Sensitivity analysis of the expected accumulated reward using Uniformization and IRK3 methods
by
Moulaye Hamza
IRISA, Rennes, FRANCE
Coauthors: Dr. Haiscam Abdallah

keyword - Computing system, Markov process, stiffness, expected accumulated reward, sensitivity, time complexity, uniformization, IRK3

This paper deals with the sensitivity computation of the expected accumulated reward (EAR) of stiff Markov models. The sensitivity of this transient measure is its derivative with respect to a parameter of the infinitesimal generator, such as the failure rate or the repair rate. Generally, we are faced with the problem of computation time, especially when the Markov model is stiff.
We consider two numerical methods : the Standard Uniformization (SU) method, and a the third order Implicit Runge Kutta (IRK3) method.
One of the advantages of the first method is the easiness of expressing the error and thus, finding some errors bounds. In our paper, we propose an error bound for the SU method. As our models are stiff, the computation time of the EAR sensitivity becomes prohibitive for large values of the mission time. We then suggest an Implicit L-stable method, the IRK3 method.
For the IRK3 method, we provide a new way of writing the system of equations, in order to have a system of the form y'=\lambday, where \lambda is a constant, and we then apply the IRK3 method with a stepsize choice different from the classical one. The new stepsize choice accelerates the execution of the IRK3 algorithm.
We illustrate our results via a concrete example. The computation time is given for different values of the mission time for each methods and both of the two methods are compared. We conclude that the SU method performs well for small values of the mission time whereas the IRK3 method is more efficient for large values.

Date received: January 19, 2000

Copyright © 2000 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caeb-05.