Optimization of Queuing Theory Based on Vague Environment

Abstract

Waiting lines or queues are commonly occurred both in everyday life and in a variety of business and industrial situations. The various arrival rates, service rates and processing times of jobs/tasks usually assumed are exact. However, the real world is complex and the complexity is due to the uncertainty. The queuing theory by using vague environment is described in this paper. To illustrate, the approach analytical results for M/M/1/8 and M/M/s/8 systems are presented. It optimizes queuing models such that the arrival rate and service rate are vague numbers. This paper results a new approach for queuing models in the vague environment that it can be more effective than deterministic queuing models. A numerical example is illustrated to check the validity of the proposed method.

Economic Analysis of the M/M/1/N Queuing System Cost Model in a Vague Environment

“…To conceptualize the vagueness, some preliminary definitions one presented below: Definition 1 (Fuzzy set) [10]. A fuzzy setà = {< u, µÃ(u) >| u ∈ U } in a universe of discourse U is characterized by a membership function, µÃ, as follows:…”

“…Definition 2 [10]. A vague setà in a universe of discourse U is characterized It is expressed by two membership functions, which is a true membership, TÃ, function and a false membership function,FÃ, as follows:…”

“…Therefore, generalized vague collections have fuzzy sets of membership degrees µÃ(u) of u in Definition 1 may be inexact in a vague set. Definition 3 [10]. The complement of a vague setà is denoted byà and is defined by…”

“…Instead of using point-relying membership as in fuzzy sets, interval-based membership is used in a vague set [9]. Defined vague sets are used by Gonzalez-Lopez et al [10] where they described the optimization of queuing theory based on vague environment.…”

Optimizing and evaluating performance quality control of the production process of disposable essentials using approach vague goal programming

“…A vague set, as well as an Intuitionistic fuzzy set, is a further generalization of a fuzzy set. We describe the Optimization of queuing theory based on vague environment [8]. In this research study, an empirical study of the fuzzy regression model was conducted to better estimate and predict.…”