Effectiveness comparisons of mixture and pure distributions models in production systems

In this study, a mixture distribution model was used when the server time in the queuing system did not fit any known theoretical pure distribution. To determine the performance of the mixture distribution, normal mixture distributions and exponential mixture distributions model of the process time were used. Chi-square test was applied to estimate the statistical distribution and parameters for the server time. An empirical distribution was established when there was no known theoretical pure distribution. However, when the empirical distribution is used, the queuing system is tried to be represented by the normal mixture distribution approach. Because the empirical distribution takes a long time to produce, especially if there is a certain amount of data accumulation. The number of components has been determined with the aid of P-P, Q-Q plot, Akaike and Bayesian information criteria. After estimating the number of components, the mean, standard deviation, and mixture proportion parameter of each component were calculated using the Expectation-Maximization algorithm. The queuing times calculated by normal mixture distribution and empirical distribution approaches were compared with the theoretical results and their performance was evaluated. Keywords: Mixture Distribution, Pure Distribution, Queue Theory, Expectation-Maximization Algorithm