1. Introduction
In today’s world, with the increase of the use of mobile devices, the location-based services are becoming increasingly popular. Since the rapidly increased satellites and GPS (Global Position System) technologies have developed, it is possible to collect a large amount of trajectory data of moving objects such as the vehicle position data, hurricane track data, and animal movement data [1, 2, 16, 17]. The analysis over these trajectory data is becoming important for many applications, such as meteorological observation and forecast, animal habits observation, road traffic situation analysis, and navigation in transportations [3-6, 8]. According to the recorded trajectory data and road networks, the moving pattern, traffic situation and road recommendation services can be supported [1, 2, 12, 15, 18]. Recently, with the continuously increasing mobile devices and vehicles, the route recommendation service is becoming more and more important [1, 5, 6, 9, 17, 19, 20]. For road network based applications, the mobility of the vehicle is road network constrained.
Most of the existing schemes try to monitor and forecast the traffic by using the recorded history trajectory data of vehicles equipped with GPS devices. The index based schemes construct an index by adopting the trajectory data of the moving objects [3, 4]. And then, the routes are recommended according to the history trajectory data of the related moving objects. Some schemes generate the density routes of the road networks by analyzing the trajectory data of vehicles [7-10]. The density regions of the road networks are evaluated by considering both the location and time of the moving objects. According to the trajectory data, the number of the moving objects within a specific road segment and timestamp is be used to identify the density regions of a road. After that, the small density regions of each road are clustered and the final density regions in the road networks are generated. However, there are three major problems of the existing schemes to be applied in real road networks: (1) the directions of the roads in the road networks are not considered; (2) the widths and lengths of the road segments are not considered; (3) the average moving speed of vehicles within a road segment is not considered. In the real road network environments, each road is divided into two directions: positive direction and negative direction. The vehicles in the road toward to different directions do not affect each other. The width and length of each road segment are different in a road network, which will also affect the accuracy of the congested routes. Furthermore, the average moving speed of vehicles within a road segment can identify the congestion of the road.
To overcome these problems, we propose a clustering method for congested routes discovering, the directions, width, and length of roads are considered in real road network environments. The proposed scheme can be divided into three steps. First, it divides each road network into segments with different width, length, and directions. Second, the congested road segments are extracted by considering the average moving speed of the vehicles and the saturation degree of each road segment in the road networks. Third, we compute the final congested routes by using a clustering scheme. The experimental results showed that the proposed scheme can efficiently discover the congested routes in different directions of the roads.
The remainder of the paper is organized as follows. Section 2 discusses related work in section 2. Section 3 presents the details of the proposed scheme. Section 4 contains experimental evaluation that demonstrates the superiority of our proposed scheme. Finally, section 5 concludes this paper.
2. Related Work
Most of the existing schemes try to monitor and forecast the traffic by using the recorded history trajectory data of vehicles equipped with GPS devices. [1] proposed the MPR scheme for discovering the popular route between two locations by observing the traveling behaviors of many previous users. The maximum probability product algorithm is used for discovering the MPR from a transfer network based on the popularity indicators in a breadth-first scheme. [7] proposed a new density-based algorithm called FlowScan. It is a robust algorithm that can handle the complexities in the data and we verify through extensive experiments. Instead of clustering the moving objects, road segments are clustered based on the density of common traffic they share. [20] studied the problem of vehicular traffic density estimation, utilizing the information cues present in the cumulative acoustic signal acquired from a roadside-installed single microphone.
Vehicles which are located in a congested area try to move to a non-congested area. [12] proposed a route discover method for alleviating traffic congestions to provides a driving route whose trip time becomes short. The proposed method does not need global traffic information but regional traffic information for each vehicle. The vehicle calculates a route for a destination where a summation of evaluation values for roadway segments in the route becomes minimal. Given a spatial range and a user preference of depth/breadth specified by a user, [15] processed a Pattern-Aware Trajectory Search (PATS) to retrieve the top K trajectories passing through popular regions-of-interest (ROIs). PATS support trip planning without requiring prior knowledge of ROIs in the specified spatial range. PATS used a user movement graph to capture travel patterns hidden in trajectories and develop an algorithm to determine the attractive scores of the ROIs and proposed an algorithm BTS for efficiently retrieving the top K trajectories.
[11] proposed a fast path algorithm of finding the best shortest paths in the road network to solve the path planning problem in route guidance systems in terms of accuracy and speed. [13] presented a routing algorithm which uses the road hierarchy and pre-computed areas to limit the search space. This improves trip duration by using upgraded roads whenever beneficial, and finds routes that take into consideration both speed and driving patterns. [14] studied the problem of finding reasonable alternative routes in road networks.
[9] presented NETSCAN which carries out the clustering of dense sections and incorporates them by forming dense routes. NETSCAN cluster the road sections based upon the network density statistics. This clustering takes into account the orientation of the trajectory. Besides, this method utilizes the network topology to create relevant clusters. To propose a model to assess the evolution for dense route pairs at two consecutive time intervals, DENSITYLINK algorithm is presented. DENSITYLINK allows the characterization of the evolution of the dense road network. [10] proposed a time-based clustering algorithm called Tk-means that adapts the k-means algorithm for trajectory data. Tk-means cluster the objects based on the time intervals of different trajectory's motions. If an object spans different time intervals, it will eventually belong to different clusters. Tk-means used two approaches, an exact method and an approximate method. The exact method computes the actual clusters visited by the object throughout its life time and the approximate method exactly computes some of the actual visited clusters and based on those computed clusters along with the clusters generated from the remaining data set, it predicts the future motion pattern of the query object.
However, none of them consider the features of each road segment such as width, length and directions in a road network, they are not suitable for some real road networks. In this paper, we propose a clustering method for congested routes discovering in real road network environments. The congested road segments are extracted by considering the average moving speed of the vehicles and the saturation degree of each road segment in the road networks.
3. The Congested Routes Discovering Scheme
3.1 Road network and trajectories
Definition 1 Road network, we assume that the road network is represented by a graph G(N, E), where N denotes the node which is the intersection between different road segments and E denotes the edge which is used to connect two adjacent nodes in the road network.
Definition 2 Road segment, Ei is used to denote a segment of the road network. ‘+’ and ‘−’ are used to represent the different directions of vehicles in a road network. Moreover, since the length and the number of lane of each road are different, the length and width of each road segment are stored. Therefore, each road segment is represented by Si(±) = {Ni, Nj, length, width}, where length is the length of a road segment and width is the number of traffic lanes.
As shown in Fig. 1, S2 and S3 are the neighbor segments of S1 in a road network G. In a road network G, each road segment Si stores the information of its directly connected road segments. This information is used for the following clustering evaluations.
Fig. 1.The data model of road network
Definition 3 Trajectory, the trajectory of a vehicle is represented by Tr. Each node Ni in the road network is represented by a point {xi, yi}. Suppose that the trajectory Tr of each vehicle is defined as follows:
, where Si denotes the segment ID and Ti is the time stamp. According to Ti, the location of each vehicle can be retrieved easily.
Since the vehicles may move continuously or stay in a position, it is necessary to have the location knowledge of each vehicle according to the timestamps.
3.2 Congested routes detection
Definition 4 Congested road segment, the road segment is considered as congested region if the evaluated complexity value is higher than the predefined threshold value. The road segments with low moving speed and high number of vehicles are determined as congested road segments.
Fig. 2 shows the procedure of computing congested routes. The initial road information and trajectory data can be used to determine the existence of vehicles in each road segment of different directions. The road network is divided into road segments with different width, length, and directions. The trajectory data of moving objects on the road networks are analyzed to discover the congested routes. Here, the congested road segments are extracted by considering the average moving speed of the vehicles and the saturation degree of each road segment in the road networks. Finally, we compute the final congested routes by using a clustering scheme.
Fig. 2.The procedure of computing congested routes
In this paper, the congested road segments are computed according to the different directions of the roads. The location and direction of each vehicle can be retrieved from the recorded trajectory data. The complexity value of each road segment is computed by considering the average speed of the vehicles in the road segment and the saturation degree of the road segment. The fast moving speed indicates that the congestion of the road segment is low. In contrast, the low moving speed indicates that the congestion of the road segment is high. The saturation degree is computed based on the number of the vehicles within a road segment and the length and width of a road segment, which are indicated in Fig. 3. We define that the congested road segments within a road network are the road segments with high complexity values.
Fig. 3.The road segment between nodes N1 and N2 in a road network
The average moving speed (Av) of the vehicles in a road segment according to different directions is computed by the following Eq. 2, where V(Obi) denotes the moving speed of a vehicle Obi . The saturation (Sat) according to the width (Swidth) and length (Slength) of a road segment is computed in Eq. 3, where Obn denotes the number of the vehicles in a road segment. As a result, the complexity value of a road segment is computed by Eq. 4 which combines Eq. 2 and Eq. 3, α denotes the weight value between the average moving speed of vehicles and the saturation of a road segment.
The complexity value of each road segment is evaluated, and the clustering algorithm is performed among congested road segments. However, since the complexity values of road segments are changed according to different timestamps, it has to be computed periodically. The congested routes of a road network are computed according to the complexity values. Fig. 4 shows the congested routes (the dotted areas) of a road network in different timestamp T. According to the recorded trajectory data of vehicles at time T =0, the congested routes of the road network of different directions are generated, such as S2(+) and S5(−) in Fig. 4(a). As shown in Fig. 4(b), when time T =1, S1(−), S5(−) and S6(−) are evaluated as congested road segments. Since S5(−) and S6(−) are neighbor road segments and have the same direction in the road network, they are clustered together.
Fig. 4.The clusters according to different timestamps
3.3 Congested routes detection algorithm
In this section, we present the algorithm of congested routes detection. The algorithm operates in two phases. In the first phase, the complexity value of each road segment in the road network according to different directions is computed. In the second phase, the congested routes of a road network are evaluated by clustering the congested road segments with each time interval. When the complexity value of a road segment is larger than the predefined threshold value the road segment is considered as a congested road segment. Finally, the congested road segments with same direction are clustered together. Fig. 5 shows the congested routes detection algorithm.
Fig. 5.The algorithm of the proposed scheme
4. Performance Evaluation
In this section, we introduce the performance evaluation by comparing the proposed scheme with the existing scheme NETSCAN [9]. The vehicles are generated by the network-based generator [21]. The complexity values and clusters are generated according to the number of vehicles in each time interval. All of the experiments are coded in Java and the experiments are performed in Intel i3 3.0GHz CPU and 4G memory. Table 1 summarizes the parameters for this performance evaluation.
Table 1.The values of parameters
In the first experiment, we show the congested routes road networks of Oldenburg city by using our proposed scheme. In this experiment, the total number of vehicles in the road network is set to 50,000 and the saturation of the road is set to 30%. As shown in Fig. 6, the results indicated that the congested routes of the road network are different according to the different directions of the road networks. The blue and red regions represent the congested routes of the road networks in positive direction and negative direction respectively.
Fig. 6.The congested route of the Oldenburg city
In Fig. 7, we compare the NETSCAN scheme with our proposed scheme. The number of the congested routes of NETSCAN and the proposed scheme are evaluated according to the number of the vehicles. For the proposed scheme, the congested routes are evaluated in different directions (positive direction and negative direction) and same direction respectively. The results show that the number of the congested routes is increased when the number of the vehicles increases. The number of the congested routes of the proposed scheme is similar when the number of the vehicles between 20,000 and 30,000. This is because the saturation of each road segment is considered in the proposed scheme, when the width and length of a road segment is large the 20,000 and 30,000 vehicles is not large for the road. Therefore, most of the road segments are not identified as congested routes at first. For NETSCAN scheme, the number of congested routes is increased proportionally with the increase of the number of vehicles.
Fig. 7.The number of congested routes according to the number of vehicles
Fig. 8 shows the number of congested routes according to the different timestamps, the time interval is set as 1 hour. The congested routes are evaluated in different directions (positive direction and negative direction) and same direction respectively. From Fig. 8, we can see that the number of the congested routes of the positive direction is larger than that of the negative direction. And the number of the congested routes that without considering the direction of the road segment is larger than the direction considered scheme.
Fig. 8.The number of congested routes according to the different timestamps
5. Conclusion
In this paper, we have proposed a congested routes discovering scheme in real road networks. The proposed scheme divides the road into segments with different widths and lengths. It extracts the congested road segments based on the average speed of the vehicles and the saturation degree of a road segment. The final congested routes are computed by performing clustering scheme. The experimental results showed that the proposed scheme can discover the congested routes in different directions over the existing schemes. In the future, we will conduct more performance evaluation of our approach by using the real trajectory data of vehicles.
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