A New Clustering Method with Fuzzy Approach Based on Takagi-Sugeno Model in Queuing Systems

A New Clustering Method with Fuzzy Approach Based on Takagi-Sugeno Model in Queuing Systems

Farzaneh Gholami Zanjanbar (Department of Management, Çankaya University, Ankara, Turkey) and Inci Sentarli (Department of Management, Çankaya University, Ankara, Turkey)
Copyright: © 2013 |Pages: 23
DOI: 10.4018/ijfsa.2013040103


In this paper, the authors propose a new hard clustering method to provide objective knowledge on field of fuzzy queuing system. In this method, locally linear controllers are extracted and translated into the first-order Takagi-Sugeno rule base fuzzy model. In this extraction process, the region of fuzzy subspaces of available inputs corresponding to different implications is used to obtain the clusters of outputs of the queuing system. Then, the multiple regression functions associated with these separate clusters are used to interpret the performance of queuing systems. An application of the method also is presented and the performance of the queuing system is discussed.
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In this paper, a new hard clustering method to extract locally linear controllers on field of fuzzy queuing systems is presented. In the most of literatures, arrival times and service times are determined by probability distributions. On the other hand, in many real-world applications, it is more adequate to describe the arrival and service patterns by linguistic terms, such as “Crowded arrivals”, “Fast” or “Slow services” instead of the probability distributions. Since both arrival times and service times are more possibilistic than probabilistic in many practical applications, so design and control of the queuing system with fuzzy concept is more realistic and applicable. Controlling the queues occupy an important place in our lives where control applications are the kinds of problems for which fuzzy logic has had the greatest success (Timothy, 2004).

Through the use of the Zadeh’s extension principle (Zadeh, 1978), the possibility concept, and fuzzy Markov chain (Stanford, 1982), the problem of fuzzy queues has been investigated by Li and Lee (1989), Buckley (1990), Negi and Le (1992) and so on. Aydın and Apaydin (2008) and Yan (2010) considered the multi channel fuzzy queuing systems and computed fuzzy queuing characteristics via different membership functions. Wang (2010) transformed the fuzzy queues to a family of crisp queues by applying the ijfsa.2013040103.m01 and Zadeh’s extension principle.

Systems that can be controlled have three key features: inputs, outputs, and control parameters, or actions (Timothy, 2004). For instance, priority dicipline machine for entering customers to different queues in the banks is a control mechanism where inputs are arrival rates of customers and service rates, outputs are the length of the queues, and the control parameters are the number of staff, capacity and etc.

Identification of dynamic systems from input-output measurements is an important topic of the scientific research with a wide range of practical applications. Usually the relationship between the input-output of a process in a fuzzy logic controller is expressed by “if-then rules”, such as:

If the interarrival is crowded then the length of queue is long.

Many real-world systems, such as queuing systems, are inherently nonlinear and cannot be represented by linear models used in conventional systems identification (Ljung, 1987). Recently, there is a strong focus on the development of methods for the identification of nonlinear systems from measured data. The TSK (Takagi, Sugeno, & Kang) method was proposed in an effort to develop a systematic approach to generating fuzzy rules from a given input-output data set (Takagi & Sugeno, 1985; Sugeno & Kang, 1988; Sugeno, 1991). In the TSK rule based fuzzy model, in each implication a linear membership function is formed to describe the real input-output relation of the system. Comparison of clustering algorithms in the identification of Takagi-Sugeno model (Fazel Zarandi, 2012; Abonyi, 2000; Johansen, 2000) are presented by Vernieuwe (2006).

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