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Implicit ODE solvers with good local error control for the transient analysis of Markov models

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  • Suñé, Víctor
  • Carrasco, Juan Antonio

Abstract

Obtaining the transient probability distribution vector of a continuous-time Markov chain (CTMC) using an implicit ordinary differential equation (ODE) solver tends to be advantageous in terms of run-time computational cost when the product of the maximum output rate of the CTMC and the largest time of interest is large. In this paper, we show that when applied to the transient analysis of CTMCs, many implicit ODE solvers are such that the linear systems involved in their steps can be solved by using iterative methods with strict control of the 1-norm of the error. This allows the development of implementations of those ODE solvers for the transient analysis of CTMCs that can be more efficient and more accurate than more standard implementations.

Suggested Citation

  • Suñé, Víctor & Carrasco, Juan Antonio, 2017. "Implicit ODE solvers with good local error control for the transient analysis of Markov models," Applied Mathematics and Computation, Elsevier, vol. 293(C), pages 96-111.
    • Handle: RePEc:eee:apmaco:v:293:y:2017:i:c:p:96-111
    DOI: 10.1016/j.amc.2016.08.009
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    References listed on IDEAS

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    1. Sidje, Roger B. & Stewart, William J., 1999. "A numerical study of large sparse matrix exponentials arising in Markov chains," Computational Statistics & Data Analysis, Elsevier, vol. 29(3), pages 345-368, January.
    2. Donald Gross & Douglas R. Miller, 1984. "The Randomization Technique as a Modeling Tool and Solution Procedure for Transient Markov Processes," Operations Research, INFORMS, vol. 32(2), pages 343-361, April.
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