Determination of Client-Server System Using Fuzzy Queue Approach

Batch arrival multi-stage retrial queue under a fuzzy environment is considered. This model can be applied in various client-server systems. One such application is processing requests by a web server or HTTP server. For this application suitable queueing model is formulated and analysed by assuming arrival rate, service rate, and vacation rate are as fuzzy numbers. The membership functions of the system characteristics are constructed. The alpha cut approach transforms a fuzzy retrial queue into a family of conventional crisp retrial queues. Zadeh extension principle is used to analyse the mean processing time of the requests by the HTTP server. A numerical example is presented to illustrate the validity of the proposed approach.