The set of limiting distributions for a Markov chain with fuzzy transition probabilities

Stanford, Robert E.

doi:10.1016/0165-0114(82)90041-0

Cited by 41 publications

(15 citation statements)

References 12 publications

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“…Based upon Zadeh's extension principle [11], the concept of possibility and fuzzy Markov chains (Stanford [26]), Li and Lee [13] have proposed a general approach for the analysis of fuzzy queues, in which they consider each fuzzy queueing model as if it were a perception of a usual queuing system, which can be called the original fuzzy queueing model. The set of all possible original queueing models of the proposed fuzzy model are those in which it holds that the arrival rate λ belongs to the support forλ and service rate µ belongs to the support forμ.…”

Section: Priority Discipline Fuzzy Queueing Modelsmentioning

confidence: 99%

Optimizing a priority-discipline queueing model using fuzzy set theory

Pardo

García

2007

Computers & Mathematics with Applications

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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 byM i /M i /1 andM 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.

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Section: Priority Discipline Fuzzy Queueing Modelsmentioning

confidence: 99%

Optimizing a priority-discipline queueing model using fuzzy set theory

Pardo

García

2007

Computers & Mathematics with Applications

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“…Based on ZadehÕs extension principle [15][16][17] and fuzzy Markov chain [18], Li and Lee [12] proposed a general approach for analyzing fuzzy queues. A straightforward idea is to apply their method to the fuzzy bulk arrival queueing problem.…”

Section: Introductionmentioning

confidence: 99%

A bulk arrival queueing model with fuzzy parameters and varying batch sizes

Chen¹

2006

Applied Mathematical Modelling

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This paper develops a nonlinear programming approach to derive the membership functions of the steady-state performance measures in bulk arrival queueing systems with varying batch sizes, in that the arrival rate and service rate are fuzzy numbers. The basic idea is based on ZadehÕs extension principle. Two pairs of mixed integer nonlinear programs (MINLP) with binary variables are formulated to calculate the upper and lower bounds of the system performance measure at possibility level a. From different values of a, the membership function of the system performance measure is constructed. For practice use, the defuzzification of performance measures is also provided via Yager ranking index. To demonstrate the validity of the proposed method, a numerical example is solved successfully.

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“…The arrival and service rate are triangular fuzzy number and the service distribution follows an Erlang distribution. The rates of arrival and service λ= [1,5,7] & µ= [9,11] per minute respectively, the system manager wants to evaluate the performance measures of the system such as the expected number of customers in the queue and waiting in the queue and to analyze optimality level of the system. It is clear the system consisting three phases and the steady state condition is …”

Section: Numerical Examplementioning

confidence: 99%

“…In [4] classical queueing models are extended in fuzzy model with more applications. The fuzzy queuing models are more truthful for the classical ones [5][6][7][8][9][10][11] have analyzed and proved important results on fuzzy applications using α-level membership function, [12][13][14] analyze the nonlinear programming for single phase fuzzy queues in general discipline [15] Provided the overview on the conceptual aspects for the phase service in different queueing model. Clearly, many researchers are analyzing the queueing system modeling.…”

Section: Introductionmentioning

confidence: 99%

Predictor Analysis on Non-parametric Bulk Arrival Fuzzy Queuing System

Kumar¹

2017

Global J Technol Optim

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In general a management does not like the arriving customer wait for service in a system. It is not possible for all the times because the situation. In this case parameter estimation is helpful to rectify this difficulty and to analyze the modeling of system performance. Practically the queue parameters are not deterministic. So in this paper we estimate the queue parameter. Initially we construct the inverse membership function of the k-phase fuzzy queueing system and proposed an algorithm of performing the system. Finally, obtained the level of uncertainty range in the system and analyze the interval optimality level of k-phase fuzzy queueing system. The idea is extended to the work. A numerical example is included.

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The set of limiting distributions for a Markov chain with fuzzy transition probabilities

Cited by 41 publications

References 12 publications

Optimizing a priority-discipline queueing model using fuzzy set theory

Optimizing a priority-discipline queueing model using fuzzy set theory

A bulk arrival queueing model with fuzzy parameters and varying batch sizes

Predictor Analysis on Non-parametric Bulk Arrival Fuzzy Queuing System

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