Steady state analysis of M/G/1 retrial queue with vacation and server timeout using a Petri net formalism

: In this paper, we analyse an M / G /1 retrial queue with vacation and server timeout. When the system is empty, the server waits for a random time. At the expiration of this time, if there is no arrival to the system, the server takes a vacation. If there is at least one customer in the system, the server commences service. So, we propose an unbounded Markov regenerative stochastic Petri net ( MRSPN ) to model this queueing system. For the qualitative analysis of this model, we combine the Markov regenerative approach and the generating function technique. Finally, numerical illustrations are performed.