Keywords Fuzzy Optimization, Normal Simulation, Queuing Theory, Web Planning Model.

Abstract

In this paper, we use both fuzzy optimization techniques and normal simulation method to solve the fuzzy web planning model problems, which are the queuing system problems for designing web servers. We apply fuzzy probabilities to the queuing system models with customers arrival rate ('lamda') and servers service rate ('mu'), and then compute fuzzy system performance variables, including Utilization, Number (of requests) in the System, Throughput, and Response Time. For the fuzzy optimization method, we apply two-step calculation, first use fuzzy calculation to get the maximum and minimum values of fuzzy steady state probabilities, and then we compute the fuzzy system performance variables. For the simulation method, we use one-step normal queuing theory to simulate the whole system performance and its variables. We deal with the queuing system with single-server case and multiple-server case, and compare the results of two examples with one server and two server cases and give a mathematical explanation of the difference.

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