Analysis of fuzzy queues

Li, R.-J.; Lee, E.S.

doi:10.1016/0898-1221(89)90044-8

Cited by 122 publications

(43 citation statements)

References 1 publication

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“…Thus, fuzzy queues are much more realistic than the commonly used crisp queues [8][9][10]. Several researchers have discussed fuzzy queueing systems, e.g., [8][9][10][11][12][13][14]; however, few articles have been published on the fuzzy bulk arrival queue with varying batch size. If the usual crisp bulk arrival queues can be extended to fuzzy bulk arrival queues, bulk arrival queueing models would have wider applications.…”

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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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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“…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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“…Stanford (1982) discussed the set of limiting distribution for a Markov chain with fuzzy transition probabilities. Li and Lee (1989) In this paper, fuzzy set theory is applied to construct the membership function for a fuzzy biserial queue network linked to a common server in which arrival rate, service rate and various possibilities are fuzzy triangular numbers.  -cut approach and fuzzy arithmetic operations are used to drive system characteristics.…”

Section: Introductionmentioning

confidence: 99%

Analysis of Biserial Servers Linked to a Common Server in Fuzzy Environment

Seema¹,

Gupta²,

Sharma³

2013

IJCA

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The present paper is an attempt to find various characteristics of a queuing network in which two parallel biserial servers are linked to a common server in series under fuzzy environment. Waiting lines or queues are extensively used to analyze the production and service processes exhibiting random variability in arrival times and service times. It is usually assumed that the time between the two consecutive arrivals and servicing time follows a special probability distribution. However, in real world this type of information is obtained using qualitative data and expressed by words like quick, medium and slow rather than the probabilistic values. The  -cut approach and fuzzy arithmetic operations are used to estimate the uncertainty associated with the input parameters. The proposed model is illustrated with a numerical illustration.

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Analysis of fuzzy queues

Cited by 122 publications

References 1 publication

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

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

Predictor Analysis on Non-parametric Bulk Arrival Fuzzy Queuing System

Analysis of Biserial Servers Linked to a Common Server in Fuzzy Environment

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