The Moments of the M/M/s Queue Length Process

Authors:
F. Marcellán;G. Pérez
Affiliations:
Departamento de Matemáticas, Universidad Carlos III de Madrid, Avda. de la Universidad 30, 28911, Leganes, Madrid, Spain Pacomarc@ing.uc3m.es;Departamento de Matemática Aplicada a la Telecomunicación, Escuela Universitaria de Ingeniería Técnica de Telecomunicación, Carretera de Valencia 7, 28031, Madrid, Spain < ...
Venue:
Queueing Systems: Theory and Applications
Year:
2003

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Abstract

A representation for the moments of the number of customers in a M/M/s queueing system is deduced from the Karlin and McGregor representation for the transition probabilities. This representation allows us to study the limit behavior of the moments as time tends to infinity. We study some consequences of the representation for the mean.