MR/GI/1 queues by positively correlated arrival stream
MR/GI/1 queues by positively correlated arrival stream
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DOI：
10.2307/3215041
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发表时间：
1994-06
影响因子：
1
通讯作者：
R. Szekli;R. Disney;S. Hur
中科院分区：
文献类型：
--
作者：
R. Szekli;R. Disney;S. Hur
研究了到达过程中的相关性（如关联性）对单服务台排队平均队长和平均等待时间的影响。马尔可夫更新到达过程与一个特定的转移矩阵的底层马尔可夫链使用，使我们能够改变依赖性质，而不会在同一时间改变分布条件。事实证明，相关性似乎不是纯粹的效果，和三个主要因素进行了研究：（a）在潜在的马尔可夫更新过程中的平均到达间隔时间的差异，（B）强度在马尔可夫更新跳跃过程，（c）在马尔可夫更新过程的点过程的变异性。结果表明，对于具有相同到达间隔分布和相同服务时间分布（固定小于一个交通强度）的排队，通过使（a）足够大和（B）足够小，可以使平均队长任意大.的存在的时刻的利益被确认和一些随机的实际等待时间的比较结果。
The effects of dependencies (such as association) in the arrival process to a single server queue on mean queue lengths and mean waiting times are studied. Markov renewal arrival processes with a particular transition matrix for the underlying Markov chain are used which allow us to change dependency properties without at the same time changing distributional conditions. It turns out that correlations do not seem to be pure effects, and three main factors are studied: (a) differences in the mean interarrival times in the underlying Markov renewal process, (b) intensity in the Markov renewal jump process, (c) variability in the point processes underlying the Markov renewal process. It is shown that the mean queue length can be made arbitrarily large in the class of queues with the same interarrival distributions and the same service time distributions (with fixed smaller than one traffic intensity), by making (a) large enough and (b) small enough. The existence of the moments of interest is confirmed and some stochastic comparison results for actual waiting times are shown.