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SET-VALUED PERFORMANCE APPROXIMATIONS FOR THE QUEUE GIVEN PARTIAL INFORMATION
Probability in the Engineering and Informational Sciences ( IF 1.1 ) Pub Date : 2020-09-25 , DOI: 10.1017/s0269964820000509 Yan Chen 1 , Ward Whitt 1
Probability in the Engineering and Informational Sciences ( IF 1.1 ) Pub Date : 2020-09-25 , DOI: 10.1017/s0269964820000509 Yan Chen 1 , Ward Whitt 1
Affiliation
In order to understand queueing performance given only partial information about the model, we propose determining intervals of likely values of performance measures given that limited information. We illustrate this approach for the mean steady-state waiting time in the $GI/GI/K$ queue. We start by specifying the first two moments of the interarrival-time and service-time distributions, and then consider additional information about these underlying distributions, in particular, a third moment and a Laplace transform value. As a theoretical basis, we apply extremal models yielding tight upper and lower bounds on the asymptotic decay rate of the steady-state waiting-time tail probability. We illustrate by constructing the theoretically justified intervals of values for the decay rate and the associated heuristically determined interval of values for the mean waiting times. Without extra information, the extremal models involve two-point distributions, which yield a wide range for the mean. Adding constraints on the third moment and a transform value produces three-point extremal distributions, which significantly reduce the range, producing practical levels of accuracy.
中文翻译:
给定部分信息的队列的定值性能近似值
为了在仅给出模型的部分信息的情况下理解排队性能,我们建议在有限信息的情况下确定性能度量的可能值的区间。我们说明了这种方法的平均稳态等待时间 $GI/GI/K$ 队列。我们首先指定到达间隔时间和服务时间分布的前两个矩,然后考虑有关这些基础分布的附加信息,特别是第三个矩和拉普拉斯变换值。作为理论基础,我们应用极值模型对稳态等待时间尾概率的渐近衰减率产生严格的上限和下限。我们通过构建理论上合理的衰减率值区间和相关的启发式确定的平均等待时间值区间来进行说明。在没有额外信息的情况下,极值模型涉及两点分布,这会产生广泛的均值范围。在三阶矩和变换值上添加约束会产生三点极值分布,
更新日期:2020-09-25
中文翻译:
给定部分信息的队列的定值性能近似值
为了在仅给出模型的部分信息的情况下理解排队性能,我们建议在有限信息的情况下确定性能度量的可能值的区间。我们说明了这种方法的平均稳态等待时间