Parametric programming to the analysis of fuzzy queues

This paper proposes a general procedure to construct the membership functions of the performance measures in queueing systems when the interarrival time and service time are fuzzy numbers. The basic idea is to reduce a fuzzy queue into a family of crisp queues by applying the α-cut approach. A pair of parametric programs is formulated to describe that family of crisp queues, via which the membership functions of the performance measures are derived. To demonstrate the validity of the proposed procedure, four fuzzy queues, namely. M/F/1, F/M/1, F/M/1, and FM/FM/1. are exemplified. The discussion of this paper is confined to systems with one and two fuzzy variables: nevertheless, the procedure can be extended to systems with more than two fuzzy variables.