A DISTRIBUTION FOR SERVICE MODEL

Abstract

In this paper, we show a distribution that describes a specific system. The system has a single server, a heavy traffic and a fast service. In addition, there is an adjustment mechanism when the number of customers increases. This distribution we call the Maximum-Conway-Maxwell-Poisson-Weibull distribution, denoted by MAXCOMPW distribution. The MAXCOMPW distribution is obtained by compound distributions in which we use the zero truncated Conway-Maxwell-Poisson distribution and the Weibull distribution. The MAXCOMPW distribution contains sub-models that describe the variations of the system, such as, Maximum-geometric-Weibull distribution, Maximum-Poisson-Weibull distribution and Maximum-Bernoulli-Weibull distribution. The properties of the proposed distribution are discussed, including formal proof of its density function and explicit algebraic formulas for their reliability function and moments. The parameter estimation is based on the usual maximum likelihood method. Simulated and real data are used to illustrate the applicability of the model.