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

He, Qi–Ming; Alfa, Attahiru Sule

doi:10.1287/ijoc.2017.0759

Cited by 19 publications

(14 citation statements)

References 11 publications

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“…In this work, the construction of a multi-dimensional Markov chain (MDMC) describing the dynamics of the system, including the proper choice of the components defining the service and retrial processes, is required for the analysis of a multi-server queuing system with PH distributed service and retrial times. There are two different ways, referred to as the TPFS (track-phase-for-server) and CSFP (count-server-for-phase) ( [16]), to keep track of the phases for service and retrial processes. In this work, CSFP approach is employed for the sake of performing computation in an efficient way since it provides comparatively much smaller state space than TSFP.…”

Section: State Of the Artmentioning

confidence: 99%

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

Raj¹,

Jain²

2022

Preprint

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The presented study elaborates a multi-server catastrophic retrial queueing model considering preemptive repeat priority policy with phase-type (PH) distributed retrial times. For the sake of comprehension, the scenario of model operation prior and later to the occurrence of the disaster is referred to as the normal scenario and as the catastrophic scenario, respectively. In the normal scenario, the incoming heterogeneous calls are categorized as handoff calls and new calls. Handoff calls are provided controllable preemptive priority over new calls. In the catastrophic scenario, when a disaster causes the shut down of the entire system and failure of all functioning channels, a set of backup channels is quickly deployed to restore services. Due to the emergency situation in the concerned area, the incoming heterogeneous calls are divided into three categories: handoff, new call, and emergency calls. Emergency calls are provided controllable preemptive priority over new/handoff calls due to the pressing need to save lives in such situations. The Markov chain's ergodicity criteria are established by demonstrating that it belongs to the class of asymptotically quasi-Toeplitz Markov chains (AQTMC). Further, a multi-objective optimization problem to obtain optimal number of backup channels has been formulated and dealt by employing non-dominated sorting genetic algorithm-II (NSGA-II) approach.

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Section: State Of the Artmentioning

confidence: 99%

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

Raj¹,

Jain²

2022

Preprint

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“…Although it has been simply presented in ref. [29] that the order statistics of multidimensional Markov chains is a Markov chain, there are still no specific methods of representing the state space and constructing the transition probability matrix of this Markov chain because of the difficulty of such a problem. The existing literature on Markov chains in the field of wireless communication is briefly given in Table 1.…”

Section: Introductionmentioning

confidence: 99%

Markov chain modelling of ordered Rayleigh fading channels in non‐orthogonal multiple access wireless networks

Chen

Zhang

Zhu

2023

IET Signal Processing

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A first‐order finite‐state Markov chain (FSMC) typically models the Rayleigh fading channel in the open literature because the first‐order FSMC is analytically tractable and can derive closed‐form results. Non‐orthogonal multiple access (NOMA) has been recognised as a novel wireless technology that addresses challenges in the next generation of mobile communications. According to the power‐domain NOMA protocol, channels in the NOMA wireless network are sorted by the channel gain. Then considering NOMA, there is insufficient information on how to further form a suitable model for ordered Rayleigh fading channels based on the first‐order FSMC. Given the mathematical statement on how to model the order statistics of multidimensional Markov chains for ordered Rayleigh fading channels, the authors consider these order statistics as a Markov chain, and propose specific processes of representing the state space and constructing the transition probability matrix accordingly. Numerical and simulation results validate the mathematical correctness and accuracy of these novel processes. In addition, for ordered Rayleigh fading channels, the performances of various methods of partitioning the entire signal‐to‐noise ratio range are compared. The performance comparison results are the same as those obtained for the individual unordered Rayleigh fading channel.

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“…Yevkin 35 proposed an approximate Markov chain method for dynamic FTA to reduce the number of states in the model, but it is fault oriented; when the number of system fault states is large, the analysis is very complex. He and Alfa 36 demonstrated that the space complexity of Markov chains can be significantly reduced by using the count-server-for-phase (CSFP) approach, but the creation of the Markov chains is quite involved.…”

Section: Introductionmentioning

confidence: 99%

Design and reliability analysis of the electrical control system of the subsea control module

Wang

Lizhang

et al. 2019

Proceedings of the Institution of Mechanical Engineers, Part I:

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The subsea control module is the core equipment of the subsea production system, and its electrical control system plays a large role in the failure modes of the subsea control module. Based on a traditional nonredundant programmable logic controller system, a parallel cross-redundancy system is proposed, designed and tested for the electrical control system of the subsea control module to enhance the reliability of the subsea control module within the given space. A success-oriented system decomposition method is proposed on the basis of the reliability block diagram and system logical relationship that effectively reduces the system dimension and solves the problem of the system state-space explosion caused by the number of system components in the Markov model, and the system reliability and mean time to failure models are created. The reliability model is solved by a Markov model successfully. Finally, the redundancy of the system is tested to validate the logical relationship in the reliability model. The reliability and mean time to failure of the system are analyzed in MATLAB. The tests and analysis show that the proposed parallel cross-redundancy system is better than the double hot-standby system, as demonstrated by a higher reliability and longer mean time to failure, and the module failure rate effects have been minimized.

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

Cited by 19 publications

References 11 publications

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

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

Markov chain modelling of ordered Rayleigh fading channels in non‐orthogonal multiple access wireless networks

Design and reliability analysis of the electrical control system of the subsea control module

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