Abstract

We use fuzzy probabilities in queuing system models for designing web servers. Following work elucidated in the recently submitted paper by Buckley, Reilly and Zheng (2002), we utilize fuzzy, finite, regular Markov chains to determine the fuzzy steady state probabilities. Subsequently, we then compute fuzzy system performance variables, including Utilization, Number (of requests) in the System, Throughput, and Response Time. Developing system outputs with different numbers of servers and states provides a basis for optimizing the design of an entire web planning system. This paper deals with the specifics of computing (fuzzy) steady state probabilities using genetic algorithms to determine required minimum and maximum of the modeling system's fuzzy number outputs. The genetic algorithm we use employs floating point computations rather than traditional binary ones. Such an approach reduces computer memory load The modeling scheme involves complex constraints which are translated into linear ones to effect a convex space for the searching process. Genetic mutation and crossover methods are readily applicable (and efficient) in this context. We also compare the result of this method, in terms of timing and precision, to other searching methods, e.g., exhaustive and naive random based methods.

Key Words:

Genetic Algorithm, fuzzy probability, optimization, queuing theory.