Fuzzy optimization and normal simulation for solving fuzzy web queuing system problems

In this paper, we use both fuzzy optimization and normal simulation methods to solve fuzzy web planning model problems, which are queuing system problems for designing web servers. We apply fuzzy probabilities to the queuing system models with customers arrival rate lambda 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 queuing systems with a single server and multiple servers' cases, and compare the results of these two cases, giving a mathematical explanation of the difference.