Retrial queueing system with several input flows

The authors consider a single-server retrial queue with several Poisson input flows and arbitrary type-dependent service times. An arriving customer who finds the server busy will join the retrial group with a certain probability, or leave the system otherwise. The inter-retrial times are exponential and type independent. The authors show how the steady-state probabilities of the Markov process describing this system can be determined recursively and they derive an explicit expression for the generating function of the stationary distribution of the size of the retrial group.