# Space Reduction for a Class of Multidimensional Markov Chains: A Summary and Some Applications

@article{He2018SpaceRF, title={Space Reduction for a Class of Multidimensional Markov Chains: A Summary and Some Applications}, author={Qiming He and Attahiru Sule Alfa}, journal={INFORMS J. Comput.}, year={2018}, volume={30}, pages={1-10} }

In this paper, we present examples of a class of Markov chains that occur frequently, but whose associated matrices are a challenge to construct efficiently. These are Markov chains that arise as a result of several identical Markov chains running in parallel. Specifically for the cases considered, both the infinitesimal generator matrix for the continuous case, and more so the transition probability matrix for the discrete equivalent, are complex to construct effectively and efficiently. We…

## 12 Citations

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A multi-server catastrophic retrial queueing model considering preemptive repeat priority policy with phase-type (PH) distributed retrial times and Behaviour of the proposed system is modelled by the level-dependent-quasi birth death (LDQBD) process.

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### Optimization of Traffic Control in MMAP[c]/PH[c]/S Catastrophic Queueing Model with PH Retrial Times and Controllable Preemptive Repeat Priority Policy

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A multi-server catastrophic retrial queueing model considering preemptive repeat priority policy with phase-type ( PH ) distributed retrial times and the Markov chain’s ergodicity criteria are established by demonstrating that it belongs to the class of asymptotically quasi-Toeplitz Markov chains (AQTMC).

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