Analysis of a Poisson queue with a threshold policy and a grand vacation process: An analytic approach (Q2736955)

\textit{B. T. Doshi}, has discussed single server queueing models with vacations in great detail in an excellent review article [Queueing Syst. 1, No. 1, 29-66 (1986; Zbl 0655.60089)]. In this paper the authors consider an M/M/1 queue with multiple vacations under a threshold policy. They derive the probability generating function of the stationary distribution of the queue size and show that it can be decomposed into three independent variables, one of which is the queue size of the M/M/1 queue.