# A Cooperative Traffic Control of Vehicle–Intersection (CTCVI) for the Reduction of Traffic Delays and Fuel Consumption

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## Abstract

**:**

## 1. Introduction

- In the first strategy, only the control center optimizes the vehicle passing sequence for all vehicles to decrease the stopped time before the intersection, and it is assumed that all the vehicles should stop as fast as possible before the intersection without traffic lights to wait for the right-of-way, by the following procedures: firstly, the vehicles can send their time of arrival before arriving at the intersection by the V2I; then, the control center optimizes the vehicle passing sequence for these vehicles to pass the intersection. Therefore, this strategy only optimizes the dynamic distribution of intersection resources based on the fixed arrival information of vehicles.
- In the second strategy, only the vehicles adjust their dynamic movements before the intersection to reduce the stopped time, and it is assumed that the intersection applies FT control. Through the V2I connection, vehicles can receive the scheduling signals far from the intersection. Then, the vehicles can adjust the operation before arriving at the intersection to avoid the stops. Therefore, this strategy only considers the optimization of the dynamic movement of vehicles before the intersection without cooperatively adjusting the traffic control strategies.

- On the one hand, the control center receives the range of vehicles’ times of arrival (instead of a fixed minimal time of arrival) when the vehicles arrive at the communication zone. Then, the vehicle passing sequence is optimized and sent to the vehicles by the control center.
- On the other hand, the vehicles adjust their speeds by changing the acceleration before the intersection, according to the given passing sequence, instead of the schedule in an FT control.

## 2. Proposed Dynamic Traffic Modeling

- Method of selecting the itineraries for vehicles. That is to say, finding the list of intersections through which each vehicle passes from its origin to its destination. The method is to choose the next intersection having the lighter traffic load based on the same minimal travel distance. For example, in Figure 1a, for a vehicle from virtual intersection 20 to 02, it can choose one of the two itineraries (20-21-22-12-02 or 20-21-11-12-02) with the same minimal trip length. When this new vehicle is in intersection 21, and the total number of vehicles in intersection 22 are greater than that in 11, it chooses 11 as its next intersection, and vice versa. This operation occurs in each simulation step for the new vehicles before getting the right-of-way.
- Vehicle passing sequence in each intersection. The control center decides the vehicle passing sequence for the vehicles based on the information collected from them, with the given objectives.

## 3. Minimization of Time Delays by Applying Dynamic Programming

- Calculation of the range of $ET3$, which means the reasonable time period for the vehicle to arrive at the intersection. In this time range, the key point is the lower bound, which is the minimal time for the vehicle to arrive at the intersection. This lower bound is the time $ET{3}^{f}$, which is achieved by the vehicle to travel in the free-flow state, because it can always travel with the maximal allowed speed in this state. Thus, it is impossible for the vehicles to arrive at the intersection before the time $ET{3}^{f}$.
- Calculation of the higher $EV3$ based on the $ET3$. The variable $ET3$ presents the time when the vehicle is allowed to pass the intersection. However, for a given $ET3$, there are countless possibilities of $EV3$ with which the vehicle can start to pass the intersection. Therefore, in the proposed strategy, the $ET3$ with the higher value is chosen to reduce the intersection travel time $TT3$. The higher $EV3$ is, the smaller the time needed by vehicles to accelerate to $V{I}_{max}$. As a result, the minimal value of $TT3$ can be achieved. Referring to sub-Section 3.1.
- Calculation of the minimal $TT3$ according to the maximal $EV3$ and the vehicles’ operations in the intersection. The reason that the variable of maximal $EV3$ affects the minimal $TT3$ is explained in the above step. The length for the vehicle to pass the intersection is various in different operations. For example, the length for the vehicle to turn left in the intersection is longer than that in the operation of turning right. The vehicle’s operation in the intersection depends on its origin, its destination, and the traffic volume in the adjacent intersections, as shown in Section 5. Referring to Section 3.2.
- The mathematical expressions of the security restrictions during the optimal process for the vehicle passing sequence. Referring to Section 3.3.
- The process of optimizing the vehicle passing sequence by DP. Referring to Section 3.4.

#### 3.1. Calculation of the Maximal $EV3$ Based on the $ET3$

#### 3.1.1. KP1—TLV (${V}_{max}$)

#### 3.1.2. KP2—TLV (${V}_{min}$)

#### 3.1.3. KP3—TLV (0)

#### 3.2. Calculation of the Minimal $TT3$

#### 3.3. The Mathematical Expressions of the Security Restrictions

- Incompatible streams. A new vehicle is permitted to start to pass the intersection iff the other vehicles located before it in the vehicle passing sequence and coming from incompatible streams have passed the intersection completely ($ET{3}_{(j,l)}^{a}\ge ET{3}_{({j}^{\prime},{l}^{\prime})}^{a}+TT{3}_{({j}^{\prime},{l}^{\prime})}^{a}({l}^{\prime}{\u25ef}l)$, vehicle ${l}_{j}$ is behind the other one ${l}_{{j}^{\prime}}^{\prime}$ in the vehicle passing sequence). This rule can exploit the intersections’ resources more effectively and dynamically.
- The same lane. The minimal headway should be respected ($|ET{3}_{(j,l)}^{a}-ET{3}_{({j}^{\prime},{l}^{\prime})}^{a}|\ge HW({l}^{\prime}=l)$).
- The other lane in the same streams. For one vehicle, if its original lane does not correspond to its operation in the intersection, it has to change lanes in the second segment. The minimal headway should be considered when two vehicles cross, as shown in Figure 5.

#### 3.4. Process of Applying Dynamic Programming to Optimize the Vehicle Passing Sequence

## 4. Minimization of Fuel Consumption by Adjusting the Speed Profile in the Second Segment

## 5. Choice of Itinerary for Each Vehicle in the Network of Intersections

- The travel distance is put in the first place. In other words, all vehicles try to find an itinerary with the minimal travel distance.
- The traffic loads in the adjacent intersections are the second element. The traffic loads in the virtual intersection is defined as infinite. If the itinerary with the same travel distance is not unique, the vehicle chooses the one where the next intersection has the least traffic loads in order to reduce the traffic delays in trip.

Algorithm 1: The algorithm for choosing the itinerary for each vehicle to enter the intersections from the east. |

Algorithm 2: The overall process of the proposed algorithm. |

## 6. Results

#### 6.1. Comparison with the Work Proposed by Abbas-Turki et al.

- The control center optimizes the vehicle passing sequence based on the range of time of arrival for each vehicle, to assure the validity of the solution obtained, instead of the fixed time of arrival. Additionally, each vehicle optimizes its speed profile according to the permission given by the control center.
- Owing to the first reason, each vehicle can enter the intersection with a higher speed, avoid stopping before it, and take less time to pass it, meaning that it can evacuate the vehicles more rapidly.
- The proposed strategy avoids needless decelerations before the intersection to save fuel consumption and travel time.
- The proposed strategy can decrease the complexity of optimization by considering a smaller part of range optimal without reducing the performance, which is proven by the calculation time for the traffic delays.

#### 6.2. Comparison with the Paper Proposed by K. Katsaros et al.

- the intersection and the vehicles are collaboratively controlled. This is two-way cooperation, instead of one-way one. As a result, the vehicles change their speeds dynamically according to the traffic control strategy to reduce the traffic delays.
- Each vehicle always finds the maximal travel speed to reduce the intersection travel time as much as possible.

## 7. Conclusions

## Author Contributions

## Conflicts of Interest

## Abbreviations

DP | Dynamic Programming |

GLOSA | Green Light Optimal Speed Advisory |

CTCVI | Cooperative Traffic Control of Vehicle-Intersection |

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**Figure 1.**Proposed traffic model without traffic lights. (

**a**) Network of intersections; (

**b**) Isolated detailed intersection.

Streams | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
---|---|---|---|---|---|---|---|---|

1 | ◯ | ◯ | ◯ | ◯ | ||||

2 | ◯ | ◯ | ◯ | ◯ | ||||

3 | ◯ | ◯ | ◯ | ◯ | ||||

4 | ◯ | ◯ | ◯ | ◯ | ||||

5 | ◯ | ◯ | ◯ | ◯ | ||||

6 | ◯ | ◯ | ◯ | ◯ | ||||

7 | ◯ | ◯ | ◯ | ◯ | ||||

8 | ◯ | ◯ | ◯ | ◯ |

Notations | Definitions |
---|---|

l | The index of lane in approaches, $l\in [1,8]$ |

$Nl$ | The number of new vehicles on lane l. |

$({j}_{l},l)$ | Subscripts. The ${j}_{l}$-th vehicle on lane l, ${j}_{l}\in [0,Nl]$. |

$({j}_{1},...,{j}_{8},l)$ | Subscripts. The ${j}_{{l}^{\prime}}$-th vehicle on the lane ${l}^{\prime}$ is included in the vehicle passing sequence, respectively, ${l}^{\prime}\in [1,8]$. The last one comes from the lane l. |

a, f | Superscripts. The value in the actual flow state or the free-flow state, respectively. |

l, r and s | Superscripts. These refer to the following operations in the intersection: turn left, turn right, and go straight, respectively. |

s | The s-th section of the communication zone, $s\in [1,4]$. |

$ETs$ | The time of arrival at the s-th section, $s\in [1,4]$. |

$EVs$ | The travel speed entering the s-th section. |

$TTs$, $TT$ | The travel time in s-th section and in all sections: $TT=TT1+...+TT4$. |

$TD$, $FUEL$ | The traffic delays or fuel consumption for the entire trip. |

$HW$ | Headways, which refer to the time (in seconds) between two successive vehicles when they get through the same point on the road. |

$Ls$ | The length of s-th section. |

${A}_{max},{D}_{max}$ | The maximal acceleration and deceleration for each vehicle. |

${V}_{max},{V}_{min}$ | The speed limit on the road (except for the intersection): maximum and minimum. |

$V{I}_{max}$ | The speed limit (maximum) on the intersection. |

${I}_{row}$, ${I}_{column}$ | The dimension of the intersection network: number of rows and columns, respectively. |

${t}_{step}$ | The time step in the simulation. |

$II{D}_{(x,y)}^{sou}$, $II{D}_{(x,y)}^{des}$ | The coordinate of intersection presenting the origin or the destination for each vehicle, referring to Figure 1a. |

Interval of $\mathit{ET}{3}^{\mathit{a}}$ | Range of $\mathit{EV}{3}^{\mathit{a}}$ | Formulation of Calculating $\mathit{EV}{3}^{\mathit{a}}$ |
---|---|---|

$[ET{3}^{f},KP1]$ | $V{I}_{max}$ | $V{I}_{max}$ |

$(KP1,KP2]$ | $[{V}_{min},V{I}_{max})$ | Equation (11) |

$(KP2,KP3)$ | $(0,{V}_{min}]$ | Equation (12) |

$[KP3,\infty )$ | 0 | 0 |

${\mathit{V}}_{\mathit{max}}$ | ${\mathit{V}}_{\mathit{min}}$ | ${\mathit{VI}}_{\mathit{max}}^{\mathit{l}}$ | ${\mathit{VI}}_{\mathit{max}}^{\mathit{r}}$ | ${\mathit{VI}}_{\mathit{max}}^{\mathit{s}}$ | $\mathit{TV}$ | ${\mathit{I}}_{\mathit{cow}}$ | ${\mathit{I}}_{\mathit{column}}$ |
---|---|---|---|---|---|---|---|

14 | 4 | 0.8 ${V}_{max}$ | 0.6 ${V}_{max}$ | ${V}_{max}$ | 500 | 2 | 2 |

${L}_{1}$ | ${L}_{2}$ | ${L}_{3}$ | ${L}_{4}$ | $HW$ | ${t}_{step}$ | ${A}_{max}$ | ${D}_{max}$ |

100 | 200 | 10 | 300 | 1 | 0.1 | 2 | -2 |

**Table 5.**Comparison between the CTCVI and Reference [9].

Traffic Delays | Fuel Consumption | Travel Speed for Entering Intersection | |||

Paper [9] | CTCVI | Paper [9] | CTCVI | Paper [9] | CTCVI |

6.42 | 0.43 | 0.129 | 0.095 | 0 | 11.51 |

Intersection Travel Time | Stopped Time | Calculation Time for the Optimization of $\mathit{TD}$ | |||

Paper [9] | CTCVI | Paper [9] | CTCVI | Paper [9] | CTCVI |

2.88 | 0.75 | 5.25 | 0 | 0.0087 | 0.00029 |

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**MDPI and ACS Style**

Li, J.; Dridi, M.; El-Moudni, A.
A Cooperative Traffic Control of Vehicle–Intersection (CTCVI) for the Reduction of Traffic Delays and Fuel Consumption. *Sensors* **2016**, *16*, 2175.
https://doi.org/10.3390/s16122175

**AMA Style**

Li J, Dridi M, El-Moudni A.
A Cooperative Traffic Control of Vehicle–Intersection (CTCVI) for the Reduction of Traffic Delays and Fuel Consumption. *Sensors*. 2016; 16(12):2175.
https://doi.org/10.3390/s16122175

**Chicago/Turabian Style**

Li, Jinjian, Mahjoub Dridi, and Abdellah El-Moudni.
2016. "A Cooperative Traffic Control of Vehicle–Intersection (CTCVI) for the Reduction of Traffic Delays and Fuel Consumption" *Sensors* 16, no. 12: 2175.
https://doi.org/10.3390/s16122175