A queueing system with linear repeated attempts, Bernoulli schedule and feedback (Q1876466)

A retrial queue is studied, where customers that find the processor busy at arrival either join the queue or the retrial group with given probabilities. After the service, customers either leave the system or join the queue, again, with given probabilities. Service times are general independent and the arrival process is a Poisson one. The ergodicity of embedded Markov chain and the steady-state distribution are studied. A generating function of system size distribution that generalizes the classical Pollaczek-Khinchin formula is derived. A stochastic decomposition law is also derived. As an application, the asymptotic behavior under high rate of retrials is analyzed.