Queue Size Distribution of Geo/G/1 Queue Under the Min(N,D)-Policy  

作　　者：GU Jianxiong WEI Yingyuan TANG Yinghui YU Miaomiao 

机构地区：[1]School of Physics and Mechanical and Electrical Engineering , Hexi University, Zhangye 734000, China. [2]School of Mathematics and Statistics, Hexi University, Zhangyc 734000, China. [3]School of Mathematics and Software Science, Sichuan Normal University, Chengdu 610066, China. [4]School of Science, Sichuan University of Science and Engineering, Zigong 643000, China.

出　　处：《Journal of Systems Science & Complexity》2016年第3期752-771,共20页系统科学与复杂性学报（英文版）

基　　金：supported by the National Natural Science Foundation of China under Grant Nos.71171138,71301111,71571127;the Scientific Research Innovation&Application Foundation of Headmaster of Hexi University under Grant Nos.XZ2013-06,XZ2013-09

摘　　要：This paper considers a discrete-time Geo/G/1 queue under the Min（N, D）-policy in which the idle server resumes its service if either N customers accumulate in the system or the total backlog of the service times of the waiting customers exceeds D, whichever occurs first （Min（N, D）-policy）. By using renewal process theory and total probability decomposition technique, the authors study the transient and equilibrium properties of the queue length from the beginning of the arbitrary initial state, and obtain both the recursive expression of the z-transformation of tile transient queue length distribution and the recursive formula for calculating the steady state queue length at arbitrary time epoch n＋. Meanwhile, the authors obtain the explicit expressions of the additional queue length distribution, l^trthermore, the important relations between the steady state queue length distributions at different time epochs n , n and n＋ are also reported. Finally, the authors give numerical examples to illustrate the effect of system parameters on the steady state queue length distribution, and also show from numerical results that the expressions of the steady state queue length distribution is important in the system capacity design.

关 键 词：Min（N D）-policy discrete-time queue queue length distribution system capacity opti mum design total probability decomposition technique z-transform. 

分 类 号：O226[理学—运筹学与控制论] TN915.2[理学—数学]