The M^X/M/1 Queue with Multiple Working Vacation

We study a batch arrival MX/M/1 queue with multiple working vacation. The server serves customers at a lower rate rather than completely stopping service during the service period. Using a quasi upper triangular transition probability matrix of two-dimensional Markov chain and matrix analytic method, the probability generating function (PGF) of the stationary system length distribution is obtained, from which we obtain the stochastic decomposition structure of system length which indicates the relationship with that of the MX/M/1 queue without vacation. Some performance indices are derived by using the PGF of the stationary system length distribution. It is important that we obtain the Laplace Stieltjes transform (LST) of the stationary waiting time distribution. Further, we obtain the mean system length and the mean waiting time. Finally, numerical results for some special cases are presented to show the effects of system parameters.

基于虚假信息情况下系统收益模型及应用

针对确定队长不可见的顾客批量到达的排队系统,构建虚假信息情况下系统的收益模型,并研究其在呼叫中心排队系统的应用。模型首先引入虚假信息参数,根据生灭过程方法和区间数的依概率分布原理,得到系统收益函数,并从惩罚机制和系统间竞争的角度,对模型进行扩充。实例分析表明,当惩罚机制为空时,利用信息不对称优势,虚假信息确实可以提高系统收益,但随着虚假信息值不断增加,系统收益逐渐减小,这解释了不易察觉的虚假信息存在的原因;当惩罚机制非空时,虚假信息会降低系统收益,且不同惩罚函数对系统约束效果不同。在考虑系统间竞争时,虚假信息会降低系统收益,同时竞争有助于降低系统提供虚假信息值。实例分析证明模型的可行性,具有一定管理应用价值。

基于成批排队的自相似业务性能分析

自相似业务建模及性能分析是ATM领域当前的研究热点。讨论了当前排队模型的特点与不足,从分组层次上提出了一种新的模型。利用成批排队理论对系统的性能指标进行了分析,对模拟流量的自相似性及排队性能进行了实验仿真,研究了确定模型参数的方法,证实了理论结果的正确性。实验结果表明,从分组层次上建立的排队模型在性能上优于ON-OFF源层次上的模型。