Numerical transient analysis of Markov models
Computers and Operations Research
Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
A computationally efficient technique for transient analysis of repairable Markovian systems
Performance Evaluation
Probability and Statistics with Reliability, Queuing and Computer Science Applications
Probability and Statistics with Reliability, Queuing and Computer Science Applications
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This paper deals with the sensitivity computation of the expected accumulated reward of stiff Markov Models. Generally, we are faced with the problem of computation time, especially when the Markov process is stiff. We consider the standard uniformization method for which we propose a new error bound. Because the time complexity of this method becomes large when the stiffness increases, we then suggest an ordinary differential equations method, the third order implicit Runge-Kutta method. After providing a new way of writing the system of equations to be solved, we apply this method with a stepsize choice different from the classical one in order to accelerate the algorithm execution. Finally, we compare the time complexity of both of the methods on a numerical example.