A new distribution for service model with state dependent service rate

In this paper, we introduced a new distribution for the minimum service time in the system with a superserver, the Minimum-Conway-Maxwell-Poisson-exponential distribution (or MINCOMPE distribution). The service was attached to the arrival. Owing this fact, the service finishes when a customer arrives. The MINCOMPE distribution contains submodels, such as, the Minimum-geometric-exponential, Minimum-Poisson-exponential and Minimum-Bernoulli-exponential. As a result, it incorporates the variability of the system when the pressure parameter changes due to the decrease of the interarrival times. The properties of the proposed distribution were discussed and explicit algebraic formulas for their reliability and moments, including the mean and the variance. The parameter estimation was based on the usual maximum likelihood method. The methodology was illustrated on real data.