Abstract
This scientific article sets out to solve the following fundamental problem to calculate the performance parameters of the FM/FM/1 queuing system in transient state. To resolve this problem the fuzzy arithmetic of ∝ − cuts and intervals was used in transient state (TS). To achieve the expected results of our work, we used the analytical method with its different stages which are : selecting textual or visual documents ( books, articles, conferences, seminars,... with or without internet); read and analyze the content of these documents; record selected documents related to our research topic; interpret during the reading and the classification, the data obtained. This method helped us to identify the appropriate mathematical approach to evolve the performance of the queuing system under study. This is precisely the relaxed a-cuts and intervals. To illustrate this approach, a numerical example is given in the sixth section. The membership function enabled us to represent the graphs of the performance parameters of the FM/FM/1 queuing system in the three-dimensional space in the transient regime in a fuzzy environment
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