A Working Vacation Queue in Moscow that is Partially Broken Down and Whose Arrival Rate Depends on the Server State

Abstract

Consideration has been given to a single server Markovian queueing system that alternates between operating in regular busy state, repair state, and working vacation state. The system operates as a single server Markovian queue when it is busy. It operates once again as a single server Markovian queue with varying arrival and service rates when it is undergoing maintenance or vacation. The vacation time is negative exponential, and the vacation policy is multiple vacation policy. Furthermore, if a server malfunctions while being used, repairs are initiated right away. Two distinct negative exponential distributions are used to represent the breakdown and repair periods. The server provides the customer with service during the repair period at a rate that is negatively exponentially different from the service rate. Additionally, several interesting cases are given.