A Distribution for Service Model

Silvia Prado, Francisco Louzada, Gilberto Rinaldi, Benedito Galvão Benze
In this paper, we developed a flexible service model for the minimum service time called Minimum-Conway-Maxwell-Poisson-exponential distribution, denoted by MINCOMPE distribution , with the service rate dependent on the state of the system including the idle period. This distribution is a new approach where it is possible to look only at the service and capture variations of the system. In addition, this distribution is to model the dependency between the interarrival and service times. The
more » ... vice times. The MINCOMPE distribution contains submodels, such as Minimum-geometric-exponential, Minimum-Poisson-exponential and Minimum-Bernoulli-exponential, which express variations of the system. The properties of the proposed distribution are discussed, including formal proof of its probability density function and explicit algebraic formulas for their reliability and moments. The parameter estimation is based on the usual maximum likelihood method. Simulated and real data are shown to illustrate the applicability of the model.