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

Fazlollahtabar, Hamed; Gholizadeh, Hadi

doi:10.5391/ijfis.2019.19.3.192

Cited by 7 publications

(3 citation statements)

References 15 publications

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“…The results obtained are defuzzified by the "integral centroid" approach named "COA method", i.e. "Center of Area" defined by (Fazlollahtabar, H., & Gholizadeh, H. (2019).).…”

Section: Position Of the Problemmentioning

confidence: 99%

Analysis of the Performance Measures of a Non-Markovian Fuzzy Queue via Fuzzy Laplace Transforms Method

Mawa¹,

Matendo

Kanyinda

et al. 2022

JCRINN

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Laplace transforms play an essential role in the analysis of classical non-Markovian queueing systems. The problem addressed here is whether the Laplace transform approach is still valid for determining the characteristics of such a system in a fuzzy environment. In this paper, fuzzy Laplace transforms are applied to analyze the performance measures of a non-Markovian fuzzy queueing system FM/ FG/1. Starting from the fuzzy Laplace transform of the service time distribution, we define the fuzzy Laplace transform of the distribution of the dwell time of a customer in the system. By applying the properties of the moments of this distribution, the derivative of this fuzzy transform makes it possible to obtain a fuzzy expression of the average duration of stay of a customer in the system. This expression is the fuzzy formula of the same performance measure that can be obtained from its classical formula by the Zadeh extension principle. The fuzzy queue FM/ FE_k /1 is particularly treated in this text as a concrete case through its service time distribution. In addition to the fuzzy arithmetic of L-R type fuzzy numbers, based on the secant approximation, the properties of the moments of a random variable and Little's formula are used to compute the different performance measures of the system. A numerical example was successfully processed to validate this approach. The results obtained show that the modal values of the performance measures of a non-Markovian fuzzy queueing system are equal to the performance measures of the corresponding classical model computable by the Pollaczeck-Khintchine method. The fuzzy Laplace transforms approach is therefore applicable in the analysis of a fuzzy FM/FG/1 queueing system in the same way as the classical M/G/1 model.

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“…The results obtained are defuzzified by the "integral centroid" approach named "COA method", i.e. "Center of Area" defined by (Fazlollahtabar, H., & Gholizadeh, H. (2019).).…”

Section: Position Of the Problemmentioning

confidence: 99%

Analysis of the Performance Measures of a Non-Markovian Fuzzy Queue via Fuzzy Laplace Transforms Method

Mawa¹,

Matendo

Kanyinda

et al. 2022

JCRINN

View full text Add to dashboard Cite

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“…Cruz and Woensel [18] provided an overview of different modeling issues, the performance evaluation, and optimization behavior of the finite queueing models based on cycle time, work-in-process. Fazlollahtabar and Gholizadeh [19] developed a finite capacity M/M/1/N queueing model using vague numbers and they proposed the corresponding economic analysis through a novel cost model. Recently, Prameela and Kumar [20] analyzed a finite capacity single-server queueing model with triangular, trapezoidal and hexagonal fuzzy numbers using α-cuts and made various estimations of α.…”

Section: Introductionmentioning

confidence: 99%

Optimization of M/M/s/N Queueing Model with Reneging in a Fuzzy Environment

Panta¹,

Ghimire²,

Panthi³

et al. 2021

AJOR

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This paper deals with the study of multi-server queueing model in a fuzzy environment with imposition of reneging of customers. Entry of the customers in the system is assumed to be Poisson process and exponential service time distribution under first-come-first-served basis. Specific of this investigation is to derive the various fuzzy performance measures such as fuzzy queue length, fuzzy waiting time in queue, fuzzy response time and fuzzy optimal number of servers in explicit form for the finite capacity multi-server queueing system by using recursive method. For the validity of the model we have obtained the numerical illustrations in tabular form which shows that fuzzy-queue can be more realistic than crisp queue.

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“…In addition, Ghorui et al [20] applied FAHP and FTOPSIS for shopping mall site selection, and Ghosh et al [21] applied FAHP and FTOPSIS for selecting the best e-rickshaw available. Moreover, Abtahi et al [22] proposed a skew-normal uncertainty distribution to capture the skewness in the portfolio selection problem, and Fazlollohtabar and Ghlizadeh [23] studied a single-server finite-capacity Markovian queuing system with encouraged arrivals. Kaufman [24] extended the ZBB approach to a fuzzy environment, introduced a numerical example to explain how to use this extended tool, and described the selection procedure.…”

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confidence: 99%