Title :
A new distribution for service model with state dependent service rate
Author :
Prado, Silvia Maria ; Louzada, Francisco ; Rinaldi, Jose Gilberto ; Galvao Benze, Benedito
Author_Institution :
Univ. Fed. de Mato Grosso, Cuiaba, Brazil
Abstract :
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.
Keywords :
Poisson distribution; algebra; customer services; exponential distribution; maximum likelihood estimation; MINCOMPE distribution; explicit algebraic formulas; interarrival times; maximum likelihood method; mean; minimum service time; minimum-Bernoulli-exponential; minimum-Conway-Maxwell-Poisson-exponential distribution; minimum-geometric-exponential; moments; parameter estimation; pressure parameter; reliability; service model; state dependent service rate; superserver; system variability; variance; Acceleration; Equations; Mathematical model; Maximum likelihood estimation; Queueing analysis; Random variables; Reliability; Conway; Maxwell-Poisson distribution; minimum service time; super-server;
Conference_Titel :
Informatics and Applications (ICIA),2013 Second International Conference on
Conference_Location :
Lodz
Print_ISBN :
978-1-4673-5255-0
DOI :
10.1109/ICoIA.2013.6650272