Abstract
We apply the external uniformization (EU) method for the transient study of continuous-time Markov chain models in which the transition rates could be either constant or time-dependent. In the method, we run an exponential clock for watching the Markov chain. Each realization epoch of the random clock is considered as an absorption epoch. The approximate transient probability that the Markov chain is found at a particular state is then found as the probability of absorption from that state. The convergence of the method to the analytical value has been proved. In the case of infinite/huge dimensional Markov chains, implementation of the method needs truncation of the state-space into a finite window of states. A comparison of the results obtained using the EU method with some of the existing analytical results shows that the described method produces highly accurate results on numerical implementation. Several examples considered also reveal that the EU method required much less computational time when compared to the uniformization/randomization (U/R) method.
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Viswanath, N.C. Transient study of Markov models with time-dependent transition rates. Oper Res Int J 22, 2209–2243 (2022). https://doi.org/10.1007/s12351-020-00613-2
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DOI: https://doi.org/10.1007/s12351-020-00613-2