Scaling Limits of a Tandem Queue with Two Infinite Orbits

Abstract

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.

Analysis of a Two-Stage Tandem Queuing System with Priority and Clearing Service in the Second Stage

“…Yang et al [11] analyzed a two-stage tandem queuing system featuring a single service in the first stage and a batch service in the second stage, both provided by a single switched server under N policy. Recently, Nazarov et al [12] studied a queuing network with two servers in series and two infinite orbits using the asymptotic analysis method. Dudin, Dudina, and Dudin [13] considered a dual queuing model with multiple servers in the second stage.…”