This paper is concerned with the analysis of a single-server queue with Bernoulli vacation schedules and general retrial times. We assume that the customers who find the server busy are queued in the orbit in accordance with an FCFS (first-come-first-served) discipline and only the customer at the head of the queue is allowed access to the server. We first present the necessary and sufficient condition for the system to be stable and derive analytical results for the queue length distribution, as well as some performance measures of the system under steady-state condition. We show that the general stochastic decomposition law for M/G/1 vacation models holds for the present system also. Some special cases are also studied.
Krishna Kumar, B., & Arivudainambi, D. (2002). The M/G/1 retrial queue with Bernoulli schedules and general retrial times. Computers and Mathematics with Applications, 43(1–2), 15–30. https://doi.org/10.1016/S0898-1221(01)00267-X