Optimizing a priority-discipline queueing model using fuzzy set theory

Abstract

The aim of this paper is to provide a more realistic description of priority-discipline queueing models by using Fuzzy Set Theory. It develops and optimizes two fuzzy queueing models with priority-discipline, a model with nonpreemptive priorities system and a model with preemptive priorities system, denoted by M ̃ i / M ̃ i / 1 and M ̃ i / F i / 1 . The first symbol is for a queueing system where arrivals and services from a single server follow a Poisson process with fuzzy parameter and the last symbol is for a queueing model with arrivals follows a Poisson process with fuzzy rate and fuzzy deterministic service rate. Zadeh’s extension principle is the basic approach to this research into fuzzy stochastic processes. Our results are the basis for a discussion of optimal selection of priority-discipline. Two fuzzy queueing systems that are commonly found in real situations are solved, and serve as examples that highlight the validity of the procedure we propose. Fuzzy queueing models are more realistic than the crisp queues that are commonly used in reality. Furthermore, extending queueing models to the fuzzy environment widens their scope of application.