Gaussian asymptotics for a multiclass M/M/1/1 retrial queueing system

Anatoly Nazarov, Tuan Phung-Duc, Yana Izmailova
In this paper, we consider the multiclass M/M/1/1 retrial queueing system where customers of each type have type-dependent arrival process, service time distribution and retrial rate. In this system, a blocked customer enters the orbit of its own type and retries for service after an exponentially distributed time with the parameter depending on its type. Under the condition that the retrial rates are small, i.e., long retrial time, we obtain the asymptotic joint stationary distribution of the numbers of customers in the orbits, which turns out to be Gaussian with explicit means and covariance matrix.