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題名：Analysis of Two Queueing Models with Explicit Rate Operators and Stationary Distributions
書刊名：International Journal of Information and Management Sciences
作者：Zhang, Hongbo／Shi, Dinghua
出版日期：2011
卷期：22:2
頁次：頁177-188
主題關鍵詞：QBD process with countable phases；Rate operator；Stationary distribution；The T-SPH/M/1 queue；The M/T-SPH/1 queue
原始連結：連回原系統網址new window
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For QBD(quasi-birth-and-death) processes with countably many phases, it is well known that stationary distributions have operator-geometric forms. However, it is a challenging problem to determine the closed-form of both the rate operator (an infinite matrix) and stationary distribution for a given QBD process. In this paper, we will derive explicit rate operators and the stationary distributions for two special models: the T-SPH/M/1 queue and the M/T-SPH/1 queue, where T-SPH denotes the phase type distribution defined on the birth-and death process with countably many states.
期刊論文
1.Zhang, Hongbo、Shi, Dinghua(200912)。The M/M/1 qaueue with Bernoulli-schedule-controlled vacation and vacation interruption。International Journal of Information and Management Sciences，20:4，579-587。new window  new window
2.Miller, D. R.(1981)。Computation of steady-state probabilities for M/M/1 priority queues。Operations Research，29，945-958。  new window
3.Ramaswami, V.、Taylor, P. G.(1996)。Some properties of the rate operators in level dependent quasi birth and death processes with a countable number of phases。Stochastic Models，12，143-164。  new window
4.Zhang, H. B.、Shi, D. H.(2008)。Tail analysis of the stationary queue length distributions for two T-SPH queues (in chinese)。OR Transactions，12，60-70。  new window
5.Zhang, H. B.、Shi, D. H.(2010)。Explicit Solution for M/M/1 Preemptive Queue。International Journal of Information and Management Sciences，21，197-208。  new window
6.Sakuma, Y.、Miyazama, M.(2005)。On the effect of finite buffer truncation in a two-node Jackson network。Journal of Applied Probability，42，199-222。  new window
7.Shi, D. H.、Guo, J. L.、Liu, L. M.(2005)。On the SPH-distribution class。Acta Mathematica Scientia，25B，201-214。  new window
8.Tian, N. S.、Zhao, X. Q.(2008)。The M/M/1 queue with single working vacation。International Journal of Information and Management Sciences，19，621-634。  new window
9.Takahashi, Y.、Fujimoto, K.、Makimoto, N.(2001)。Geometric decay of the steady-state probabilities in a quasi-birth-and-death process with countable number of phases。Stochastic Models，1，1-24。  new window
10.Tweedie, R. L.(1982)。Operator-geometric stationary distributions of Markov chains with application to queueing models。Advances in Applied Probability，14，368-391。  new window
11.Alfa, A. S.(2000)。Discrete time queues and matrix-analytic methods。TOP，10，147-210。  new window
12.Li, H.、Miyazawa, M.、Zhao, Y. Q.(2007)。Geometric decay in a QBD process with countable background states with applications to a join-the-shortest-queue model。Stochastic Models，23，413-438。  new window
圖書
1.Neuts, M. F.(1981)。Matrix-geometric solutions in stochastic models: an algorithmic approach。The Johns Hopkins University Press。  new window
2.Brualdi, R. A.(2004)。Introductory Combinatorics。  new window
3.Breuer, L.、Baum, D.(2005)。An introductin to queueing theory and matrix-analytic methods。  new window
4.Shi, D. H.、Guo, J. L.、Liu, L. M.(1997)。SPH-distributions and the rectangle-iterative algorithm。Matrix-analysis methods in stochastic models。New York。  new window
 
 
 
 
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