Computer Science Department
School of Computer Science, Carnegie Mellon University


Necessary and Sufficient Conditions for Representing
General Distributions by Coxians

Takayuki Osogami, Mor Harchol-Balter

September 2002

Keywords: Moment matching, Cosian distribution, busy period, phase-type distribution, normalized moemnt, queueing, matrix analytic

A common analytical technique involves using a Coxian distribution to model a general distribution G, where the Coxian distribution agrees with G on the first three moments. This technique is motivated by the analytical tractability of the Coxian distribution. Algorithms for mapping an input distribution G to a Coxian distribution largely hinge on knowing a priori the necessary and sufficient number of stages in the representative Coxian distribution. In this paper, we formally characterize the set of distributions G which are well-represented by an n-stage Coxian distribution, in the sense that the Coxian distribution matches the first three moments of G. We also discuss a few common, practical examples. Lastly, we derive a partial characterization of the set of busy period durations which are well-represented by an n-stage Coxian distribution.

30 pages

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