Mathematics, Vol. 11, Pages 1494: Estimating the Rate of Convergence of the PH/M/1 Model by Reducing to Quasi-Birth-Death Processes

Mathematics, Vol. 11, Pages 1494: Estimating the Rate of Convergence of the PH/M/1 Model by Reducing to Quasi-Birth-Death Processes

Mathematics doi: 10.3390/math11061494

Authors: Ilya Usov Yacov Satin Alexander Zeifman

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).