Fuzzy random renewal process with queueing applications
Fuzzy random renewal process with queueing applications
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DOI：
10.1016/j.camwa.2009.01.030
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发表时间：
2009-04
期刊：
影响因子：
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通讯作者：
Shuming Wang;Yian-Kui Liu;J. Watada
中科院分区：
文献类型：
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作者：
Shuming Wang;Yian-Kui Liu;J. Watada
利用与一类连续阿基米德三角范数相关的延拓原理，研究了一类模糊随机更新过程，其中到达间隔时间假设为独立同分布的模糊随机变量。在连续阿基米德三角范数算法的基础上，证明了模糊随机变量和的机会测度和期望值的极限定理。在此基础上，讨论了模糊随机更新过程，得到了关于长期期望更新率的模糊随机初等更新定理。本文得到的更新定理在随机更新过程中可以退化为相应的经典结果。最后，给出了两个排队系统的实例，说明了模糊随机初等更新定理的应用。
Using extension principle associated with a class of continuous Archimedean triangular norms, this paper studies a fuzzy random renewal process in which the interarrival times are assumed to be independent and identically distributed fuzzy random variables. Some limit theorems in chance measure and in expected value for the sum of fuzzy random variables are proved on the basis of the continuous Archimedean triangular norm based arithmetics. Furthermore, we discuss the fuzzy random renewal process based on the obtained limit theorems, and derive a fuzzy random elementary renewal theorem for the long-run expected renewal rate. The renewal theorem obtained in this paper can degenerate to the corresponding classical result in stochastic renewal process. Finally, two case studies of queueing systems are provided to illustrate the application of the fuzzy random elementary renewal theorem.