马氏骨架过程与一个排队系统的瞬时队长

Markov skeleton processes and the transient queue length of a queueing system

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 {vm}均为相互独立但不一定同分布的随机变量序列 ,每个τn及每个vn 的分布均与系统的瞬时状态有关。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 ,可以得到一个马尔可夫骨架过程 ,借助马尔可夫骨架过程理论 。

Studies a queueing system wherein the interarrival times τ_m(m=1,2,…) are mutually independent but not have to be identically distributed random variables, and so are the service times v_n(n=1,2,…). Both the distribution of every τ_m and the distribution of every v_n depend on the transient state of the system. Clearly, the queueing system is generalization of GI/G/l queue. Using supplementary variable technique in stochastic models, a multi-dimensional Markov skeleton process which includes the transient queue length of the queue mentioned here as a component is constructed. Then, by means of the theory of Markov skeleton processes, integral representation of the transient distribution of the queue length of the above queue is obtained.