Parametric nonlinear programming for analyzing fuzzy queues with finite capacity

This paper proposes a procedure for constructing the membership functions of the performance measures in finite-capacity queueing systems with the arrival rate and service rate being fuzzy numbers. The basic idea is to transform a fuzzy queue with finite capacity to a family of conventional crisp queues with finite capacity by applying the α-cut approach. A pair of parametric nonlinear programs is formulated to describe the family of crisp finite-capacity queues, via which the membership functions of the performance measures are derived. To demonstrate the validity of the proposed procedure, two fuzzy queues often encountered in real life serve as examples. Since the performance measures are expresssed by membership functions rather than by crisp values, more information is provided for designing queueing systems in real life. By extending to fuzzy environment, the finite-capacity queueing models would have wider applications.