A solution to the fixed-cycle traffic light problem for compound Poisson arrivals

1968 ◽  
Vol 5 (3) ◽  
pp. 624-635 ◽  
Author(s):  
Donald R. McNeil
Keyword(s):  
Traffic Flow ◽  
Cycle Time ◽  
Mathematical Theory ◽  
Basic Problem ◽  
Arrival Process ◽  
Traffic Light ◽  
Compound Poisson ◽  
Factors Affecting ◽  
Poisson Arrivals ◽  
Pass Through

A basic problem in the mathematical theory of traffic flow is to obtain the expected delay to a vehicle at a fixed-cycle traffic light controlling an intersection. The factors affecting this expected delay are the cycle time, the fraction of time the traffic light is effectively red, the number of vehicles which can pass through when the signal is green, and the nature of the (random) arrival process for the vehicles. Once a solution is known, it is possible to fix the cycle time and the effective red period in such a way that the expected delay is minimized.

A solution to the fixed-cycle traffic light problem for compound Poisson arrivals

1968 ◽  
Vol 5 (03) ◽  
pp. 624-635 ◽  
Author(s):  
Donald R. McNeil
Keyword(s):  
Traffic Flow ◽  
Cycle Time ◽  
Mathematical Theory ◽  
Basic Problem ◽  
Arrival Process ◽  
Traffic Light ◽  
Compound Poisson ◽  
Factors Affecting ◽  
Poisson Arrivals ◽  
Pass Through

A basic problem in the mathematical theory of traffic flow is to obtain the expected delay to a vehicle at a fixed-cycle traffic light controlling an intersection. The factors affecting this expected delay are the cycle time, the fraction of time the traffic light is effectively red, the number of vehicles which can pass through when the signal is green, and the nature of the (random) arrival process for the vehicles. Once a solution is known, it is possible to fix the cycle time and the effective red period in such a way that the expected delay is minimized.

The fixed cycle traffic light problem: a note on a paper by Mcneil

1970 ◽  
Vol 7 (01) ◽  
pp. 245-248 ◽  
Author(s):  
Victor Siskind
Keyword(s):  
Poisson Process ◽  
Cycle Time ◽  
Compound Poisson Process ◽  
Constant Time ◽  
Traffic Light ◽  
Compound Poisson ◽  
Light Green ◽  
Light Form

Both paper and author (D. R. McNeil, (1968)) will be referred to below as DRM. The said paper deals with the following situation: an intersection is controlled by a traffic light with a fixed cycle time, T; the possibility of other delays, e.g., due to turning vehicles, is ignored; arrivals at the light form a compound Poisson process; if vehicles arrive to find the light green and the queue empty they are not delayed, while in the contrary case they depart when they reach the head of the queue, providing the light is green, each vehicle taking a constant time to move off. The length of the effective red period is R. For further details and discussion, DRM may be consulted.

The fixed cycle traffic light problem: a note on a paper by Mcneil

1970 ◽  
Vol 7 (1) ◽  
pp. 245-248 ◽  
Author(s):  
Victor Siskind
Keyword(s):  
Poisson Process ◽  
Cycle Time ◽  
Compound Poisson Process ◽  
Constant Time ◽  
Traffic Light ◽  
Compound Poisson ◽  
Light Green ◽  
Light Form

Both paper and author (D. R. McNeil, (1968)) will be referred to below as DRM. The said paper deals with the following situation: an intersection is controlled by a traffic light with a fixed cycle time, T; the possibility of other delays, e.g., due to turning vehicles, is ignored; arrivals at the light form a compound Poisson process; if vehicles arrive to find the light green and the queue empty they are not delayed, while in the contrary case they depart when they reach the head of the queue, providing the light is green, each vehicle taking a constant time to move off. The length of the effective red period is R. For further details and discussion, DRM may be consulted.

scholarly journals Optimization of cycle time on signalized intersections of H.E.A Mokodompit Street – M.T Haryono – H.A. Nasution Kendari city based on traffic flow volume

2021 ◽  
Vol 1 (1) ◽  
pp. 039-048
Author(s):  
Ridwan Syah Nuhun ◽  
Usman Rianse ◽  
Marsuki Iswandi ◽  
Adris Ade Putra ◽  
Abdul Kadir ◽  
...  
Keyword(s):  
Traffic Flow ◽  
Cycle Time ◽  
Traffic Control ◽  
Service Level ◽  
Light Signal ◽  
Signalized Intersections ◽  
Degree Of Saturation ◽  
Traffic Light ◽  
The North ◽  
Control Light

Intersection of H.E.A. Mokodompit Street – M.T. Haryono – H.A. Nasution is one of the signalized intersections in Kendari City which has congestion problems, vehicle accumulation and vehicle queues at each arm of the intersection at rush hour due to the large volume of traffic flow and not optimal cycle timing from the traffic light signal. The purpose of this study is to optimize the cycle time of traffic control light signals based on traffic volume and to analyze the performance of these intersections. The results of the analysis based on the volume of traffic flow obtained the optimal cycle time of 72 seconds with the division of green time in each approach by 18 seconds for the north approach, 14 seconds for the eastern approach and 28 seconds for the south approach. The degree of saturation at each intersection arm is 0.82 which is at the service level D.

An analysis of the fixed-cycle traffic-light problem

1981 ◽  
Vol 18 (03) ◽  
pp. 672-683 ◽  
Author(s):  
Richard Cowan
Keyword(s):  
Arrival Process ◽  
Traffic Light ◽  
Traffic Lights ◽  
Poisson Arrival ◽  
Pass Through ◽  
Poisson Arrival Process

A realistic non-Poisson arrival process is used in a model for intersections controlled by fixed-cycle traffic lights. Average delays, queue sizes and percentage of delayed vehicles are derived. The distribution of the number of vehicles which pass through during the green phases is found. Certain model anomalies which are inherent in earlier work are eliminated by the use of this model.

An analysis of the fixed-cycle traffic-light problem

1981 ◽  
Vol 18 (3) ◽  
pp. 672-683 ◽  
Author(s):  
Richard Cowan
Keyword(s):  
Arrival Process ◽  
Traffic Light ◽  
Traffic Lights ◽  
Poisson Arrival ◽  
Pass Through ◽  
Poisson Arrival Process

A realistic non-Poisson arrival process is used in a model for intersections controlled by fixed-cycle traffic lights. Average delays, queue sizes and percentage of delayed vehicles are derived. The distribution of the number of vehicles which pass through during the green phases is found. Certain model anomalies which are inherent in earlier work are eliminated by the use of this model.

scholarly journals Formation of the Traffic Flow Rate under the Influence of Traffic Flow Concentration in Time at Controlled Intersections in Tyumen, Russian Federation

2021 ◽  
Vol 13 (15) ◽  
pp. 8324
Author(s):  
Viacheslav Morozov ◽  
Sergei Iarkov
Keyword(s):  
Traffic Flow ◽  
Flow Rate ◽  
Traffic Congestion ◽  
Traffic Management ◽  
System Analysis ◽  
Motor Vehicle ◽  
Experimental Studies ◽  
Transport Systems ◽  
Experiment Planning ◽  
Traffic Light

Present experience shows that it is impossible to solve the problem of traffic congestion without intelligent transport systems. Traffic management in many cities uses the data of detectors installed at controlled intersections. Further, to assess the traffic situation, the data on the traffic flow rate and its concentration are compared. Latest scientific studies propose a transition from spatial to temporal concentration. Therefore, the purpose of this work is to establish the regularities of the influence of traffic flow concentration in time on traffic flow rate at controlled city intersections. The methodological basis of this study was a systemic approach. Theoretical and experimental studies were based on the existing provisions of system analysis, traffic flow theory, experiment planning, impulses, probabilities, and mathematical statistics. Experimental data were obtained and processed using modern equipment and software: Traficam video detectors, SPECTR traffic light controller, Traficam Data Tool, SPECTR 2.0, AutoCad 2017, and STATISTICA 10. In the course of this study, the authors analyzed the dynamics of changes in the level of motorization, the structure of the motor vehicle fleet, and the dynamics of changes in the number of controlled intersections. As a result of theoretical studies, a hypothesis was put forward that the investigated process is described by a two-factor quadratic multiplicative model. Experimental studies determined the parameters of the developed model depending on the directions of traffic flow, and confirmed its adequacy according to Fisher’s criterion with a probability of at least 0.9. The results obtained can be used to control traffic flows at controlled city intersections.

Effect of pedestrian traffic light on traffic flow accompany with pedestrian crossing

2021 ◽  
pp. 126059
Author(s):  
Yanhong Wang ◽  
Chong Zhang ◽  
Pengbin Ji ◽  
Tianning Si ◽  
Zhenzhen Zhang
Keyword(s):  
Traffic Flow ◽  
Traffic Light ◽  
Pedestrian Traffic ◽  
Pedestrian Crossing

scholarly journals Fractal Dynamical Model of Vehicular Traffic Flow within the Local Fractional Conservation Laws

2014 ◽  
Vol 2014 ◽  
pp. 1-5 ◽  
Author(s):  
Long-Fei Wang ◽  
Xiao-Jun Yang ◽  
Dumitru Baleanu ◽  
Carlo Cattani ◽  
Yang Zhao
Keyword(s):  
Fractional Calculus ◽  
Conservation Laws ◽  
Traffic Flow ◽  
Mathematical Theory ◽  
Conservation Equation ◽  
Vehicular Traffic ◽  
New Model ◽  
Local Fractional Calculus ◽  
Vehicular Traffic Flow ◽  
Fractal Network

We suggest a new model of the scale conservation equation in the mathematical theory of vehicular traffic flow on the fractal network based on the local fractional calculus.

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