Example: Fuzzy Arrival/Service Rates

Abstract

In this chapter we will look at two examples. The values of the parameters c and M are chosen to match those used in the two examples discussed in Chapters 7 and 9. We can not directly compare the numerical results $\left( {\overline U ,\overline N ,\overline X ,\overline R } \right)$ between those in Chapters 7 and 9 to those in this chapter because the two models are very different. In Chapters 7 and 9 we started with fuzzy probabilities, computed a fuzzy transition matrix and then the fuzzy steady state probabilities before we obtained the fuzzy numbers for $\left( {\overline U ,\overline N ,\overline X ,\overline R } \right)$. In this chapter we start with fuzzy numbers for the arrival rate and the service rate, then find the fuzzy steady state probabilities and the fuzzy numbers for $\left( {\overline U ,\overline N ,\overline X ,\overline R } \right)$. In the model based on fuzzy probabilities we do not relate the fuzzy steady state probabilities, fuzzy arrival rate and the fuzzy service rate as in the balance equations (equation (11.3), Chapter 11). The expressions for $\left( {\overline U ,\overline N ,\overline R } \right)$ are the same in both models, $\overline X$ is computed differently in the two models. What we can compare is the computations needed in the model presented in Chapter 11 and this chapter to those seen in Chapters 7 and 9.