Numerical computation for stationary indices of finite T-IPH/Geo/1/N queue
ZHANG Hong-bo1,2, ZHENG Qun-zhen1
1. School of Mathematics and Statistics, Henan Institute of Education, Zhengzhou 450046, China
2. School of Mathematics and Statistics, Central South University, Changsha, 410075, China
Abstract A finite T-IPH/Geo/1/N queue system is considered, where T-IPH denotes the discrete-time phase type distribution defined on a birth and death chain with countably many states. The queue model can be described by a quasi-birth-and-death (QBD) process with finite phases. The iterative formula to calculate nonzero values in the rate matrix of the QBD process is proved firstly. Furthermore, based on the obtained results, the stationary queue length and waiting time distribution of the T-IPH/Geo/1/N queue are given.
ZHANG Hong-bo, ZHENG Qun-zhen. Numerical computation for stationary indices of finite T-IPH/Geo/1/N queue. Applied Mathematics A Journal of Chinese Universities, 2015, 30(2): 139-149.
