Algorithms for computing moments of the length of busy periods of single-server systems

Authors:
António Pacheco;Helena Ribeiro
Affiliations:
Department of Mathematics and CEMAT, Instituto Superior Técnico, Lisboa, Portugal;Department of Mathematics and CEMAT, Instituto Politécnico de Leiria, Leiria, Portugal
Venue:
ICCOMP'06 Proceedings of the 10th WSEAS international conference on Computers
Year:
2006

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Abstract

We compute moments of the length of the busy period of MX/G/1/n systems starting with an arbitrary number of customers in the system using a recursive algorithm that is based on the fact that the length of a busy period initiated by multiple customers in a system of some fixed capacity can be expressed in terms of the lengths of busy periods of systems with smaller or equal capacities and initiated by a single customer. The computational complexity of the algorithm proposed in the paper is derived and numerical examples provided.