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This section explains the evaluation of the proposed sub-model 1, MCFQ-2Pr, sub- model 2, MCCQ-ESR-2Pr, sub-model 3, MCCQ-GSR-2Pr and TrMF-UF model. The evaluation was done by comparing the models with several models, such as with

Step 3 Step 4 Step 5 Step 1 Step 2 Yes No

Simulate several experiments on each proposed sub model to compute the average estimations of the PM

for each proposed sub model

Choose the best proposed sub model via smallest of MSE Generate fuzzy arrival rates Class One and Class Two

Design the fuzzy subsets intervals

Generate fuzzy service rates Start

End

Input the initial values of basic elements which are arrival rates Class One and Class Two, and service rates (exponential and gamma)

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the fuzzy multiple channel queueing and other existing models for single fuzzy queues under two classes of arrival rates.

To evaluate the UF which represents the level of the busy server, the proposed TrMF-UF model was compared to the characteristics of fuzzy numbers model and the expected values model. The latter was done by using simulation experiments in relation to the multiple channel queueing system. These evaluations on the proposed sub-models and model were done to achieve Objective 6. The following subsections explain further on the evaluation procedures.

4.9.1 Comparison of the MCFQ-2Pr: Sub-Model 1

The comparison of the sub-model 1, MCFQ-2Pr was performed to investigate how good our model is by comparing it with two models and different criteria. The first model is by Bagherinejad and Pishkenari (2016) who constructed the membership functions by using characteristics of fuzzy numbers and computed the fuzzy values,

q

W and L_sby PNLP technique. On the other hand, our sub-model 1, was developed

based on the analysis of PM of the expected waiting time of trucks in the queue,W_q

and the number of trucks in the system,L_sfor two types of arrivals rates, Class One

and Class Two, by using the PNLP technique. The comparison was made based on and

q s

W L because the sub-model 1 focus on developing these values of PM under an uncertain environment. Moreover, the PM for sub-model 1, was computed also based on fuzzy subset intervals which are used to construct the membership functions of fuzzy queues. The second model for comparison is also similar to sub- model 1 by Thangaraj and Rajendran (2016) who used the minimum and maximum values to compute the values of L_swhich are based on the level method.

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The evaluation of the proposed sub-model 2, MCCQ-ESR-2Pr and sub-model 3, MCCQ-GSR-2Pr was done simultaneously to find out how good our sub-models are compared to the model by Bagherinejad and Pishkenari (2016) which adopted defuzzification the RR technique to convert the values of fuzzy arrival rates and service rates into deterministic crisp values.

The comparison was made based on two criteria. The first criterion is the construction of a single membership function to represent the fuzzy arrival rates service rates. The second criterion is based on the characteristics of fuzzy numbers to the values of Po and . In addition, an appropriate and realistic scenario was

conducted to be a part of comparative evaluations by using the same defuzzification technique to obtain the values of W_q and L . _s

The sub-model 2, MCCQ-ESR-2Pr and sub-model 3, MCCQ-GSR-2Pr were able to demonstrate the impact of designing the membership functions by using fuzzy subset intervals. On the other hand, these two models also demonstrated the impact of using different service rates. Results of the implementation can be obtained in the real manufacturing industry.

4.9.3 Comparison of the Proposed TrMF-UF Model

The evaluation of the proposed TrMF-UF model was performed by comparing the UF obtained with two existing models. The first model by Bagherinejad and Pishkenari (2016) the employed the characteristics of fuzzy numbers to obtain the UF for the whole queueing system. On the other hand, the second model by Vajargah

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and Ghasemalipour (2015) they used simulation experiments with the expected values model based on generating fuzzy arrival and service rates to compute the UF. Figure 4.7 shows the simulation procedure for comparison between the proposed TrMF-UF model and the single crisp values of this parameter.

Figure 4.7. Simulation Procedure for Comparing the Proposed TrMF-UF Model

Generate sample size represented Exponential fuzzy service time rates

Construct triangular membership functions for each basic element

As design fuzzy subset intrervals

Use the RR technique to convert fuzzy arrival rates and service rates as the crisp

value

Compute

Construct triangular membership function for each basic element as recommended by

Vajargah and Ghasemalipour (2015)

Use the expected value model to convert fuzzy arrival rate and service rate as the crisp value

Compute and

Compare , and

Best Generate sample size represented

Poisson fuzzy arrival rates for Class One and Class Two

Start

End

Simulate experiments via increasing of the average arrival rates for Class One and Class two, and service rates

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These evaluations and comparisons for the proposed sub-model 1, MCFQ-2Pr, sub- model 2, MCCQ-ESR-2Pr, sub-model 3, MCCQ-GSR-2Pr and the proposed TrMF- UF model, were done to achieve Objective 6. All results are discussed in more detail in Chapter Five.