摘要
In this paper we study a Geo/T-IPH/1 queue model,where T-IPH denotes the discrete time phase type distribution defined on a birth-and-death process with countably many states.The queue model can be described by a quasi-birth-anddeath(QBD)process with countably phases.Using the operator-geometric solution method,we first give the expression of the operator and the joint stationary distribution.Then we obtain the probability generating function(PGF)for stationary queue length distribution and sojourn time distribution,respectively.
基金
This work was supported by the National Natural Science Foundation of China(No.61174160)
Post-Doctoral Science Foundation of Central South University(No.125011)
The authors are grateful to the three anonymous referees and the editor for their careful reading and invaluable comments and suggestions,which are helpful to improve the paper.This research completed when the first author was a post-doctoral fellow in School of Mathematics,Central South University。
