Mathematics, Vol. 11, Pages 2454: Scaling Limits of a Tandem Queue with Two Infinite Orbits

Mathematics, Vol. 11, Pages 2454: Scaling Limits of a Tandem Queue with Two Infinite Orbits

Mathematics doi: 10.3390/math11112454

Authors: Anatoly Nazarov Tuan Phung-Duc Svetlana Paul Mariya Morozova

This paper considers a tandem queueing network with a Poisson arrival process of incoming calls, two servers, and two infinite orbits by the method of asymptotic analysis. The servers provide services for incoming calls for exponentially distributed random times. Blocked customers at each server join the orbit of that server and retry to enter the server again after an exponentially distributed time. Under the condition of low retrial rates, we prove that the joint stationary distribution of scaled numbers of calls in the orbits weakly converges to a two-variable Normal distribution.