
CMUCS03114
Computer Science Department
School of Computer Science, Carnegie Mellon University
CMUCS03114
A Closedform Solution for Mapping
General Distributions to Minimal PH Distributions
Takayuki Osogami, Mor HarcholBalter
February 2003
CMUCS03114.ps
CMUCS03114.pdf
Keywords:Closed form, algorithm, moment matching, Coxian
distribution, phasetype distirbution, EC distribution, normalized
moment, matrix analytic
Approximating general distributions by phasetype (PH) distributions
is a popular technique in queueing analysis, since the Markovian
property of PH distributions often allows analytical tractability.
This paper proposes an algorithm for mapping a general distribution G
to a PH distribution where the goal is to find a PH distribution which
matches the first three moments of G. Since efficiency of the
algorithm is of primary importance, we first define a particular
subset of the PH distributions, which we refer to as EC
distributions. The class of EC distributions has very few free
parameters, which narrows down the search space, making the algorithm
efficient  In fact we provide a closedform solution for the
parameters of the EC distribution. Our solution is general in that it
applies to any distribution whose first three moments can be matched
by a PH distribution. Also, our resulting EC distribution requires a
nearly minimal number of phases, always within one of the minimal
number of phases required by any acyclic PH distribution.
Lastly, we discuss numerical stability of our solution.
25 pages
