Estimating the Rate of Convergence of the PH/M/1 Model by Reducing to Quasi-Birth-Death Processes

Abstract

We are studying the quasi-birth-death process and the property of weak ergodicity. Using the C-matrix method, we derive estimates for the rate of convergence to the limiting regime for the general case of the PH/M/1 model, as well as the particular case when m=3. We provide a numerical example for the case m=3, and construct graphs showing the probability of an empty queue and the probability of p1(t).

Keywords

• bounds on the rate of convergence
• C-matrix method
• limiting regime
• logarithmic norm method
• queuing system