (PH) distribution. We analyzed the model with breakdown, repair, single working vacation and standby server. A standby server works only when the main server is breakdown while serving the customer during a busy or vacation period. Using the matrix-geometric approach, we examined the model. A few real-world examples have been given, and several graphical and numerical examples have also been provided.