A two-phase queueing system with repeated attempts and Bernoulli vacation schedule (Q840611)

Summary: This paper deals with the steady-state behaviour of an \(M\)/\(G\)/\(1\) queue with repeated attempts in which the server provides two phases of heterogeneous service under Bernoulli vacation schedule. We carry out an extensive analysis of the system, including existence of stationary regime, embedded Markov chain, steady-state distribution of the server state, the number of customers in the orbit and some system performance measures. This model generalises both the classical \(M\)/\(G\)/\(1\) retrial queue and the \(M\)/\(G\)/\(1\) queue with two phases of service and Bernoulli vacation model.