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Time Cost Optimization at Single-Signalized Intersections Based on the Energy–Energy Flux Model

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Abstract

Traffic waves occur when the density of vehicles exceeds a critical threshold, and traffic management draws more and more attention due to the increasing need to alleviate traffic congestion in metropolises. In the present study, energy–energy flux models were introduced into the modeling of start and stop waves of vehicles, based on analysis of characteristics of traffic waves. An indicator system was established to evaluate the service quality of single-signalized intersections. The results showed that under given time costs the service quality was negatively correlated to the energy and the absolute value of energy flux of the stop wave, which highlights the need to optimize the time cost. To this end, we built a stop-wave time cost model on the basis of the energy–energy flux models and simulation data. The model was then optimized by the formulation of a multi-objective optimization problem that can be solved by adjusting the parameters of the \(fgoalattain\) function in Matlab. It was found that under certain constraints, the optimal service quality was achieved when the traffic signal cycle length was 150 s and green/cycle ratio was 0.5; with the aid of optimization, the average energy density of the stop wave reduced by 37.10%, while the energy flux density increased by 1.50%. Additionally, the \(Elman\) algorithm was employed to forecast the energy and energy flux of the stop wave, the forecast error of which was controlled within 5% under the optimal time cost. A visualization window to monitor the single-signalized intersection was produced to improve the service quality. It is therefore expected that main findings from current study may contribute to promoting construction of intelligent traffic management systems.

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Data Availability

All data generated or analyzed during this study are included in this article.

Abbreviations

\({u}_{w}\) :

Traffic wavfront velocity wavefront

\({k}_{i}\) :

Traffic density, \(i=\text{1,2}\)

\({k}_{j}\) :

The jammed traffic density

\({u}_{i}\) :

Traffic average speed, \(i=\text{1,2}\)

\({q}_{i}\) :

Traffic flow rate, \(i=\text{1,2}\)

\({\eta }_{i}\) :

Standard traffic density for neighboring zone, \(i=\text{1,2}\)

\(c\) :

Traffic signal cycle

r:

Red traffic signal interval

g:

Green traffic signal interval

\(dm\) :

Volume element

\(dV\) :

Speed element

\(m\) :

The mass

\(v\) :

The vibration velocity

\(\rho\) :

The density

\(V\) :

The volume

\(f\) :

Frequency

\(T\) :

Cycle

\(k\) :

Restoring force coefficient of the oscillation system

\(A\) :

Amplitude

\(\omega\) :

Angular frequency or the circular frequency

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Authors and Affiliations

  1. Jiangsu University of Science and Technology, Zhenjiang, 212100, Jiangsu, China

    Zhe-yi Su & Jun-min Wu

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  1. Zhe-yi Su
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Correspondence to Zhe-yi Su.

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Su, Zy., Wu, Jm. Time Cost Optimization at Single-Signalized Intersections Based on the Energy–Energy Flux Model. Wireless Pers Commun 126, 3515–3541 (2022). https://doi.org/10.1007/s11277-022-09877-7

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