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Keywords = Kendall notation

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21 pages, 11713 KiB  
Article
Minimizing Intersection Waiting Time: Proposal of a Queue Network Model Using Kendall’s Notation in Panama City
by Carlos Rovetto, Edmanuel Cruz, Ivonne Nuñez, Keyla Santana, Andrzej Smolarz, José Rangel and Elia Esther Cano
Appl. Sci. 2023, 13(18), 10030; https://doi.org/10.3390/app131810030 - 6 Sep 2023
Cited by 3 | Viewed by 3296
Abstract
The paper presents a proposed queuing model based on Kendall’s notation for the intersection of two streets in Panama City (53 East and 56 East). The proposed model is based on a set of traffic lights that controls the flow of vehicles at [...] Read more.
The paper presents a proposed queuing model based on Kendall’s notation for the intersection of two streets in Panama City (53 East and 56 East). The proposed model is based on a set of traffic lights that controls the flow of vehicles at the intersection according to a predetermined schedule. The model analyzes the stability of the system and simulations are performed to evaluate its performance. The main objective of the paper is to optimize the vehicle flow by minimizing the waiting time for passage. In the study, it was observed that the current traffic light system on Calle 50 (50th Street) is unstable and oversaturated during weekdays, which generates large vehicle queues with no estimated exit times. It was proposed to increase the system capacity to 1300 vehicles per hour to achieve reasonable stability and provide a solution to improve traffic signal timing on 50th Street. The need to increase the system capacity has been demonstrated and an optimal value has been suggested. The evaluation of other models and the use of AI can further strengthen the system and improve the prediction accuracy in different traffic scenarios. Full article
(This article belongs to the Special Issue Smart Cities in Applied Sciences)
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11 pages, 2073 KiB  
Article
A New Method for Markovian Adaptation of the Non-Markovian Queueing System Using the Hidden Markov Model
by Ilija Tanackov, Olegas Prentkovskis, Žarko Jevtić, Gordan Stojić and Pamela Ercegovac
Algorithms 2019, 12(7), 133; https://doi.org/10.3390/a12070133 - 28 Jun 2019
Cited by 5 | Viewed by 4939
Abstract
This manuscript starts with a detailed analysis of the current solution for the queueing system M/Er/1/∞. In the existing solution, Erlang’s service is caused by Poisson’s arrival process of groups, but not individual clients. The service of individual clients is still exponentially distributed, [...] Read more.
This manuscript starts with a detailed analysis of the current solution for the queueing system M/Er/1/∞. In the existing solution, Erlang’s service is caused by Poisson’s arrival process of groups, but not individual clients. The service of individual clients is still exponentially distributed, contrary to the declaration in Kendall’s notation. From the related theory of the Hidden Markov Model (HMM), for the advancement of queueing theory, the idea of “hidden Markov states” (HMS) was taken. In this paper, the basic principles of application of HMS have first been established. The abstract HMS states have a catalytic role in the standard procedure of solving the non-Markovian queueing systems. The proposed solution based on HMS exceeds the problem of accessing identical client groups in the current solution of the M/Er/r queueing system. A detailed procedure for the new solution of the queueing system M/Er/1/∞ is implemented. Additionally, a new solution to the queueing system M/N/1/∞ with a normal service time N(μ, σ) based on HMS is also implemented. Full article
(This article belongs to the Special Issue Algorithms for Multi-Criteria Decision-Making)
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