Traffic sensors serve as an important way to a number of intelligent transportation system applications which rely heavily on realtime data. However, traffic sensors are costly. Therefore, it is necessary to optimize sensor placement to maximize various benefits. Arterial street traffic is highly dynamic and the movement of vehicles is disturbed by signals and irregular vehicle maneuver. It is challenging to estimate the arterial street travel time with limited sensors. In order to solve the problem, the paper presents travel time estimation models that rely on speed data collected by sensor. The relationship between sensor position and vehicle trajectory in single link is investigated. A sensor location model in signalized arterial is proposed to find the optimal sensor placement with the minimum estimation error of arterial travel time. Numerical experiments are conducted in 3 conditions: synchronized traffic signals, green wave traffic signals, and vehicleactuated signals. The results indicate that the sensors should not be placed in vehicle queuing area. Intersection stop line is an ideal sensor position. There is not any fixed sensor position that can cope with all traffic conditions.
Traffic sensors (e.g., magnetic detectors, cameras, and bluetooth detectors) are widely used in transportation system for systematic surveillance. Various traffic applications need different sensor data. OD estimation may require the traffic counting information on links. Travel time estimation asks for information about link travel time or path travel time. These information can be obtained either from float vehicle such as taxi or cameras which are able to read plate license number. One of the most intuitive pieces of information for advanced traveler information system is travel time. Therefore, a simple and implementationwise easy method is needed to estimate travel time.
Attempt to estimate arterial street travel time is very challenging. Arterial street traffic is highly dynamic and the movement of vehicles is disturbed by signals and irregular vehicle maneuver. Zhang [
Sensor location problem works for this purpose. It aims to find an optimal sensor placement pattern either in transportation network or freeway. The purpose of sensor placement is mainly for various flow estimations which are OD trips estimation, link flows estimation, path flows estimation, and its related application. Yang and Zhou [
Sensor location problem on freeway is relatively limited, particularly for travel time estimation. Kim et al. [
Due to the complexity of urban transportation system, none of current studies consider combining travel time estimation method with a sensor location pattern to seek an optimal sensor placement pattern. Another important characteristic of urban transportation system is traffic signal control. This paper attempts to find optimal sensor location pattern with traffic signals. A simulation tool is used to generate basic traffic flow data. The rest of this paper is organized as follows. Section
In our model, a signalized arterial street is partitioned into sections. Each section is associated with a sensor, and the speed of section is represented by the average instantaneous speed (normally, it is collected from the 30s time interval) at the sensor spot. The estimated travel time of each section is calculated by the length and speed of the section. By summing up estimated travel time across all sections, the estimated arterial travel time can be obtained.
In our study, the boundary of section is determined by three sensors, which are located at the section and the adjacent upstream and downstream section, respectively. The total length of signalized arterial is set to
There are many travel time estimation models, among which the speedbased travel time estimation model is easytooperate and widely applied [
The first model is instantaneous model. A vehicle is supposed to enter the arterial street at time
In the instantaneous model, speeds from only one point on each section are used to estimate travel time, while ignoring the speed variations within a section. This does not meet the authentic traveling situation of vehicles. However, from the perspective of calculation, when the travel time is fixed, its corresponding average speed is fixed. Therefore, the sensor location pattern is very critical. A suitable senor location pattern can accurately capture the average travel time of its spatial influence area. On the other hand, all speeds are collected at the time of vehicle entering the arterial. The speed associated with the downstream section will not change dramatically when the vehicle traverses the arterial. These two reasons result in travel time estimation error. The other two speed estimation models are Time Slice Model and Dynamic Time Slice Model.
The difference among the three travel time estimation models lies in the calculation method for vehicle speed on each section, which is the main factor that affects error. These three models all use the speed measured by sensors, so the travel time estimation error is caused by not only inevitable calculation error, but also the error arising from the location of sensor in arterial street. Different combinations of sensor locations generate different section partitions, thus, resulting in different estimation errors.
To compare the differences among these three models, numerical experiments are conducted for the identical sensor location pattern. In our study, a traffic simulation tool is used for a street with length 1 km as shown in Figure
Partitioned arterial street with traffic signal.
In order to compare the resulted obtained by these three methods, we use three measures for evaluation which are the mean absolute error (MAE), root mean square error (RMSE), and mean absolute relative error (MARE), respectively.
Errors and their standard deviations versus number of sensors.
As shown in Figure
In the urban transportation network, the movement of vehicles is with some regularity due to the traffic signal control. Generally it can be summarized as, after passing through previous intersection, vehicles enter the street at low speed or original speed. Then, the vehicles accelerate to the maximum allowable speed and keep moving. When approaching the next intersection, it determines whether to slow down or keep moving at the original speed according to traffic signals. The speed contour profile is shown in Figure
Speed contour profile in a signal cycle.
The key point of estimating vehicle’s travel time on a certain link is to find the vehicle’s average speed on that link. Vehicle moves with different speed at different positions of the link. In order to accurately estimate travel time, we need to find an appropriate location for the sensor, making sure that the instantaneous speed is close to the average speed. Therefore, the location of sensor has great impact on the travel time estimation error. Figure
Estimate error versus different sensor locations.
As can be seen from Figure
Sensor location pattern is closely related to the vehicle’s trajectory on the link. (i) If a vehicle enters the intersection at a slow speed and the sensor is placed at the inlet (0 m) position, where the average speed is small, the estimation error will be large. (ii) If the vehicle accelerates to the maximum speed after entering the link, the vehicle speed varies greatly within this distance (from 3.6 to 56.6 km/h), so it is easy to find a position that can represent the average speed of the link. (iii) The vehicle runs at the limited speed in the middle section of the link, and the speed fluctuation is small. Therefore, no matter where the sensor is placed, the detected speed is almost equal to the maximum speed. Thus, it cannot reflect the average speed on the link. (iv) Within the 100 m in the downstream, vehicles enter the queuing area. The length of queue increases as the arrival rate increases. When the sensor is closer to the intersection, the sensor is likely to be occupied by vehicles. When the sensor is occupied, it cannot detect speed. The estimation error is large. However, when the arrival rate is less than the saturation volume, the number of queuing vehicles is small. All the vehicles can pass through the intersection in a signal cycle. The proportion of sensor’s occupied time is small. Therefore, the travel time can be estimated. When the arrival rate is greater than the saturated volume, vehicles at the tail of the queue need to wait for two or more signal cycles before passing through the intersection. The sensor is more likely to be occupied and cannot obtain vehicle speed during a long period of time.
A signalized arterial street is usually composed of many links, and there is a traffic signal between every two links. In order to study sensor placement pattern in such a signalized arterial street, we divide arterial street into equallength cells, as shown in Figure
Partitioned arterial street.
Assume that the entire horizon of the study is
M1:
In M1,
In this section, a mathematic model is proposed to solve the sensor placement problem in arterial street. It is a 01 programming model. The objective function is to minimize the relative travel time estimation error between estimated and actual travel time. The input data of the model is travel time information of all vehicles in computer simulation which is treated as groundtruth travel time. Once the groundtruth travel time information is given, and our proposed mathematical programming model can decide the optimal sensor placement pattern that minimizes the relative travel time estimation error. Therefore, our model is a mathematical model. In addition, the model is deterministic.
In this study, we only consider the influence of vehicle arrival rate and traffic signal strategy on sensor placement pattern which are two major factors that affect travel time on urban network. In the simulation, the signalized arterial street is set as 3 km long, and it is composed of 6 links. Each link is 0.5 km long. Each link is divided into five cells, and each cell is 0.1 km long. The limited speed is 57.6 km/h. Vehicle arrival rate at the entrance is set as 400 vph, 800 vph, 1200 vph, and 1600 vph, respectively, and arrival rate obeys Poisson distribution. When the arrival rate exceeds the intersection capacity, there will be congestion. In each simulation, the arrival rate is fixed. In the urban transportation network, traffic signals strategy can greatly affect the capacity of each intersection and thereby affect the trajectory of vehicle after entering the arterial street. Therefore, we need to consider different traffic signals strategies. In this study, we consider three common traffic signals strategies: synchronized traffic signals, green wave traffic signals, and vehicleactuated signals. In the experiment, we analyzed three strategies separately under different vehicle arrival rates.
Synchronized control refers that all intersections of the arterial street use the same signal configuration and display the same traffic signal at the same time. In the simulation, the signal cycle is set as 100 s, and green ratio is 50%. Vehicle’s speed trajectories under different arrival rates are shown in Figure
Speed contour plot in synchronized traffic signals.
Arrival rate is 400 vph
Arrival rate is 800 vph
Arrival rate is 1200 vph
Arrival rate is 1600 vph
According to Figure
Table
Comparison among different arrival rates.
Arrival rate (vph)  Number of sensors  Sensor location pattern 

400 
6  500, 600, 1100, 1700, 2900, 3000 


400 
5  1100, 1200, 1300, 1500, 1700 


400 
4  500, 800, 1900, 2300 
In Figure
Comparison among MARE in different number of sensors for synchronized traffic signals.
Green ratio is an important parameter in traffic signals strategy. Congestion occurs when traffic volume is greater than the intersection capacity. In order to timely dissipate queuing vehicles, green ratio should be lengthened. When traffic volume is less than the intersection capacity, the green ratio should be carefully reduced. Green ratio will directly affect intersection capacity. When the arrival rate is a constant, vehicle queuing will change, thus affecting the position of sensor.
In order to study the influence of sensor location on estimated travel time under different green ratios, we set three green ratios, which are 40%, 50%, and 60%, respectively. Other parameters are the same as previous section. By using genetic algorithm, the optimal sensor placement pattern and the travel time estimation errors are obtained. As shown in Figure
Comparison among different green ratios.
Green wave control means that if a vehicle passes through one intersection at a given speed with a green light phase, it will pass through all the downstream intersections at green light phase [
In our simulation, the signal cycle is set as 100 s. Green ratio is 50%. Each link is 0.5 km long. The limited vehicle speed is 57.6 km/h. The relative offset time between adjacent intersections is 32 s. Therefore, there will be a band along with the arterial street. As long as the vehicle arrives within the band and keeps moving at the limited speed of 57.6 km/h, it can travel smoothly through the all intersections. Figure
Table
Comparison among different arrival rates.
Arrival rate (vph)  Number of sensors  Sensor location pattern 

400 
6 
600, 700, 900, 1500, 2600, 3000 


400 
5  1400, 1900, 2200, 2500, 3000 


400 
4  1200, 1500, 2200, 2800 
Speed contour plot in green wave traffic signals.
Arrival rate is 400 vph
Arrival rate is 800 vph
Arrival rate is 1200 vph
Arrival rate is 1600 vph
Figure
Comparison among MARE in different number of sensors for green wave traffic signals.
Speed contour plot in vehicleactuated traffic signals.
Arrival rate is 400 vph
Arrival rate is 800 vph
Arrival rate is 1200 vph
Arrival rate is 1600 vph
The above two traffic signals strategies are fixed traffic signal control method. They are developed based on historical data. The disadvantage of these strategies is that it is unable to meet realtime changes of traffic flow. In order to overcome this deficiency, vehicleactuated signals [
In the simulation of vehicleactuated control, we set each intersection’s signal cycle as 100 s. The minimum green time is 50 s. The maximum green time is 70 s. The unit extension interval is 3 s. When the arterial street gets the access right, the signal system will first give the signal phase a minimum green time of 50 s, enabling the vehicle that has arrived at the intersection to pass through the intersection. If there is no vehicle after this, the access right will be transferred to the subsequent link. If a vehicle is detected within the green time, the green time will be extended a unit time interval of 3 s. The maximum extension can be 70 s.
Figure
The optimal sensor location pattern under vehicleactuated traffic signals control is shown in Table
Comparison among different arrival rates.
Arrival rate (vph)  Number of sensors  Sensor location pattern 

400 
6  200, 300, 500, 1100, 1400, 1800 


400 
5  600, 700, 1300, 1500, 2200 


400 
4  600, 1000, 1100, 1700 
Comparison among MARE in different number of sensors for vehicleactuated traffic signals.
Through experimental analyses of these three traffic signals strategies, observations are stated as follows: (i) when the sensor is located in the queuing area, its corresponding influence area is short. Its length should be close to the queuing length. Therefore, when a sensor is located in the queuing area, some sensors should be set in the adjacent upstream and downstream areas in a cooperative manner. (ii) Stop line is an ideal sensor position place. Compared with other location places, the average speed of vehicles at stop lines has the largest variations. Small arrival rate may cause fewer queuing vehicles. The average speed is high. A large arrival rate may cause more queuing vehicles, where the average speed is low. The sensor can timely and flexibly reflect the traffic conditions. (iii) Under simple traffic situation where vehicle speed is stable with small speed fluctuation, few sensors can accurately estimate travel time. Otherwise, more sensors are needed.
The paper studies the sensor location problem in urban arterial street for travel time estimation and proposes optimal sensor location model (M1) to obtain the minimum travel time estimation error. Based on this model, the influence of traffic signals strategies on sensor location is also discussed. By comparing the synchronized traffic signals, green wave traffic signals, and vehicleactuated signals, it is found that sensor should not be placed in vehicle queuing area. If the sensor is located in the queuing area, its associated coverage area should include the vehicle queuing area as precise as possible. Intersection stop line is an ideal sensor position. There is not any fixed sensor position that can cope with all traffic conditions, and the sensor location should be determined according to the characteristics of traffic flow on the road. Under simple traffic situation where vehicle speed is stable and speed fluctuation is small, few sensors can accurately estimate travel time. In case of complex traffic conditions with large fluctuations of vehicle speed, more sensors are required to estimate travel time.
The future research direction can be considered as follows: (i) our study only takes into account the traffic condition of single lane with fixed traffic volume, and the future research can consider more complex traffic situations, such as the dynamic changes of multilane road with dynamic traffic volume and other real phenomena that match with actual road conditions. (ii) The future research can take this study on urban arterial street as background, taking into account the vehicle turnings, and study the sensor location under the road network layout. (iii) A more efficient model for algorithm should be explored in the future research, although the genetic algorithm used in the paper is an effective solution model. (iv) The study only seeks the optimal sensor location for travel time estimation. Future research can focus on optimized combination of more traffic information applications or more information applications.
The authors declare that there is no conflict of interests regarding the publication of this paper.
This research was supported by the National Natural Science Foundation Council of China under Projects 71301115, 71431005, 71271150, and 71101102 and Specialized Research Fund for the Doctoral Program of Higher Education of China (SRFDP) under Grant no. 20130032120009.