# Investigating the Effect of Network Traffic Signal Timing Strategy with Dynamic Variable Guidance Lanes

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## Abstract

**:**

## 1. Introduction

## 2. Literature Review

#### 2.1. Network Signal Control and Optimization Methods

#### 2.2. Variable Guidance Lane and Its Development

#### 2.3. Conclusions from the Literature Review

## 3. Methodology

#### 3.1. General Framework

#### 3.2. The Two-Step Approach

#### 3.2.1. Vehicle Delay of Road Network

_{ijk}is the vehicle delay in the k lane of the j entrance at the i intersection, (s); ${D}_{ijk}^{\prime}$ is vehicle delay in crossing the intersection of the k lane in the j entrance lane at the i intersection, (s).

_{ijk}is obtained by subtracting the theoretical travel time from the actual travel time, as shown in Formula (2).

_{ijk}is actual queue length of the k lane of the j entrance at the i intersection, (pcu); S

_{ijk}is saturated flow rate of the k lane of the j entrance at the i intersection, (pcu/s). J is the length of each vehicle, (m); v

_{ijk}is the average speed of vehicles in the k lane of the j entrance at the i intersection, (m/s).

_{ijkt}is the vehicle speed of the k lane in the j entrance lane passing through the i intersection, (m/s); v

_{ijk}

_{0}is the initial vehicle speed of the k lane in the j entrance lane passing the i intersection, (m/s); L

_{ijk}is the length of the intersection (the distance from the k lane in the j entrance lane at the i intersection stop line of the upstream entrance to the exit of downstream intersection), (m).

#### 3.2.2. Signal Control Optimization of Road Network

_{n}is lost time of the n phase, (s); y

_{nk}is flow ratio of the k lane in the n phase; N is the number of phases of the i intersection.

_{m}is the common signal cycle in the road network, (s).

- Minimum green time of coordinated phase at critical intersection

_{EGm}is the minimum green time for coordinated phase, (s); l

_{m}is total lost time of the critical intersections, (s); y

_{m}is the coordination phase of critical intersections and the critical traffic flow ratio, (s); Y

_{m}is the sum of the critical traffic flow ratios of each phase at critical intersections, (s).

_{m}= max (y

_{ij−l}, y

_{ij−v}); if d = 0, meaning the variable guidance lane is a going-straight lane, then y

_{m}= max (y

_{ij−sr}, y

_{ij−v}).

_{ij−l}is the flow ratio of the left-turn lane of the j entrance at the i intersection; y

_{ij−v}is the flow ratio of the variable guidance lane of the j entrance at the i intersection; y

_{ij−sr}is the flow ratio of the straight and right-turn lane of the j entrance at the i intersection.

_{n}is traffic flow ratio of phase n at critical intersection.

- Minimum green time of non-coordinated phases at non-critical intersection

_{EGn}is the minimum green time of the n phase in the non-coordinated phases at non-critical intersection, (s); q

_{n}is the critical traffic flow of the n phase in the non-coordinated phase at a non-critical intersection, (pcu/h); S

_{n}is saturated flow of the critical lane of the n phase in the non-coordinated phase at non-critical intersection, (pcu/h); y

_{n}is traffic flow ratio of the critical lane of the n phase in the non-coordinated phase at non-critical intersection; x

_{p}is saturation of non-coordinated phases at non-critical intersections.

_{n}= max (y

_{ij−sr}, y

_{ij−v}); if d = 0, meaning the variable guidance lane is straight lane, then y

_{n}= (y

_{ij−l}, y

_{ij−v}).

- Effective green time of the coordinated phases at non-critical intersections

_{EG}is minimum green time of the coordinated phase, (s); L

_{n}is total lost time at non-critical intersections, (s); K is the total number of the non-coordinated phases at non-critical intersections.

_{i,i+1}is the off-set of the coordinated phase between intersection i and intersection i + 1, (s); L

_{i,i+1}is the distance from the stop line at the entrance of intersection i to the stop line of the intersection i + 1, (m); D

_{i,i+1}is the vehicle delay of the coordinated phase between intersection i and intersection i + 1, (s).

## 4. Numerical Case

#### Case Description

## 5. Result and Discussion

#### 5.1. Effect of Variable Guidance Lanes

Time Period | Total Vehicle Delay (s) | ||
---|---|---|---|

Before Optimization | After Optimization | Vehicle Delay Reduced | |

0:00–6:00 | 92.43 | 75.38 | 18.45% |

6:00–9:00 | 88.88 | 74.11 | 16.61% |

9:00–16:00 | 88.38 | 70.71 | 19.99% |

16:00–19:00 | 82.47 | 67.08 | 18.66% |

19:00–0:00 | 87.18 | 76.41 | 12.35% |

Average | 17.14% |

#### 5.2. Effect of Network Coordinated Signal Control with Variable Guidance Lane

Intersection No. | Time Period | Phase 1 (s) | Phase 2 (s) | Phase 3 (s) | Phase 4 (s) | Cycle (s) | Off-Set (s) |
---|---|---|---|---|---|---|---|

—— | —— | ||||||

1 | 0:00–6:00 | 19 | 25 | 22 | 27 | 93 | - |

6:00–9:00 | 32 | 40 | 24 | 31 | 127 | - | |

9:00–16:00 | 36 | 29 | 24 | 25 | 114 | - | |

16:00–19:00 | 22 | 34 | 27 | 28 | 111 | - | |

19:00–0:00 | 30 | 25 | 19 | 22 | 96 | - | |

2 | 0:00–6:00 | 21 | 26 | 24 | 22 | 93 | 33 |

6:00–9:00 | 25 | 36 | 24 | 42 | 127 | 42 | |

9:00–16:00 | 30 | 32 | 28 | 24 | 114 | 33 | |

16:00–19:00 | 26 | 34 | 28 | 23 | 111 | 43 | |

19:00–0:00 | 20 | 28 | 25 | 23 | 96 | 32 | |

3 | 0:00–6:00 | 18 | 24 | 28 | 23 | 93 | 36 |

6:00–9:00 | 36 | 40 | 28 | 23 | 127 | 46 | |

9:00–16:00 | 30 | 30 | 25 | 29 | 114 | 38 | |

16:00–19:00 | 23 | 27 | 29 | 32 | 111 | 48 | |

19:00–0:00 | 20 | 25 | 28 | 23 | 96 | 33 | |

4 | 0:00–6:00 | 19 | 26 | 28 | 20 | 93 | 35 |

6:00–9:00 | 25 | 35 | 37 | 30 | 127 | 46 | |

9:00–16:00 | 25 | 30 | 32 | 27 | 114 | 34 | |

16:00–19:00 | 23 | 33 | 27 | 28 | 111 | 45 | |

19:00–0:00 | 19 | 28 | 26 | 23 | 96 | 33 |

- -
- The study time length is 15 min;
- -
- The simulation interval length is 3600 s;
- -
- The free speed is 30 km/h;
- -
- Speed limit is 60 km/h;
- -
- The lost time for each phase of all intersections is 2 s;
- -
- Yellow time is 3 s.

Time Period | Vehicle per Delay (s) | ||
---|---|---|---|

Before Optimization | After Optimization | Vehicle Delay Reduced | |

0:00–6:00 | 84.25 | 61.34 | 27.19% |

6:00–9:00 | 79.28 | 57.72 | 27.19% |

9:00–16:00 | 78.91 | 61.82 | 21.66% |

16:00–19:00 | 78.86 | 59.70 | 24.30% |

19:00–0:00 | 79.00 | 58.89 | 25.46% |

Average | 25.06% |

#### 5.3. Results for Each Intersection

Time Period | Intersection No. | Vehicle per Delay (s) | |||||
---|---|---|---|---|---|---|---|

Effect of Variable Guidance Lane | Effects of Network Coordinated Signal Control | ||||||

Before Optimization | After Optimization | Delay Reduced | Before Optimization | After Optimization | Delay Reduced | ||

0:00–6:00 | 1 | 21.31 | 17.38 | 18.44% | 19.84 | 14.29 | 27.97% |

2 | 25.63 | 21.23 | 17.17% | 23.38 | 16.12 | 31.05% | |

3 | 25.12 | 20.04 | 20.22% | 22.41 | 15.25 | 31.95% | |

4 | 20.37 | 16.73 | 17.87% | 18.62 | 15.68 | 15.79% | |

6:00–9:00 | 1 | 21.59 | 19.07 | 11.67% | 19.45 | 13.1 | 32.65% |

2 | 19.11 | 15.58 | 18.47% | 18.56 | 14.27 | 23.11% | |

3 | 24.52 | 20.23 | 17.50% | 21.03 | 14.56 | 30.77% | |

4 | 23.66 | 19.23 | 18.72% | 20.24 | 15.79 | 21.99% | |

9:00–16:00 | 1 | 23.51 | 18.45 | 21.52% | 21.97 | 16.34 | 25.63% |

2 | 21.12 | 17.83 | 15.58% | 17.68 | 14.26 | 19.34% | |

3 | 20.73 | 15.14 | 26.97% | 18.72 | 14.37 | 23.24% | |

4 | 23.02 | 19.29 | 16.20% | 20.54 | 16.85 | 17.96% | |

16:00–19:00 | 1 | 20.42 | 17.16 | 15.96% | 20.11 | 16.27 | 19.09% |

2 | 23.92 | 19.03 | 20.44% | 21.26 | 15.55 | 26.86% | |

3 | 18.98 | 15.59 | 17.86% | 19.35 | 14.67 | 24.19% | |

4 | 19.15 | 15.3 | 20.10% | 18.14 | 13.21 | 27.18% | |

19:00–0:00 | 1 | 22.43 | 19.76 | 11.90% | 20.46 | 14.52 | 29.03% |

2 | 21.05 | 18.64 | 11.45% | 19.27 | 14.69 | 23.77% | |

3 | 25.42 | 21.27 | 16.33% | 20.98 | 16.45 | 21.59% | |

4 | 18.28 | 16.74 | 8.42% | 18.29 | 13.23 | 27.67% | |

Average | 17.14% | 25.06% |

## 6. Sensitive Analysis

## 7. Conclusions, Limitation and Future Work

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## Appendix A

_{u}is the uniform phase queue length, (pcu); N

_{0}is the oversaturated queue length, (pcu); q

_{ijk}is arrival rate of vehicles in the k lane of the j entrance at the i intersection, (pcu/s); v

_{ijk}is the average speed of vehicles in the k lane of the j entrance at the i intersection, (m/s).

_{u}and the over saturated queue length N

_{0}. When queuing vehicles, assuming that the length of each vehicle is J (m), then the actual length of the vehicles in the queue is (N

_{u}+ N

_{0})∗J (m), and the average vehicle speed is v (m/s). The time is (N

_{u}+ N

_{0)}∗J/v (s); S

_{ijk}is saturated flow rate of the k lane of the j entrance at the i intersection, (pcu/s).

_{0}is saturation initial value of the oversaturated queue length function; g

_{eijk}is green light time of the k lane of the j entrance at the i intersection, (s).

_{ijk}, the calculation of the vehicle queue length in lanes is different.

_{i}is the signal cycle of the i intersection, s.

_{ij−l}is the saturation of the left-turn lane of the j entrance at the i intersection; x

_{ij−v}is the saturation of the variable guidance lane of the j entrance at the i intersection; x

_{ij−sr}is the saturation of the straight and right-turn lane of the j entrance at the i intersection; q

_{ij−l}is the actual vehicle arrival rate of the left-turn lane of the j entrance at the i intersection, (pcu/s); q

_{ij−v}is the actual vehicle arrival rate of the variable guidance lane of the j entrance at the i intersection, (pcu/s); q

_{ij−sr}is the actual vehicle arrival rate of the straight and right-turn lane of the j entrance at the i intersection, (pcu/s); Q

_{ij−l}is the capacity of the left-turn lane of the j entrance at the i intersection, (pcu/s); Q

_{ij−v}is the capacity of the variable guidance lane of the j entrance at the i intersection, (pcu/s); Q

_{ij−sr}is the capacity of the straight and right-turn lane of the j entrance at the i intersection, (pcu/s); d

_{ij}is the number of variable guidance lanes of the j entrance at the i intersection.

_{ij−l}is the saturated flow rate of the left-turn lane of the j entrance at the i intersection, (pcu/s); S

_{ij−v}is the saturated flow rate of the variable guidance lane of the j entrance at the i intersection, (pcu/s); S

_{ij−sr}is the saturated flow rate of the straight and right-turn lane of the j entrance at the i intersection, (pcu/s); L

_{i}is the total lost time of vehicles at the i signal control intersection, s; y

_{n}is flow ratio of the n phase; Y

_{i}is the total flow ratio of the i intersection.

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**Figure 1.**An Example of Variable Guidance Lane. (可变车道: variable guidance lane; 左转: turn left; 直行: go straight; 六日, 法定节假日, 寒暑假期间全天直行: Saturday, Sunday, Holidays, Winter and Summer Vacations go straight all day).

**Figure 3.**The distribution of lanes at the entrances of the road network. (1–4 represent the number and order of intersections).

**Figure 4.**Comparison of model and simulation results of four intersections: (

**a**) Comparison of the intersection 1; (

**b**) Comparison of the intersection 2; (

**c**) Comparison of the intersection 3; (

**d**) Comparison of the intersection 4; 1 represents the effect of variable guidance lane before optimization; 2 represents the effect of variable guidance lane after optimization; 3 represents the effect of network coordinated signal control before optimization; 4 represents the effect of network coordinated signal control after optimization.

Intersection No. | Time Periods | South (pcu/h) | North (pcu/h) | West (pcu/h) | East (pcu/h) | ||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|

LT | TH | RT | LT | TH | RT | LT | TH | RT | LT | TH | RT | ||

1 | 0:00–6:00 | 74 | 63 | 28 | 39 | 27 | 12 | 34 | 68 | 10 | 48 | 12 | 7 |

6:00–9:00 | 392 | 296 | 132 | 384 | 98 | 25 | 352 | 290 | 37 | 255 | 71 | 19 | |

9:00–16:00 | 572 | 218 | 79 | 645 | 171 | 29 | 455 | 364 | 85 | 417 | 121 | 54 | |

16:00–19:00 | 310 | 107 | 46 | 289 | 99 | 24 | 208 | 164 | 63 | 261 | 62 | 49 | |

19:00–0:00 | 149 | 76 | 23 | 174 | 71 | 13 | 97 | 116 | 21 | 149 | 35 | 12 | |

2 | 0:00–6:00 | 84 | 135 | 45 | 63 | 36 | 9 | 30 | 69 | 16 | 54 | 84 | 16 |

6:00–9:00 | 330 | 468 | 80 | 231 | 193 | 36 | 297 | 378 | 72 | 360 | 468 | 105 | |

9:00–16:00 | 492 | 540 | 95 | 531 | 356 | 84 | 495 | 582 | 124 | 594 | 693 | 89 | |

16:00–19:00 | 198 | 273 | 60 | 228 | 186 | 49 | 192 | 294 | 65 | 300 | 384 | 126 | |

19:00–0:00 | 120 | 183 | 37 | 156 | 105 | 17 | 96 | 165 | 40 | 48 | 147 | 31 | |

3 | 0:00–6:00 | 30 | 69 | 14 | 63 | 81 | 12 | 45 | 72 | 13 | 93 | 114 | 20 |

6:00–9:00 | 363 | 402 | 51 | 222 | 294 | 33 | 195 | 279 | 28 | 231 | 312 | 67 | |

9:00–16:00 | 540 | 522 | 102 | 483 | 513 | 105 | 288 | 384 | 63 | 408 | 510 | 138 | |

16:00–19:00 | 289 | 245 | 67 | 252 | 297 | 46 | 126 | 135 | 85 | 177 | 204 | 92 | |

19:00–0:00 | 90 | 165 | 34 | 156 | 213 | 69 | 99 | 120 | 26 | 147 | 183 | 26 | |

4 | 0:00–6:00 | 48 | 75 | 17 | 42 | 60 | 14 | 51 | 78 | 10 | 33 | 54 | 15 |

6:00–9:00 | 339 | 453 | 94 | 303 | 540 | 76 | 180 | 246 | 85 | 345 | 444 | 134 | |

9:00–16:00 | 438 | 504 | 125 | 486 | 609 | 111 | 318 | 405 | 70 | 360 | 507 | 91 | |

16:00–19:00 | 147 | 228 | 87 | 264 | 291 | 63 | 81 | 120 | 56 | 123 | 210 | 72 | |

19:00–0:00 | 81 | 129 | 23 | 159 | 225 | 58 | 99 | 144 | 48 | 96 | 162 | 51 |

Intersection No. | Time Period | Phase 1 (s) | Phase 2 (s) | Phase 3 (s) | Phase 4 (s) | Cycle (s) |
---|---|---|---|---|---|---|

—— | ||||||

1 | 0:00–6:00 | 16 | 20 | 25 | 28 | 89 |

6:00–9:00 | 20 | 25 | 29 | 32 | 106 | |

9:00–16:00 | 24 | 27 | 26 | 25 | 102 | |

16:00–19:00 | 32 | 28 | 30 | 24 | 114 | |

19:00–0:00 | 22 | 25 | 20 | 24 | 91 | |

2 | 0:00–6:00 | 25 | 28 | 22 | 25 | 100 |

6:00–9:00 | 30 | 25 | 26 | 32 | 113 | |

9:00–16:00 | 25 | 28 | 24 | 26 | 103 | |

16:00–19:00 | 25 | 30 | 35 | 25 | 115 | |

19:00–0:00 | 20 | 24 | 28 | 22 | 94 | |

3 | 0:00–6:00 | 18 | 22 | 20 | 24 | 84 |

6:00–9:00 | 26 | 30 | 28 | 25 | 109 | |

9:00–16:00 | 24 | 28 | 25 | 20 | 97 | |

16:00–19:00 | 28 | 30 | 34 | 26 | 118 | |

19:00–0:00 | 20 | 20 | 22 | 24 | 86 | |

4 | 0:00–6:00 | 20 | 24 | 24 | 20 | 88 |

6:00–9:00 | 26 | 35 | 28 | 30 | 119 | |

9:00–16:00 | 25 | 28 | 32 | 24 | 109 | |

16:00–19:00 | 25 | 35 | 30 | 28 | 118 | |

19:00–0:00 | 20 | 18 | 22 | 25 | 85 |

Intersection No. | Time Period | South | North | West | East | Cycle(s) | Delay(s) |
---|---|---|---|---|---|---|---|

d1 | d2 | d3 | d4 | C | D | ||

1 | 0:00–6:00 | 0 | 0 | 0 | 0 | 92 | 15.38 |

6:00–9:00 | 1 | 1 | 0 | 1 | 127 | 21.23 | |

9:00–16:00 | 1 | 0 | 0 | 0 | 114 | 19.04 | |

16:00–19:00 | 0 | 1 | 0 | 1 | 100 | 16.73 | |

19:00–0:00 | 0 | 0 | 0 | 0 | 96 | 16.07 | |

2 | 0:00–6:00 | 0 | 0 | 0 | 0 | 93 | 15.58 |

6:00–9:00 | 0 | 1 | 0 | 1 | 121 | 20.23 | |

9:00–16:00 | 0 | 1 | 0 | 0 | 105 | 17.23 | |

16:00–19:00 | 1 | 0 | 0 | 0 | 111 | 18.45 | |

19:00–0:00 | 0 | 0 | 0 | 0 | 95 | 15.83 | |

3 | 0:00–6:00 | 0 | 0 | 0 | 0 | 91 | 15.14 |

6:00–9:00 | 1 | 1 | 0 | 0 | 116 | 19.29 | |

9:00–16:00 | 0 | 0 | 0 | 1 | 103 | 17.16 | |

16:00–19:00 | 0 | 0 | 1 | 1 | 108 | 18.03 | |

19:00–0:00 | 0 | 0 | 0 | 0 | 88 | 14.59 | |

4 | 0:00–6:00 | 0 | 0 | 0 | 0 | 92 | 15.30 |

6:00–9:00 | 0 | 0 | 1 | 0 | 113 | 18.76 | |

9:00–16:00 | 0 | 0 | 0 | 0 | 100 | 16.64 | |

16:00–19:00 | 0 | 1 | 0 | 1 | 104 | 17.27 | |

19:00–0:00 | 0 | 0 | 0 | 0 | 94 | 15.74 |

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## Share and Cite

**MDPI and ACS Style**

Zhao, F.; Fu, L.; Pan, X.; Kwon, T.J.; Zhong, M.
Investigating the Effect of Network Traffic Signal Timing Strategy with Dynamic Variable Guidance Lanes. *Sustainability* **2022**, *14*, 9394.
https://doi.org/10.3390/su14159394

**AMA Style**

Zhao F, Fu L, Pan X, Kwon TJ, Zhong M.
Investigating the Effect of Network Traffic Signal Timing Strategy with Dynamic Variable Guidance Lanes. *Sustainability*. 2022; 14(15):9394.
https://doi.org/10.3390/su14159394

**Chicago/Turabian Style**

Zhao, Fei, Liping Fu, Xiaofeng Pan, Tae J. Kwon, and Ming Zhong.
2022. "Investigating the Effect of Network Traffic Signal Timing Strategy with Dynamic Variable Guidance Lanes" *Sustainability* 14, no. 15: 9394.
https://doi.org/10.3390/su14159394