The Dynamic Adjusting Model of Traffic Queuing Time—A Monte Carlo Simulation Study
Abstract
:1. Introduction
2. Literature Review
3. Methodology
3.1. The Dynamic Adjusting Model of Traffic Queuing Time
3.1.1. The Notations
ARt,i | The real-time-accumulated vehicles of ith intersection road at period t. |
ALC t,i | The average length of the vehicles of ith intersection road at period t. |
CIt,i | The reaching vehicles of ith intersection road at period t. |
COt,i | The reducing number of vehicles of ith intersection road at period t. |
MAXt,j | Maximum length of jth reaching vehicle at period t. |
MINt,j | Minimum length of jth reaching vehicle at period t. |
N | The average passing time of the vehicles. |
PT | The time of the traffic light changed from green to red. |
RTt,i | The road capacity of vehicles of ith intersection road at period t. |
Rt,i | The length of ith intersection road at period t. |
St,i | The initial time of the traffic light on ith intersection road at period t. |
St+1,i | The adjusting time of the traffic light on ith intersection road at period t + 1. |
SCWt,i | The initial queued vehicles of ith intersection road at period t. |
ΔTt,i | The dynamic adjusting time of green light on ith intersection road at period t. |
3.1.2. The Dynamic Adjusting Model
3.1.3. The Procedure of Monte Carlo Simulation
4. The Monte Carlo Simulation and Experimental Results
4.1. An Illustrative Example of the Dynamic Adjusting Model
4.2. The Procedure of Our Approach
4.3. The Monte Carlo Simulation
4.4. Statistics Regarding Monte Carlo Simulation
4.5. Discussion
5. Conclusions
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
References
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Loading (%) | Length of Vehicle | Initial Seconds | Initial Queued Vehicles | Passing Time | ||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
Scenario | Max | Min | R1 | R2 | R3 | R1 | R2 | R3 | R1 | R2 | R3 | |
1 | 80 | 15 | 10 | 40 | 40 | 40 | 6 | 6 | 6 | 5 | 6 | 7 |
2 | 100 | 20 | 15 | 60 | 40 | 80 | 9 | 6 | 12 | 6 | 7 | 5 |
3 | 120 | 25 | 20 | 80 | 40 | 120 | 12 | 6 | 18 | 7 | 5 | 6 |
4 | 150 | 30 | 10 | 40 | 40 | 40 | 6 | 6 | 6 | 5 | 6 | 7 |
5 | 80 | 15 | 15 | 60 | 40 | 80 | 9 | 6 | 12 | 6 | 7 | 5 |
6 | 100 | 20 | 20 | 80 | 40 | 120 | 12 | 6 | 18 | 7 | 5 | 6 |
7 | 120 | 25 | 10 | 40 | 40 | 40 | 6 | 6 | 6 | 5 | 6 | 7 |
8 | 150 | 30 | 15 | 60 | 40 | 80 | 9 | 6 | 12 | 6 | 7 | 5 |
9 | 80 | 15 | 20 | 80 | 40 | 120 | 12 | 6 | 18 | 7 | 5 | 6 |
10 | 100 | 20 | 10 | 40 | 40 | 40 | 6 | 6 | 6 | 5 | 6 | 7 |
11 | 120 | 25 | 15 | 60 | 40 | 80 | 9 | 6 | 12 | 6 | 7 | 5 |
12 | 150 | 30 | 20 | 80 | 40 | 120 | 12 | 6 | 18 | 7 | 5 | 6 |
(1) | (2) | (3) | (4) | (5) | (6) | (7) | (8) | (9) | (10) | (11) | (12) | (13) | (14) | (15) | (16) | ||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Simulation Runs | i | Rt,i | MAXt,j | MINt,j | C | St,i | PT | N | SCWt,i | CIt,i | COt,i | ALCt,i | RTt,i | ARt,i | ΔTt,i | St+1,i | ΔTt+1,i |
1 | 330 | 20 | 10 | 40 | 40 | 5 | 6 | 13 | 36 | 30 | 15 | 22 | 19 | (−69) | 109 | ↑ | |
1 | 2 | 240 | 15 | 10 | 60 | 60 | 6 | 6 | 10 | 24 | 20 | 13 | 19 | 14 | (−18) | 78 | ↑ |
3 | 850 | 25 | 10 | 75 | 75 | 7 | 6 | 25 | 96 | 80 | 18 | 49 | 41 | (−164) | 239 | ↑ | |
1 | 330 | 25 | 10 | - | 109 | 5 | 6 | 19 | 24 | 30 | 18 | 19 | 13 | 36 | 73 | ↓ | |
2 | 2 | 240 | 20 | 10 | - | 78 | 6 | 6 | 14 | 16 | 20 | 15 | 16 | 10 | 24 | 54 | ↓ |
3 | 850 | 30 | 20 | - | 239 | 7 | 6 | 41 | 64 | 80 | 25 | 34 | 25 | 96 | 143 | ↓ | |
1 | 330 | 20 | 10 | - | 73 | 5 | 6 | 13 | 36 | 30 | 15 | 22 | 19 | (−36) | 109 | ↑ | |
3 | 2 | 240 | 15 | 10 | - | 54 | 6 | 6 | 10 | 16 | 20 | 13 | 19 | 6 | 24 | 30 | ↓ |
3 | 850 | 25 | 15 | - | 143 | 7 | 6 | 25 | 96 | 80 | 20 | 43 | 41 | (−96) | 239 | ↑ |
(1) Reducing Number of Vehicles | (2) The Queued Vehicles | (3) Traffic Jam Amount | (4) Traffic Jam Time | |
---|---|---|---|---|
Average rate for FIFO (%) | 9.79 | 24.68 | 1.35 | 1570.6 |
Standard deviation for FIFO (%) | 2.27 | 10.02 | 0.08 | 91.54 |
Average rate for the dynamic adjusting queueing model (%) | 15.56 | 20.27 | 0.34 | 1245.9 |
Standard deviation for the dynamic adjusting queueing model (%) | 7.96 | 10.79 | 0.09 | 88.43 |
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Huang, W.-T.; Dang, J.-F. The Dynamic Adjusting Model of Traffic Queuing Time—A Monte Carlo Simulation Study. Appl. Sci. 2020, 10, 6364. https://doi.org/10.3390/app10186364
Huang W-T, Dang J-F. The Dynamic Adjusting Model of Traffic Queuing Time—A Monte Carlo Simulation Study. Applied Sciences. 2020; 10(18):6364. https://doi.org/10.3390/app10186364
Chicago/Turabian StyleHuang, Wen-Tso, and Jr-Fong Dang. 2020. "The Dynamic Adjusting Model of Traffic Queuing Time—A Monte Carlo Simulation Study" Applied Sciences 10, no. 18: 6364. https://doi.org/10.3390/app10186364