Nonlinear Programming Models for Robust Queuing Systems under Fuzzy Sets

This paper proposes a procedure for constructing the membership functions of performance measures in finite-capacity queuing systems where both arrival and service rates are represented as fuzzy numbers. By applying the (\alpha)-cut method, a fuzzy queue with finite capacity is transformed into a family of conventional crisp queues, allowing for more precise modeling of system characteristics. The study focuses on a queuing model with an unreliable server, where key parameters such as service and breakdown rates are fuzzy values. The developed parametric nonlinear programming approach facilitates the derivation of new constraints, providing a robust framework for analyzing queuing behaviors under uncertainty. The findings demonstrate that the proposed fuzzy mathematical model yields more realistic outcomes than traditional crisp models, thereby enhancing the applicability of queuing theory in practical scenarios.