Analysis of a queue with joining strategy and interruption repeat or resumption of service

Consider an $M/M/1$ queueing system with service interruption. If the server is busy at the arrival epoch, the arriving customer decides to join the queue with probability $q$ and balk with probability $1-q$. The service is assumed to get interrupted according to a Poisson process. The interrupted service is either resumed or restarted according to the realization of two competing independent, non-identically distributed random variables, the realization times of which follow exponential distributions. An arriving customer, finding the server under interruption does not join the system. We analyze the Nash equilibrium customers' joining strategies and give some numerical examples.