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
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.