Development of a method for multi-channel fuzzy exponential queueing systems and solution procedure

This paper proposes a procedure to construct the membership functions of the performance measures in multi-channel fuzzy queueing systems when the arrival rate and service rate are fuzzy numbers. The basic idea is to transfrom a fuzzy queue with multi-channel server to a family of conventional crisp queues with multi-channel server by applying the a-cut approach. On the basis of a-cut representation and the extension principle, a pair of parametric nonlinear programs is formulated to describe that family of crisp multi-channel queues, via which the membership functions of the performance measures are derived. To demonstrate the validity of the proposed procedure, a fuzzy queue is exemplified. Since the performance measures are expressed by membership functions rather than by crisp values, they completely conserve the fuzzyiness of input information when some data of multi-channel queueing systems are ambiguous. Thus the proposed approach for vague systems can represent the system more accurately, and more information is provided for designing queueing systems in real life. By extending to fuzzy environment,the multi-channel server queueing systems would have wider applications.

Keywords:

Fuzzy sets , Queueing , Multi-Channel , Exponential , Performance measures , Non linear Programming