Analysis for stationary indices of discrete-time T-IPH/Geo/1 queue

详细信息    查看全文

• 作者：Hongbo Zhang (1) (2)
  Zhenting Hou (1)
  Dinghua Shi (3)
  
  1. School of Mathematics and Statistics ; Central South University ; Changsha聽 ; 410075 ; China
  2. Department of Mathematics ; Henan Institute of Education ; Zhengzhou聽 ; 450046 ; China
  3. Department of Mathematics ; Shanghai University ; Shanghai聽 ; 200444 ; China
  
• 关键词：T ; IPH/Geo/1 queue ; QBD process ; Joint stationary distribution ; Stationary queue length ; Stationary waiting time ; 60K25 ; 90B22
• 刊名：Journal of Applied Mathematics and Computing
• 出版年：2015
• 出版时间：February 2015
• 年：2015
• 卷：47
• 期：1-2
• 页码：417-428
• 全文大小：246 KB
• 参考文献：1. Alfa, A.S.: Discrete time queues and matrix-analytic methods. TOP 10(2), 147鈥?10 (2000) CrossRef
  2. Alfa, A.S.: Queueing Theory for Telecommunications, Discrete Time Modeling of a Single Node System. Springer, New York (2010) CrossRef
  3. Breuer, L., Baum, D.: An Introduction to Queueing Theory and Matrix-Analytic Methods. Springer, Dordrecht (2005)
  4. Brualdi, R.A.: Introductory Combinatorics. Prentice Hall, Redwood (2004)
  5. Haque, L., Zhao, Y.Q., Liu, L.M.: Sufficient conditions for a geometric tail in a QBD process with many countable levels and phases. Stoch. Models 21(1), 77鈥?9 (2005) CrossRef
  6. Hunter, J.J.: Mathematical Techniques of Applied Probability, vol. 2. Academic Press, New York (1983)
  7. Li, Q.L., Zhao, Y.: Q.: \(\beta \) -invariant measure for transition matrices of GI/M/1 type. Stoch. Models 19(2), 201鈥?33 (2002)
  8. Miller, D.R.: Computation of steady-state probabilities for M/M/1 priority queues. Oper. Res. 29(5), 945鈥?58 (1981) CrossRef
  9. Neuts, M.F.: Matrix-Geometric Solutions in Stochastic Models: An Algorithmic Approach. The Johns Hopkins University Press, Baltimore (1981)
  10. Ramaswami, V., Taylor, P.G.: Some properties of the rate operators in level dependent quasi birth and death processes with a countable number of phases. Stoch. Models 12(1), 143鈥?64 (1996) CrossRef
  11. Shi, D.H., Guo, J.L., Liu, L.M.: PH-distributions and the rectangle-iterative algorithm. In: Chakravarthy, S.R., Alfa, A.S. (eds.) Matrix-Analysis Methods in Stochastic Models, pp. 207鈥?24. Marcel Decker, New York (1997)
  12. Tweedie, R.L.: Operator-geometric stationary distributions of Markov chains with application to queueing models. Adv. Appl. Probab. 14(2), 368鈥?91 (1982) CrossRef
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Computational Mathematics and Numerical Analysis
  Applied Mathematics and Computational Methods of Engineering
  Theory of Computation
  Mathematics of Computing
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：1865-2085

文摘

In this paper, we study a T-IPH/Geo/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-and-death process with countably phases. Using operator-geometric solution method, we first give the expression of the operator and the joint stationary distribution. Then we obtain the steady-state distributions for the number of customers in the system, and waiting time for an arbitrary customer.