Performance evaluation of open queueing networks with fuzzy parameters

Queueing network models have wide applications in performance measures of real-world systems. This paper proposes a mathematical programming approach to construct the membership functions of the performance measures in open queueing network, in that the arrival rates from outside of the system and service rates are fuzzy numbers. The idea is based on Zadeh's extension principle and the a-cut representation. A pair of parametric nonlinear programs is formulated to derive the a-cut of the performance measure, via which the membership function of the performance measure is constructed. Two numerical examples are solved successfully to demonstrate the validity of the proposed approach. Since the performance measure is expressed by a membership function rather than by a crisp value, a more realistic performance measure could be obtained, which completely conserves the fuzziness of input information and provides the decision-maker with more knowledge of the queueing network to make superior decisions.