A mathematical programming approach to fuzzy queues with batch arrivals

This paper proposes a mathematical programming approach for constructing the membership functions of the performance measures in batch-arrival queueing systems with constant batch size and the arrival rate and service rate being fuzzy numbers. The basic idea underlying the proposed method is to transform a fuzzy batch-arrival queue to a family of conventional crisp queues with batch arrivals by applying the α-cut approach. Then the family of crisp batch-arrival queues is described by formulating a pair of parametric nonlinear programs, through which the membership functions of the performance measures can be derived. A numerical example is solved successfully to demonstrate the validity of the proposed approach. Since the performance measures are completely expressed by membership functions rather than by crisp values, more information is provided for designing queuing systems. The successful extension of batch-arrival queues to fuzzy environments permits queueing models to have wider applications in the real world.