The Geom/Geom/1+1 queueing system with changing service rate

This paper studies the Geom/Geom/1+1 queueing system with changing service rate. The system contains a limited capacity of the queue and a capacity infinite queue, and the service rates of the two queues are different. Using the quasi birth and death process and matrix geometric solution method, we obtain steady state probability distribution of queue length, the average queue length, the average waiting time and the probability of busy period. Furthermore, we analyze these indicators through the numerical examples.