Finding a route with shortest travel time according to the traffic condition can help travelers to make better route choice decisions. In this paper, the shortest travel time based on FCD (floating car data) which is used to assess overall traffic conditions is proposed. To better fit FCD and road map, a new map matching algorithm which fully considers distance factor, direction factor, and accessibility factor is designed to map all GPS (Global Positioning System) points to roads. A mixed graph structure is constructed and a route analysis algorithm of shortest travel time which considers the dynamic edge weight is designed. By comparing with other map matching algorithms, the proposed method has a higher accuracy. The comparison results show that the shortest travel time path is longer than the shortest distance path, but it costs less traveling time. The implementation of the route choice based on the shortest travel time method can be used to guide people’s travel by selecting the space-time dependent optimal path.
There is an urgent need to obtain the traffic dynamics in a city for traffic guidance. By providing effective traffic information, it can help travelers to make better route choice decisions. Queries of the type “how do we get traffic information?” and “which path is the shortest distance between two vertices in a graph?” are widely addressed, while queries of the type “how do we get traffic information efficiently and economically?” and “which path is the shortest travel time between two vertices in a graph?” need further analysis.
Although traffic information on road networks can be collected by induction loops or visual systems, it is difficult to obtain an accurate estimation of the instantaneous travel time from the local traffic speed and flow data [
In recent years, an increasing number of cars have been equipped with GPS (Global Positioning System). FCD (floating car data) collects traffic information including real-time position, direction, speed, and other information. If this FCD system achieves more than 1.5% of penetration rate [
In comparison to fixed traffic sensors, FCD is capable of providing a robust overview of current road traffic conditions at significantly less cost [
Pfoser et al. showcased a system which facilitates the collection of FCD, produces dynamic travel time information, and provides value-added services based on the dynamic travel times [
Because of GPS measurement errors and road geometric errors in digital maps, the GPS locations of probe vehicles may not appear on network links [
Analysis studies of traffic conditions based on FCD were becoming more prominent. Mean link travel time based on the classification for the traffic flow, offset control, and moving direction at downstream signalized intersections in urban traffic networks was studied [
In this paper, there are two important problems to be addressed in order to better guide the route choice. The first is the acquisition of the road traffic situation from FCD. The second is to find a route with the shortest travel time by designing an optimal route analysis algorithm.
The two main contributions of this paper are the following. A new map matching algorithm which fully considers the distance factor, direction factor, and accessibility factor is proposed. This algorithm can be used to acquire the road traffic situation. A shortest travel time algorithm is designed. An improved Dijkstra algorithm is proposed and travel time is assigned to edges as the dynamic weight of the road.
The paper is organized as follows. In Section
The original FCD is collected from over 11 thousand taxicabs from Wuhan in September, 2009, at regular intervals (average 20–60 seconds) during the courses of six days. Wuhan is the capital of Hubei province, China. It is located in the eastern Jianghan Plain at the intersection of the middle reaches of the Yangtze and Han Rivers. It is a major transportation hub, with dozens of railways, roads, and expressways passing through the city. It has a population of 91,000,000 people in 2009 [
The FCD samples achieve a sufficient penetration rate with 1.9% to calculate the traffic information. There are more than 85 million records in total (over 14 million per day) with attributes of timestamp, CarID,
Samples of typical FCD records.
Timestamp | CarID |
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Speed | Angle |
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1236441601 | 124410 | 114.311215 | 30.610151 | 16.511 | 124.38 |
1236441601 | 123259 | 114.305106 | 30.613588 | 10.16 | 124.99 |
1236441701 | 117247 | 114.29426 | 30.619716 | 10.653 | 299.87 |
Because of the GPS error or digital map measurement error, the deviation phenomenon between FCD and map often exists. The objective of this section is to develop a map matching algorithm for FCD to assess the traffic condition. The core of this map matching algorithm proceeds as follows (Figure
The process of the map matching algorithm.
In the location determination phase, a comprehensive model (formula (
The shortest path algorithm is to find a path between two vertices in a graph such that the sum of the weights of its constituent edges is minimized. Dijkstra’s algorithm [
In Step 1 (initialization), road networks data is preloaded into memory in order to search the shortest path. Quadtree index is constructed in order to facilitate the spatial query in the road network. Each road segment is constructed as a rectangle which is inserted into the Quadtree.
In Step 2 (searching), searching rectangle is constructed to index the related roads. Two adjacent GPS points are introduced to construct the bounding box. There is a distance limitation in a given time period for a taxicab. So, the maximum distance in a given time is applied to extend the searching area. After construction of the searching area, the related roads to calculate the shortest path can be selected.
In Step 3 (shortest path calculation), Dijkstra’s algorithm is designed to solve the shortest path problem. Because the road networks can be viewed as a sparse graph, list structure is defined to accelerate the route searching. By connecting all the adjacent points, the taxicab route can be acquired.
The shortest path problem is to find a path between two vertices (or nodes) in a graph such that the sum of the edge weights is minimized. Route choice of the shortest travel time can also be taken as the shortest path problem. The edge weight is the travel time. The difference from the traditional shortest path problem is that the edge weight is dynamically changed over time. This section introduces the calculation method for the route choice of the shortest time.
Road network is constructed to conduct the route analysis. Node Information and Edge Information are created firstly from road segments for further analysis. The Node Information includes three parts:
According to the Node Information and Edge Information, the network can be constructed. Because some road segments are single way, sharing a common node does not mean that the two segments can have access to each other. In the following section, single way and two-way road segments are further discussed.
Road network is a typical mixed graph (Figure
Analysis of a mixed graph.
Three classes including
Hierarchical relationship of Graph, Node, and Edge Classes.
Based on Figure
The process of the shortest travel time for Figure
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A case study for the shortest travel time.
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(c) If the
(d) If, in the
Thirdly, the minimum weight of the edge relating to other points which is named
Because road length is not equal to road weight which is dynamically changed over time, edges cannot be sorted by length. This algorithm runs in
Continuous trajectory of the taxicabs can be acquired by the proposed map matching method. Firstly, GPS points are projected to roads. Then, the shortest path algorithm is used to acquire the path of the adjacent points. Finally, the spatiotemporal position of taxicabs is obtained (Figure
Map matching of FCD. (a) FCD of the five taxicabs. (b) Trajectory of the taxicabs after map matching.
The weekend and weekday have different patterns in traffic [
Three roads are selected randomly to calculate the average driving speed of every weekday from FCD: that is, Dingziqiao Road (in the lower right corner of Figure
The position of the roads and the mean speed. (a) Position of roads in Wuhan. (b) Mean speed of Dingziqiao Road. (c) Mean speed of Wuhan Yangtze River Bridge. (d) Mean speed of Xinhua Road.
The four weekdays in the same road present a similar pattern in Figures
Since the average speed of roads can reflect the traffic information of roads, the spatiotemporal distribution of the road speed at every slice is investigated. Figure
Illustration of spatiotemporal distribution of the average road speed (weekdays). (a) Average road speed at six AM. (b) Average road speed at eight AM.
Following conclusions can be drawn from Figure
According to the improved Dijkstra algorithm, the route choice prototype is developed. Both the shortest distance path and the shortest travel time path function are implemented. Since they may produce different results, the same starting point and end point are chosen for route analysis in the following three experiments. The experimental results show the different characteristics (Figure
Prototype of the route choice. (a) The shortest distance path. (b) The shortest travel time path (departure time, six AM, weekdays). (c) The shortest travel time path (departure time, eight AM, weekdays).
The accuracy of map matching algorithm has a significant impact on the acquirement of road situation. Therefore, the accuracy is an important factor in the experiment. All FCD within a day (over 14 million records) are selected to verify the proposed algorithm.
Seven sets of values are assigned to the parameters in formula (
Therefore, the values of
The average speed of historical FCD for a certain time may reflect road traffic conditions at a particular moment. CV (coefficient of variation) is introduced to express the dispersion degree of the driving speed of roads:
CV of the driving speed about three roads (Figure
CV of the driving speed about Dingziqiao Road, Wuhan Yangtze River Bridge, and Xinhua Road, respectively. (a) CV of the driving speed about Dingziqiao Road. (b) CV of the driving speed about Wuhan Yangtze River Bridge. (c) CV of the driving speed about Xinhua Road.
Distance factor and time factor are used to evaluate the proposed shortest travel time algorithm. The distance and time cost of the planning paths in Figures
The distance and time cost of planning paths in Figure
Planning path in Figure |
Planning path in Figure |
Planning path in Figure |
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Distance | 12,432.79 | 13,424.16 | 18,058.25 |
Time | Null | 1,094.26 | 1,160.66 |
If the traffic condition is good, the planning paths (the shortest distance path and the shortest travel time path) may be close in spatiality and partly overlap (Figures
If traffic jams have occurred in some roads of the city center, there is usually a big difference between the shortest travel time path and the shortest distance path, since the traffic condition of highway is usually better than that of other roads. For example, the shortest travel time path in Figure
The planning paths in different time are also different although they apply the same algorithm. The road traffic condition varies over time, so the shortest travel time paths are totally different in different departure time (Figures
In this study, an effective map matching algorithm is proposed and the results show that the proposed method has a higher accuracy. Based on the results of three roads’ CV, we conclude that traffic distribution in four weekdays for each road has a similar pattern. By comparing with routes of the shortest travel time and the shortest distance, the results show that the shortest travel time paths cost less traveling time than the shortest distance path.
Although more than 85 million records are collected and analyzed, traffic conditions may be influenced by other factors, such as weather and holiday. However, we have not considered the influence of these factors on traffic in this study. For the proposed map matching algorithm, because some map matching algorithms are not open source, we have not computed the accuracy of these algorithms.
Clearly, the research in this article can be regarded as an initial step in the application of FCD. Because FCD has the characteristic of big data, future research is planned to apply distributed computing technology to speed up the analysis rate of large-scale GPS records. In addition, multisource data will be used to analyze the traffic condition in the future work.
The authors declare that there is no conflict of interests regarding the publication of this paper.
This work is sponsored by the National Natural Science Foundation of China (no. 41301417), State-Sponsored Scholarship Program, the Chongqing Natural Science Foundation (no. cstc2014jcyjA20017), the Fundamental Research Funds for the Central Universities (no. XDJK2015B022), and Open Research Fund by Sichuan Engineering Research Center for Emergency Mapping & Disaster Reduction (no. K2015B015).