
CMUCS02178
Computer Science Department
School of Computer Science, Carnegie Mellon University
CMUCS02178
Necessary and Sufficient Conditions for Representing
General Distributions by Coxians
Takayuki Osogami, Mor HarcholBalter
September 2002
CMUCS02178.ps
CMUCS02178.pdf
Keywords: Moment matching, Cosian distribution, busy period,
phasetype 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 wellrepresented by an nstage 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 wellrepresented by an nstage Coxian distribution.
30 pages
