Ameur Lounes, Bachioua Lahcene
Department of Technology, 20 August 1955 University of Skikda, Skikda, Algeria.
Department of Basic Sciences, Preparatory Year, University of Ha'il, P.O. Box 2440, Hail, Kingdom of Saudi Arabia.
Arab J Math. 2021;10(3):527-542. doi: 10.1007/s40065-021-00344-y. Epub 2021 Sep 27.
Queueing systems are modeled by equations which depend on a large number of input parameters. In practice, significant uncertainty is associated with estimates of these parameters, and this uncertainty must be considered in the analysis of the model. The objective of this paper is to propose a sensitivity analysis approach for a queueing model, presenting parameters that follow a Gaussian distribution. The approach consists in decomposing the output of the model (stationary distribution of the model) into a polynomial chaos. The sensitivity indices, allowing to quantify the contribution of each parameter to the variance of the output, are obtained directly from the coefficients of decomposition. The proposed approach is then applied to M/G/1/N queueing model. The most influential parameters are highlighted. Finally several numerical and data examples are sketched out to illustrate the accuracy of the proposed method and compare them with Monte Carlo simulation. The results of this work will be useful to practitioners in various fields of theoretical and applied sciences.
排队系统由依赖大量输入参数的方程建模。在实际中，这些参数的估计存在显著不确定性，并且在模型分析中必须考虑这种不确定性。本文的目的是为一个排队模型提出一种灵敏度分析方法，该模型的参数服从高斯分布。该方法包括将模型的输出（模型的平稳分布）分解为多项式混沌。直接从分解系数中获得灵敏度指标，这些指标用于量化每个参数对输出方差的贡献。然后将所提出的方法应用于M/G/1/N排队模型。突出了最具影响力的参数。最后给出了几个数值和数据示例，以说明所提方法的准确性，并将其与蒙特卡罗模拟进行比较。这项工作的结果将对理论和应用科学各个领域的从业者有用。
