输入和服务均与系统状态相依的排队模型——其队长的瞬时分布  

Transient Distribution of the Length of a Queueing Model with Input and Service Dependent on the System State

作　　者：何宁卡[1] 俞政[1] 胡达轩[1] 

机构地区：[1]中南大学数学科学与计算技术学院,湖南长沙410075

出　　处：《中山大学学报（自然科学版）》2004年第1期21-24,共4页Acta Scientiarum Naturalium Universitatis Sunyatseni

基　　金：国家自然科学基金资助项目(10171009);高校博士点基金资助项目(20010533001);"985行动计划"和"211工程"资助项目

摘　　要：探讨了一个有如下特征的排队系统:系统的到达间隔序列{τm}及服务过程{υn}均为相互独立但不一定同分布的随机变量序列。每个τ_m及每个υ_n的分布均与系统的瞬时状态有关。易见,此系统是经典的GI/G/1排队系统的拓广。利用补充变量技术,可以得到一个多维马氏过程,使得上述系统的瞬时队长过程为此多维过程的一个分量过程,借助马氏过程理论,系统的瞬时队长分布的积分表示被导出。在一定条件下,该积分表示的被积项能够递归地求取。A quequeing system is studied where the arrival times {τm } and service times { vn} are independent between each other and not identically distributed random variables. Both the distribution of every τm and the distribution of evrey vn depend on the transient state of the system. Clearly, the queueing system is generalization of GI/G/1 queue. Using supplementary variable technique in stochastic models, a multi-dimensional Markov process which includes the transient queue length of the queue mentioned here as a component is constructed. Then, the integral representation of the transient distribution of the queue length is obtained, under certain conditions, the integrated term in the above representation can be calculated recursively.

关 键 词：排队系统 瞬时队长 补充变量 

分 类 号：O211.62[理学—概率论与数理统计]