Uniformization and hybrid simulation/analytic models of renewal processes
Operations Research
Computing Poisson probabilities
Communications of the ACM
Numerical transient analysis of Markov models
Computers and Operations Research
Computing bounds on steady state availability of repairable computer systems
Journal of the ACM (JACM)
Probability, stochastic processes, and queueing theory: the mathematics of computer performance modeling
Simulation Modeling and Analysis
Simulation Modeling and Analysis
Numerical Solution of Non-Homogeneous Markov Processes through Uniformization
Proceedings of the 12th European Simulation Multiconference on Simulation - Past, Present and Future
Continuous System Simulation
Computing Battery Lifetime Distributions
DSN '07 Proceedings of the 37th Annual IEEE/IFIP International Conference on Dependable Systems and Networks
Numerical analysis of continuous time Markov decision processes over finite horizons
Computers and Operations Research
Product Form Approximation of Transient Probabilities in Stochastic Reaction Networks
Electronic Notes in Theoretical Computer Science (ENTCS)
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Inhomogeneous continuous-time Markov chains play an important role in different application areas. In contrast to homogeneous continuous-time Markov chains, where a large number of numerical analysis techniques are available and have been compared, few results about the performance of numerical techniques in the inhomogeneous case are known. This paper presents a new variant of the uniformization technique, the most efficient approach for homogeneous Markov chains. The new uniformization technique allows for the stable computation of strict bounds for the transient distribution of inhomogeneous continuous-time Markov chains, which is not possible with other numerical techniques that provide only an approximation of the distribution and asymptotic bounds. Furthermore, another variant of uniformization is presented that computes an approximation of the transient distribution and is shown to outperform standard differential equation solvers if transition rates change slowly.