Markov and Semi-Markov Chains, Processes, Systems, and Emerging Related Fields

Vassiliou, P.-C. G.; Georgiou, Andreas C.

doi:10.3390/math9192490

Cited by 6 publications

(4 citation statements)

References 21 publications

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“…However, an important fact ignored by current research is that the Pearson correlation coefficient between traffic flow samples is actually distributed in a large range [0. 4,1]. This shows that the correlation strength of traffic flow samples fluctuates greatly with different detectors and weekdays.…”

Section: Correlation Analysis Of Traffic Flow Datamentioning

confidence: 87%

“…Navigation map can only collect traffic information by acquiring users' basic information, but it obviously can't describe the real traffic. According to the characteristics of the expressway system, the expressway company can use its own system data to perfectly describe the real-time operation status of the road network, and provide a more reasonable and feasible vehicle path planning application [1].…”

Section: Introductionmentioning

confidence: 99%

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A Real Time Traffic Flow Model Based on Deep Learning

2022

KSII TIIS

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Urban development has brought about the increasing saturation of urban traffic demand, and traffic congestion has become the primary problem in transportation. Roads are in a state of waiting in line or even congestion, which seriously affects people's enthusiasm and efficiency of travel. This paper mainly studies the discrete domain path planning method based on the flow data. Taking the traffic flow data based on the highway network structure as the research object, this paper uses the deep learning theory technology to complete the path weight determination process, optimizes the path planning algorithm, realizes the vehicle path planning application for the expressway, and carries on the deployment operation in the highway company. The path topology is constructed to transform the actual road information into abstract space that the machine can understand. An appropriate data structure is used for storage, and a path topology based on the modeling background of expressway is constructed to realize the mutual mapping between the two. Experiments show that the proposed method can further reduce the interpolation error, and the interpolation error in the case of random missing is smaller than that in the other two missing modes. In order to improve the real-time performance of vehicle path planning, the association features are selected, the path weights are calculated comprehensively, and the traditional path planning algorithm structure is optimized. It is of great significance for the sustainable development of cities.

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Section: Correlation Analysis Of Traffic Flow Datamentioning

confidence: 87%

Section: Introductionmentioning

confidence: 99%

A Real Time Traffic Flow Model Based on Deep Learning

2022

KSII TIIS

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“…However, in the classification phase, a deviation arises. While [17] solely focuses on the calculation of a posteriori probabilities for a given observed connection within each Markovian model, ref. [18] expands upon this by con-sidering both directions of the TCP connection.…”

Section: State Of the Artmentioning

confidence: 99%

Assessment of Communication Resource Allocation by the Transmission Control Protocol for the Target Virtual Connection under Competitive Conditions

Kovtun,

Grochla

et al. 2024

Electronics

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The mathematical framework presented in this article focuses on the controlled-transmission protocol’s asynchronous process of bandwidth allocation for the target virtual connection implemented under competition for communication resources. The studied process is formalized as a two-dimensional discrete Markovian chain, taking into account the distributions of queue lengths of TCP data fragments from competing client nodes. Such a chain describes the dynamics of filling the stack of transmitted but unacknowledged data fragments of the investigated end device. Distributions of the chain states were found for various ratios of the target virtual-connection bandwidth, transmission-protocol parameters, and communication-channel characteristics. Analytical dependencies for computing the performance of the target virtual connection for different operating modes were obtained. The results of experiments conducted based on the obtained analytical constructions showed that the performance of the virtual connection with a selective repeat mode is mainly determined by the data-loss intensity, the queue size distribution in transit nodes, and the ratio between the protocol window size and the route length.

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“…In this respect, it is well known that semi-Markov processes are among the most important modeling techniques for real-world issues in diverse applied fields, like reliability, financial mathematics, earthquake studies, bioinformatics, etc. (see, e.g., [2][3][4][5]). Furthermore, there are valuable theoretical reasons supporting the semi-Markov choice.…”

Section: Introductionmentioning

confidence: 99%

On a Mixed Transient–Asymptotic Result for the Sequential Interval Reliability for Semi-Markov Chains

D’Amico,

Gkelsinis

2024

Mathematics

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In this paper, we are concerned with the study of sequential interval reliability, a measure recently introduced in the literature. This measure represents the probability of the system working during a sequence of nonoverlapping time intervals. In the cited work, the authors proposed a recurrent-type formula for computing this indicator in the transient case and investigated the asymptotic behavior as all the time intervals go to infinity. The purpose of the present work is to further explore the asymptotic behavior when only some of the time intervals are allowed to go to infinity while the remaining ones are not. In this way, we provide a unique indicator that is able to describe the process evolution in the transient and asymptotic cases as well. It is important to mention that this is not a straightforward result since, in order to achieve it, we need to develop several mathematical ingredients that generalize the classical renewal and Markov renewal frameworks. A numerical example illustrates our theoretical results.

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Markov and Semi-Markov Chains, Processes, Systems, and Emerging Related Fields

Abstract: Probability resembles the ancient Roman God Janus since, like Janus, probability also has a face with two different sides, which correspond to the metaphorical gateways and transitions between the past and the future[...]

Cited by 6 publications

References 21 publications

A Real Time Traffic Flow Model Based on Deep Learning

A Real Time Traffic Flow Model Based on Deep Learning

Assessment of Communication Resource Allocation by the Transmission Control Protocol for the Target Virtual Connection under Competitive Conditions

On a Mixed Transient–Asymptotic Result for the Sequential Interval Reliability for Semi-Markov Chains

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