# 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

Two Extensions of Kingman's GI/G/1 Bound

- MathematicsAbstracts of the 2019 SIGMETRICS/Performance Joint International Conference on Measurement and Modeling of Computer Systems
- 2019

Simulations show that the bounds on waiting time distributions are almost exact in heavy-traffic, including the cases of 1) heterogeneous input, e.g., mixing Weibull and Erlang-k classes and 2) Generalized Markovian Arrival Processes, a new class extending the Batch Markovians Arrival processes to continuous batch sizes.

Two Extensions of Kingman's GI/G/1 Bound

- MathematicsProc. ACM Meas. Anal. Comput. Syst.
- 2018

Simulations show that the bounds on waiting time distributions are almost exact in heavy-traffic, including the cases of 1) heterogeneous input, e.g., mixing Weibull and Erlang-k classes and 2) Generalized Markovian Arrival Processes, a new class extending the Batch Markovians Arrival processes to continuous batch sizes.

Point of queue size change analysis of the PH/PH/k system with heterogeneous servers

- Mathematics, Computer ScienceOper. Res. Lett.
- 2017

Multi-Layer MMFF Processes and the MAP/PH/K+GI Queue: Theory and Algorithms

- Computer Science
- 2019

This paper combines the MMFF approach and the count-server-for-phase (CSFP) method to make it possible to analyze it, and to develop an algorithm for computing queueing quantities related to customer abandonment, waiting times, and queue lengths.

Retrial multi-server queuing system with PHF service time distribution as a model of a channel with unreliable transmission of information

- Computer ScienceApplied Mathematical Modelling
- 2019

Problem of Calculation of Reliability of Hierarchical Complex Technical Systems

- EngineeringLecture Notes in Mechanical Engineering
- 2019

An algorithm for assessing reliability based on dividing a complex object into elements, the evaluation of the reliability of which is determined by one of the most suitable methods, such as the Markov models of states and transitions or statistical models, has been developed.

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

- Computer ScienceArXiv
- 2022

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.

Optimization of traffic control in $ MMAP\mathit{[2]}/PH\mathit{[2]}/S$ priority queueing model with $ PH $ retrial times and the preemptive repeat policy

- Computer ScienceJournal of Industrial & Management Optimization
- 2022

A multi-server priority queueing model considering the preemptive repeat policy and phase-type distribution for retrial process and an optimization problem for optimal channel allocation and traffic control has been formulated and dealt by employing appropriate heuristic approaches.

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

- Computer ScienceArXiv
- 2022

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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