Estimating the parameters of the two-parameter Weibull distribution and their impact on the performance measures of the M/G/1 queuing system - A case study

According to the evolution of programming technology, the study of queueing system and simulations have become complementary in providing an overall picture of a system. When considering the future role of simulation in the communication sector, it must be considered as part of the overall solution. A simulation gives a more realistic picture of the systems from a variety of angles, allowing for fewer assumptions and more accurate results, while not oversimplifying certain parts. Due to the difficulty of determining the number of arriving customers and the time required to provide service in a call center, performance measurements must be obtained prior to implementing the queuing system, as well as an understanding the effect of the estimation methods assuming the parameter to be measured is constant. The practical section includes the application of the Monte Carlo (MC) simulation in the generation of data for the Weibull distribution with two parameters. We used two methods of parameter estimation for the distribution's parameters: Ordinary Least Square (OLS) and Maximum Likelihood Estimator (MLE) with statistical measures Mean Square Error (MSE) to determine the best model estimation method. The distribution of the service time data was determined using the Easyfit5.5 and tests of good conformity. The study used real data from the Customer Service Center at the Communications and Informatics Company, one of the Ministry of Communications companies. The results indicate that the M/G/1 Queue model is data conformant. Additionally, the simulation results showed that the MLE method is the optimal method for parameter estimation because it achieves the lowest mean square error and sample size has an effect on the estimated values.