Transient analysis of acyclic markov chains
Performance Evaluation
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
The uniformed power method for transient solutions of Markov processes
Computers and Operations Research
Regenerative randomization: theory and application examples
Proceedings of the 1995 ACM SIGMETRICS joint international conference on Measurement and modeling of computer systems
A computationally efficient technique for transient analysis of repairable Markovian systems
Performance Evaluation
Point and expected interval availability analysis with stationarity detection
Computers and Operations Research
Sensitivity analysis via likelihood ratios
WSC '86 Proceedings of the 18th conference on Winter simulation
Stochastic approximation for Monte Carlo optimization
WSC '86 Proceedings of the 18th conference on Winter simulation
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 Markov models. Very often, we are facing the problem of the computation time, especially when the Markov process is stiff. We consider the standard uniformization method for which the global error may be easily bounded. 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. This method is interesting for stiff Markov models but unfortunately, it is difficult to control the global error. We propose a new approach based on the uniformized power technique. This method will save computation time if the mission time is long and the state space is not too large. Moreover, this method integrates an efficient error control mechanism. The time complexities of the three methods are compared via a concrete example.