# Understanding the Shortest Route Selection Behavior for Private Cars Using Trajectory Data and Navigation Information

Authors: Shiguang Wang; Heng Ding; Zeyang Cheng
Journal: Journal of Advanced Transportation
 (2022)

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## Abstract

Traffic information and driving preference play critical roles in the route selection of drivers and further impact transport management in practice. Some studies have explored the difference between actual and shortest paths for private cars during route selection. However, the quantification of the difference and deviation as well as the impacts of the date on route selection is still seldom investigated. The study proposed a method to quantify the deviation between actual and shortest paths based on big trajectory data and the digital map. Firstly, the rules of private car travel are determined according to the definition of a trip, and the travel trajectory is divided based on these rules to attain many trips. Then, the trip routes and their attributes are generated by geographical information methods. Baidu Map’s path planning collects the shortest routes with the optimal distance and time, and the deviation between actual and recommended paths is compared. Finally, the results of 2860 private car trips of nearly 400 drivers in Chongqing, China, reveal that only about 67% of the actual trips match well with the shortest path, which was significantly higher compared to existing studies. However, the deviation between the actual and shortest paths is limited to 9 minutes or 2 kilometers. There was no significant difference between the weekday and weekend in the proportion. Compared with the weekday, the indicators of the weekend are more deviated. Path selection and the deviation vary in travel modes, OD types, drivers’ preferences, travel time intervals, and distance intervals.


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## Body

## 1. Introduction

In 1952, Wardrop proposed the first principle of traffic equilibrium (user equilibrium, UE), which laid the foundation for traffic assignment. The first principle is that when the road users know the traffic state of the network and choose the shortest path, the network will reach the equilibrium state [1]. It is difficult for travelers to know the traffic status of the road network, so they can only choose the shortest path through estimation or their experiences. At the same time, some travelers have preferences in route selection. Traffic scholars know that there are differences between the actual path and the shortest path for private cars. However, due to the limitation of data, the quantitative empirical research on the discrepancy and deviation between them is minimal. Meanwhile, drivers enjoy more and more navigation services during a trip. However, the impacts of traffic information on route selection (e.g., whether drivers follow the recommended optimal routes, the difference between the weekday and weekend) are not studied very well. For example, most studies failed to quantify a precise relative proportion for shortest route selection or compliance ratio of route suggestions with accurate data [2–4]. Moreover, studies about the deviation between actual routes and recommended routes are minor; only the study of Minneapolis-St. Paul described the deviation between the commuters’ actual path and the shortest path [5].The shortest path principle is often used as the route choice standard for road users in many research and practices of traffic. “Shortest” is the road network attribute to be considered in the choice of the travel path. However, some studies have pointed out a big difference between the actual path and the shortest path for private car travel [2, 5]. Even in some cases, no residents use the shortest distance path unless the shortest distance path is consistent with the fastest time path [6]. Most drivers tend to choose the familiar travel path and only choose the most straightforward path recommended by the guidance system in an emergent condition [7]. The proportion of fastest path selection in existing studies worldwide is shown in Table 1. The path choice behavior of residents generated by simulation based on the travel survey data shows the opposite conclusion for the shortest distance and the shortest time path. The residents in Boston prefer less journey time; however, Turin residents like shorter travel distances [3, 4]. Although the proportion varies in the existing cases, they support that most drivers take a path that differs from the shortest path.Table 1
The shortest path selection proportion in existing studies.
AreaData profileShortest distanceShortest time (%)Boston [3]Traffic survey of 188 respondents (1997)#Simulation28%45Turin [4]276 observations of Turin Polytechnic facultySimulation30.93%18.22Lexington [2]216 drivers over a week, more than 3000 tripsNull∗Minneapolis-St. Paul [6]143 subjects, 25157 trips (2008)Null@34Minneapolis-St. Paul [5]50 persons, 124 commute trips (2011)12.26%24.19Enschede [8]317 respondents, 624 trips54%41A European country [9]526 users over 18 months47%The Philippines and Japan [7]17 driver participantsNull21.6Note:#survey time of the data; ∗most drivers choose a path that deviates from the shortest path; @the ratio that excludes shortest time paths is 0.The first principle of Wardrop equilibrium is rarely verified by measured data, and only a few empirical studies reveal the characteristics of the path chosen by travelers. Meanwhile, there is no analysis result of private car travel of Chinese urban residents in similar studies, only that of taxi travel in Beijing, Shenzhen, and the proportion of taxi drivers choosing the shortest path is less than 40% [10–12]. Whether Chinese urban residents have such characteristics or what characteristics exist in private car travel path selection needs to be further studied. This is our first motivation to do such a study. We also noticed that the difference and comparison of shortest path selection between weekdays and weekends are rarely involved in the existing literature. This is the second question to answer in the study. Moreover, in the information and self-driving automobile driving eras, drivers increasingly use GPS and smartphones to provide real-time travel information, generating more complex nonaggregate path results. It will be beneficial to examine the practicality of using widely used digital maps to collect shortest path information and quantify the difference and deviation between actual and shortest paths.The contributions of the study mainly lie in the three following aspects:(1)
To quantify the similarities and differences in the private car route selection between the selected Chinese city and other countries.(2)
To analyze the impacts of weekdays or weekends on route selection and the deviation between actual and shortest paths.(3)
To verify whether it is possible to assess the deviation between actual and shortest paths based on the digital map and trajectory data and test it in a mountain city seldom covered in the current study.The remainder of this paper is organized as follows. Section2 presents the deviation quantification method, including route selection extraction based on GIS and shortest path data extraction, and selects a case for further analysis. Section 3 is the research results and discussions of the deviation between the two kinds of paths in the case of Chongqing, China. The conclusions are drawn and future extensions are discussed in Section 4.


## 2. Materials and Methods

### 2.1. Data and Area

As shown in Figure1, Chongqing is one of four cities (Beijing, Shanghai, Tianjin, and Chongqing) that are directly under the central government in China. It is a mountain city seldom reported in existing transport research. The travelers in the mountain city may have different route selection behaviors compared with cases in the existing studies. We collected private car trajectory data with vehicle GPS devices from nearly 400 volunteers over a month in 2015, consisting of about 10 million travel track records, including vehicle ID, longitude, latitude, speed, direction, and vehicle time. The sampling frequency is 5 seconds. This study considered the similarity of residents’ travel cycles and the influence of traditional Chinese festivals such as Teachers’ Day and Mid-Autumn Festival. A consecutive week from September 14, 2015, to September 20, 2015, was selected for the analysis. Taking the OD distribution of residents on September 14, 2015, as an example, Figure 2 shows that the collected samples cover the whole urban road network, especially the urban center.Figure 1
The location of Chongqing in China and its area.Figure 2
OD distribution of sampled residents in Chongqing. (a) Origin. (b) Destination.
(a)(b)Considering the travel similarity [13–15], we chose one day of the weekdays and weekends, respectively, as the representative days proved reasonable in some studies [16]. Trajectory data on September 14, 2015 (Monday), and September 19, 2015 (Saturday), were selected for follow-up analysis. The analysis process of the study is shown in Figure 3.Figure 3
Analysis process in the study.


### 2.2. Route Selection Data Extraction from Trajectory Data Based on GIS

According to the actual travel situation of private cars and the characteristics of the trajectory data, the critical travel indicators were defined. A single trip of a private car and the trip chain of the same resident were extracted. The trip is defined as the movement process: city dwellers with a specific purpose move from point a to point b in some or many kinds of transportation, and the transport distance is usually more than 300 meters. Private car trips and trajectory data are unique. The continuous travel trajectory is divided by the following key indicators to acquire each trip for the same resident over a day:(1)
The travel distance is more significant than 1000 meters.(2)
The travel time shall not exceed 2 hours.(3)
If the car parks for more than 30 minutes continuously, it will take two different trips.(4)
Records with an interrupt interval of 5∼20 minutes will be regarded as a trip; interruption data over 20 minutes will be treated as two trips.Then the vector path is generated in ArcGIS according to the technical process shown in Figure4, and the projection can attain the distance information. First, match the tracks to the nearest road. Then ArcGIS toolbox produces point elements and line elements, respectively, by time order. ModelBuilder can do this operation to design a toolbox for batch processing. Finally, the generated line map layer is manually modified to determine the final travel path.Figure 4
The technical flow of path generation from locus points.According to the above methods, the sample tracks were processed and analyzed on September 14 and September 19, 2015. The travel frequency with a 1-hour interval was calculated based on the departure time, as shown in Figure5. The weekday in the figure represents September 14, 2015, and the rest day represents September 19, 2015. The travel frequency distribution of sampled residents is consistent with the time evolution trend of trips in the previous studies [15, 17], indicating that the sample data can reflect the overall situation of residents’ travel relatively comprehensively. The basic information, such as the number of vehicles (i.e., drivers) and trips, is shown in Table 2.Figure 5
Travel frequency distribution of sampled residents in Chongqing.Table 2
Sampling quantity of the drivers and trips.
DateResidentsTripsSame driversSame drivers’ tripsSep.14, 201539114342881093Sep.19, 201538314891211


### 2.3. Shortest Path Data Extraction from Navigation Information

The shortest path analyzed in this section includes the shortest distance path and the shortest time path. The shortest distance path of any OD is fixed in the road network, but the shortest time path varies with the change in a traffic state. Most existing research uses simulation, weighted solution of historical average speed, or the sum of historical travel time to obtain the shortest time path, which may have a significant error with the actual traffic operation. This paper considers using the navigation path of the electronic map to extract the shortest path. The mainstream electronic map users in Chongqing have reached a certain magnitude, which makes it possible to compare the recommended paths (including the shortest distance path, the shortest time path, and the path that coincides with the actual travel) with the actual travel paths. Combined with the development of autonomous driving, the future will rely more on electronic map navigation. Therefore, this shortest path data acquisition method can also realize the comparative analysis of the route selection in autonomous and human driving.Some web maps, like Google Maps and Baidu Maps, provide API tools (e.g., Directions Service in Google Maps) to develop new applications or attain navigation data. Route planning is a primary function of these API tools; it offers direction service with a route request between a specific origin and destination. The navigation data used here is from Baidu Maps. Residents generally need to travel through the community roads, which are not open to all social vehicles. Taking the community roads of a residential area in Chongqing, Figure6 shows the residential area’s actual navigation areas on three maps (Baidu, Amap, and Google). Compared with Baidu and Amap, Google Maps fails to show the community roads, so the navigation path within the community cannot be given in the actual navigation process, resulting in a significant error between the navigation path and the actual travel path. When it comes to the two Chinese software programs (i.e., Baidu and Amap), the district roads displayed in Amap were more detailed than those in Baidu Maps. However, in the navigation, the community roads in Amap failed to be set as the origin and destination of a trip, which will cause errors similar to that of Google Maps. Therefore, this study chooses the recommended paths of the Baidu Maps to identify the shortest paths.Figure 6
Road conditions on different maps of a residential area in Chongqing. (a) Baidu Maps, (b) Amap (AutoNavi Map), and (c) Google Maps.
(a)(b)(c)After determining the electronic map, we considered the problem of statistical time. In order to be consistent as possible with the actual traffic state, we divided the period according to the travel frequency of residents over a day, as shown in Table3. The collection time division is a process to identify traffic state (congestion or not). If there is a noticeable congestion difference between the two nearest periods, the period must be divided into two; otherwise, only one period needs to be reserved. Here the traffic state or degree of congestion is determined by the travel frequency of travelers. The statistical periods of shortest path data are determined according to the travel time of each trip. The path statistics time division may vary due to the changes in dates and cities. The main input parameters include longitude and latitude of origin and destination, route tactics, coordinate type, and the access key. After entering the link, the platform will output the recommended route’s distance, duration, traffic condition, and so forth. The data is used for route selection analysis.Table 3
Path statistics time division.
DatePeriod 1Period 2Period 3Period 4Period 5Sep.14, 20150:00–7:007:00–9:0017:00–19:009:00–17:0019:00–22:0022:00–24:00Sep.19, 20150:00–6:006:00–21:0021:00–24:00Overlap (O) compares the similarity between the shortest path and the actual path. Similar to path statistics time division, it may also vary in different cities.(1)O=∑ss∈sp,s∈rpls∑rr∈rplr,where s represents the road section ID (the sth road section) on the shortest path; sp represents the shortest path; r represents the road section ID (the rth road section) on the actual selected path, and rp represents the actual selected path for drivers. In (1), ls is the length (unit: kilometers) of the road segment s on the shortest path and real selected path and lr is the length of the road segment r that is on a selected path.The consistency criterion is more than 80% coincidence. Because the actual route choice of residents may be influenced by the compliance with traffic rules, the establishment of new traffic signs, the parking situation, the error of electronic maps, and so on, there is a certain degree of deviation from the recommended path of electronic map. Setting a specific error range can better reflect the real situation. Figure7 shows the actual path and the shortest path of a private car trip. The electronic map directly gives the shortest distance path, including time, distance, and other information. The one with shortest time among the recommended paths is chosen as the shortest time path. As shown in Figure 7, O of the trip is close to 1, so this actual path is the shortest distance path. The shortest time path is determined similarly.Figure 7
Path comparison. (a) Shortest distance path of Baidu; (b) the actual path.
(a)(b)After getting the data of the actual and shortest paths, we use the selected proportion (P) of the shortest paths to show the difference between the actual and shortest paths. The residual (R), the absolute residual (AR), and the standard deviation (SD) of trip measures are selected to display the deviation between the two kinds of travel paths.The proportion of choosing the shortest paths for drivers is shown as follows:(2)P=∑i=1AaiA,ai=1,O≥80%,0,O<80%,where ai is the possibility of choosing the shortest path in a trip and A is the number of total trips. In particular, we carry out the preliminary comparative analysis of the travel path for the commuter. The commuter regularly travels to and from work; he or she usually has a relatively fixed OD and route. They account for a considerable proportion of all travelers, and their route choices tend to have a certain regularity and may be optimized by traffic measures. The path similarity is measured by overlap (O). The two paths with more than 90% coincidence are considered the same path pairs; the OD pairs with 80%∼90% overlap are similar path pairs. Less than 50% of overlap paths are identified as different path pairs.Travel time is the fundamental travel indicator and is selected as an example to calculate the deviation measures. The quantitative method of travel distance is the same as that of travel time.(3)RT=T−TS,ART=T−TS,SDT=1A−1∑i=1AT−TS2,where T is the actual travel time of a trip and TS is the shortest travel time of a trip. R is the residual, AR denotes the absolute residual, and SD is the standard deviation.


## 2.1. Data and Area

As shown in Figure1, Chongqing is one of four cities (Beijing, Shanghai, Tianjin, and Chongqing) that are directly under the central government in China. It is a mountain city seldom reported in existing transport research. The travelers in the mountain city may have different route selection behaviors compared with cases in the existing studies. We collected private car trajectory data with vehicle GPS devices from nearly 400 volunteers over a month in 2015, consisting of about 10 million travel track records, including vehicle ID, longitude, latitude, speed, direction, and vehicle time. The sampling frequency is 5 seconds. This study considered the similarity of residents’ travel cycles and the influence of traditional Chinese festivals such as Teachers’ Day and Mid-Autumn Festival. A consecutive week from September 14, 2015, to September 20, 2015, was selected for the analysis. Taking the OD distribution of residents on September 14, 2015, as an example, Figure 2 shows that the collected samples cover the whole urban road network, especially the urban center.Figure 1
The location of Chongqing in China and its area.Figure 2
OD distribution of sampled residents in Chongqing. (a) Origin. (b) Destination.
(a)(b)Considering the travel similarity [13–15], we chose one day of the weekdays and weekends, respectively, as the representative days proved reasonable in some studies [16]. Trajectory data on September 14, 2015 (Monday), and September 19, 2015 (Saturday), were selected for follow-up analysis. The analysis process of the study is shown in Figure 3.Figure 3
Analysis process in the study.


## 2.2. Route Selection Data Extraction from Trajectory Data Based on GIS

According to the actual travel situation of private cars and the characteristics of the trajectory data, the critical travel indicators were defined. A single trip of a private car and the trip chain of the same resident were extracted. The trip is defined as the movement process: city dwellers with a specific purpose move from point a to point b in some or many kinds of transportation, and the transport distance is usually more than 300 meters. Private car trips and trajectory data are unique. The continuous travel trajectory is divided by the following key indicators to acquire each trip for the same resident over a day:(1)
The travel distance is more significant than 1000 meters.(2)
The travel time shall not exceed 2 hours.(3)
If the car parks for more than 30 minutes continuously, it will take two different trips.(4)
Records with an interrupt interval of 5∼20 minutes will be regarded as a trip; interruption data over 20 minutes will be treated as two trips.Then the vector path is generated in ArcGIS according to the technical process shown in Figure4, and the projection can attain the distance information. First, match the tracks to the nearest road. Then ArcGIS toolbox produces point elements and line elements, respectively, by time order. ModelBuilder can do this operation to design a toolbox for batch processing. Finally, the generated line map layer is manually modified to determine the final travel path.Figure 4
The technical flow of path generation from locus points.According to the above methods, the sample tracks were processed and analyzed on September 14 and September 19, 2015. The travel frequency with a 1-hour interval was calculated based on the departure time, as shown in Figure5. The weekday in the figure represents September 14, 2015, and the rest day represents September 19, 2015. The travel frequency distribution of sampled residents is consistent with the time evolution trend of trips in the previous studies [15, 17], indicating that the sample data can reflect the overall situation of residents’ travel relatively comprehensively. The basic information, such as the number of vehicles (i.e., drivers) and trips, is shown in Table 2.Figure 5
Travel frequency distribution of sampled residents in Chongqing.Table 2
Sampling quantity of the drivers and trips.
DateResidentsTripsSame driversSame drivers’ tripsSep.14, 201539114342881093Sep.19, 201538314891211


## 2.3. Shortest Path Data Extraction from Navigation Information

The shortest path analyzed in this section includes the shortest distance path and the shortest time path. The shortest distance path of any OD is fixed in the road network, but the shortest time path varies with the change in a traffic state. Most existing research uses simulation, weighted solution of historical average speed, or the sum of historical travel time to obtain the shortest time path, which may have a significant error with the actual traffic operation. This paper considers using the navigation path of the electronic map to extract the shortest path. The mainstream electronic map users in Chongqing have reached a certain magnitude, which makes it possible to compare the recommended paths (including the shortest distance path, the shortest time path, and the path that coincides with the actual travel) with the actual travel paths. Combined with the development of autonomous driving, the future will rely more on electronic map navigation. Therefore, this shortest path data acquisition method can also realize the comparative analysis of the route selection in autonomous and human driving.Some web maps, like Google Maps and Baidu Maps, provide API tools (e.g., Directions Service in Google Maps) to develop new applications or attain navigation data. Route planning is a primary function of these API tools; it offers direction service with a route request between a specific origin and destination. The navigation data used here is from Baidu Maps. Residents generally need to travel through the community roads, which are not open to all social vehicles. Taking the community roads of a residential area in Chongqing, Figure6 shows the residential area’s actual navigation areas on three maps (Baidu, Amap, and Google). Compared with Baidu and Amap, Google Maps fails to show the community roads, so the navigation path within the community cannot be given in the actual navigation process, resulting in a significant error between the navigation path and the actual travel path. When it comes to the two Chinese software programs (i.e., Baidu and Amap), the district roads displayed in Amap were more detailed than those in Baidu Maps. However, in the navigation, the community roads in Amap failed to be set as the origin and destination of a trip, which will cause errors similar to that of Google Maps. Therefore, this study chooses the recommended paths of the Baidu Maps to identify the shortest paths.Figure 6
Road conditions on different maps of a residential area in Chongqing. (a) Baidu Maps, (b) Amap (AutoNavi Map), and (c) Google Maps.
(a)(b)(c)After determining the electronic map, we considered the problem of statistical time. In order to be consistent as possible with the actual traffic state, we divided the period according to the travel frequency of residents over a day, as shown in Table3. The collection time division is a process to identify traffic state (congestion or not). If there is a noticeable congestion difference between the two nearest periods, the period must be divided into two; otherwise, only one period needs to be reserved. Here the traffic state or degree of congestion is determined by the travel frequency of travelers. The statistical periods of shortest path data are determined according to the travel time of each trip. The path statistics time division may vary due to the changes in dates and cities. The main input parameters include longitude and latitude of origin and destination, route tactics, coordinate type, and the access key. After entering the link, the platform will output the recommended route’s distance, duration, traffic condition, and so forth. The data is used for route selection analysis.Table 3
Path statistics time division.
DatePeriod 1Period 2Period 3Period 4Period 5Sep.14, 20150:00–7:007:00–9:0017:00–19:009:00–17:0019:00–22:0022:00–24:00Sep.19, 20150:00–6:006:00–21:0021:00–24:00Overlap (O) compares the similarity between the shortest path and the actual path. Similar to path statistics time division, it may also vary in different cities.(1)O=∑ss∈sp,s∈rpls∑rr∈rplr,where s represents the road section ID (the sth road section) on the shortest path; sp represents the shortest path; r represents the road section ID (the rth road section) on the actual selected path, and rp represents the actual selected path for drivers. In (1), ls is the length (unit: kilometers) of the road segment s on the shortest path and real selected path and lr is the length of the road segment r that is on a selected path.The consistency criterion is more than 80% coincidence. Because the actual route choice of residents may be influenced by the compliance with traffic rules, the establishment of new traffic signs, the parking situation, the error of electronic maps, and so on, there is a certain degree of deviation from the recommended path of electronic map. Setting a specific error range can better reflect the real situation. Figure7 shows the actual path and the shortest path of a private car trip. The electronic map directly gives the shortest distance path, including time, distance, and other information. The one with shortest time among the recommended paths is chosen as the shortest time path. As shown in Figure 7, O of the trip is close to 1, so this actual path is the shortest distance path. The shortest time path is determined similarly.Figure 7
Path comparison. (a) Shortest distance path of Baidu; (b) the actual path.
(a)(b)After getting the data of the actual and shortest paths, we use the selected proportion (P) of the shortest paths to show the difference between the actual and shortest paths. The residual (R), the absolute residual (AR), and the standard deviation (SD) of trip measures are selected to display the deviation between the two kinds of travel paths.The proportion of choosing the shortest paths for drivers is shown as follows:(2)P=∑i=1AaiA,ai=1,O≥80%,0,O<80%,where ai is the possibility of choosing the shortest path in a trip and A is the number of total trips. In particular, we carry out the preliminary comparative analysis of the travel path for the commuter. The commuter regularly travels to and from work; he or she usually has a relatively fixed OD and route. They account for a considerable proportion of all travelers, and their route choices tend to have a certain regularity and may be optimized by traffic measures. The path similarity is measured by overlap (O). The two paths with more than 90% coincidence are considered the same path pairs; the OD pairs with 80%∼90% overlap are similar path pairs. Less than 50% of overlap paths are identified as different path pairs.Travel time is the fundamental travel indicator and is selected as an example to calculate the deviation measures. The quantitative method of travel distance is the same as that of travel time.(3)RT=T−TS,ART=T−TS,SDT=1A−1∑i=1AT−TS2,where T is the actual travel time of a trip and TS is the shortest travel time of a trip. R is the residual, AR denotes the absolute residual, and SD is the standard deviation.


## 3. Results

### 3.1. Comparisons between Travel Path and the Shortest Path

#### 3.1.1. General Results

Excluding a small number of circular routes (of the exact origins) or trips with apparent detour behavior, 1398 effective paths in the working day and 1462 effective paths in the rest day were finally obtained to compare the deviations between the selected path and the shortest path. Table4 shows the situation of sampled residents in Chongqing who choose the shortest route to travel. On Monday, 46.72% of Chongqing residents chose the shortest distance route, and 68.81% was the shortest time route. The shortest time path takes up 52.87%, among which 60.93% is also the shortest distance path. On Saturday, 46.51% of residents chose the shortest distance route, and 68.68% is also the shortest time route. The shortest time path takes up 52.94%, of which 60.85% is also the shortest distance path. According to the summary, the proportion of Chongqing residents choosing the shortest route (including the shortest time and the shortest distance) to travel on the weekday is 67.44%. On the weekend, 67.51% chose the shortest path, which was similar to the percentage on the weekday.Table 4
The proportion of residents choosing the shortest path in Chongqing.
DayData descriptionShortest distance path (%)Shortest time path (%)Monday391 residents’ 2860 private car trips46.7252.87Saturday46.5152.94Compared with Chongqing, the existing studies of cities worldwide have shown a smaller proportion of shortest path selection, and only the research of Minneapolis-St. Paul described the deviation between the commuters’ actual path and the shortest path. Next, the study will analyze the deviation between the actual travel path and the shortest path for Chongqing residents.


#### 3.1.2. Deviation between Travel Path and the Shortest Path

The shortest distance path, the shortest time path, and the recommended path that coincide with the actual travel path provided by Baidu Maps can be compared with the actual path data. The statistical description results are shown in Table5. The research results showed that the actual travel route selected by residents on the weekday consumed 3.37 and 5.41 minutes (residual) more on average. The average distance was 1.39 and 0.78 kilometers (residual), more than the shortest distance and time paths. Nevertheless, the deviation reached about 9 min and 2 km (absolute residual). Travelers saved 2 minutes on average after choosing the shortest time path compared with the shortest distance path but traveled 0.62 km more.Table 5
The statistical description of the deviation between the actual and shortest paths.
Sample groupSample sizeTravel time/minTravel distance/kmResidualAbsolute residualStandard deviationResidualAbsolute residualStandard deviationRP/SDP1398 (1462)3.37 (5.64)8.97 (10.01)11.35 (13.22)1.39 (1.69)1.95 (2.05)3.51 (4.05)RP/STP1398 (1462)5.41 (7.70)9.03 (10.11)11.38 (13.63)0.78 (1.08)1.80 (1.08)3.46 (1.84)SDP/STP1398 (1462)2.03 (2.06)2.02 (2.06)4.96 (5.61)−0.62 (−0.55)0.64 (0.62)1.90 (2.01)RP/RRP824 (1021)2.23 (4.51)6.82 (7.85)8.65 (10.03)0.16 (0.43)0.84 (0.93)2.32 (1.79)RRP/SDP824 (1021)−1.33 (−1.18)1.68 (2.00)5.25 (6.12)0.44 (0.53)0.44 (0.55)1.30 (1.56)RRP/STP824 (1021)0.31 (0.91)0.33 (1.00)2.40 (2.72)0.07 (−0.06)0.12 (0.43)0.69 (1.48)RP/SDP′824 (1021)0.90 (3.29)7.21 (8.26)9.11 (10.66)0.61 (0.94)1.12 (1.24)2.54 (2.11)RP/STP′824 (1021)2.54 (5.42)6.77 (8.03)8.34 (10.39)0.24 (0.37)0.92 (1.12)2.07 (2.02)Note. RP is the actual path; SDP is the shortest distance path; STP is the shortest time path; RRP is the recommended path that overlaps with the actual path; ' stands for deviation correction. The data outside the brackets are on the weekday, and the data inside the brackets are on the weekend. The same is below.However, we note that there is a deviation between the indexes of the actual path and the recommended path of the Baidu Maps which coincides with the actual path, so this deviation is used to correct the error between the actual path and the shortest path. Compared with the shortest distance and time paths, the actual travel route selected by the residents consumes 0.90 and 2.54 minutes more on average, and the average distance is 0.61 and 0.24 km more. Compared with the working day, the indicators of the rest day are more deviated. On the weekend, compared with the shortest distance and time paths, the actual travel route selected by residents consumed 3.33 and 5.42 minutes more on average, and the average distance was 0.96 and 0.37 km more. Although many Chinese urban residents still do not choose the shortest path, the deviation between the actual path and the shortest path is slight. Based on the residual error, the actual travel time of the selected path takes no more than 6 minutes on average, and the travel distance is no more than 1 km. Taking the absolute residual value as the benchmark, we found that the selected path takes no more than 9 minutes on average, and the travel distance is no more than 2 km.


#### 3.1.3. Deviation between Similar Route Pairs

This section uses the same OD paths of the same resident to conduct a preliminary comparative analysis of the travel paths. The path similarity is shown in Table6. There are 655 trips (45.64% of the total trips) with the fixed OD involving 259 residents (66.24% of the residents), and 205 of them are commuter routes (31.29% of the fixed OD trips) in the working day. The commuters usually have a relatively fixed OD and route. They account for a considerable proportion, and their route choices tend to have a certain regularity and may be optimized by some measures. Thus, uncovering the similarity of commuter routes is of importance to design more targeted measures. In the total path of the rest day, there were 743 trips (49.90% of the total trips) with the fixed OD, involving 259 residents (67.62% of the residents). The weekend does not differentiate between activity types.Table 6
Trip paths similarity of residents in Chongqing.
SimilaritySameSimilarDifferentActivity typeCommuterOtherCommuterOtherCommuterOtherCount/pairs4311827713387Sum/pairs161 (154)98 (112)120 (132)Note. The data outside the brackets is on the weekday, and the data inside the brackets is on the weekend.Table7 shows the comparative analysis of the residuals of three indexes of travel time, distance, and travel speed of different path pairs. The average absolute value of travel time residual of all samples is 11.34 (weekend is 12.04) minutes, and the average absolute value of travel distance residual is 2.40 (weekend is 2.10) km. Moreover, the average absolute value of the travel speed residual is 7.48 (weekend is 7.60) km/h. The absolute standard deviations of the residual values corresponding to each index are 14.74 (16.48), 5.11 (4.25), and 7.57 (7.23). The differences of each index of the same and similar path pairs are less than the whole. However, the difference between different paths is greater than the whole.Table 7
Absolute residual values and standard deviations of trip indicators for the path pairs.
Activity typeCommutingOtherWholePair typeResidualAbsoluteStandard deviationAbsoluteStandard deviationAbsoluteStandard deviationSameTravel time/min9.4213.526.5110.916.48 (7.11)9.69 (9.83)Distance/km0.730.681.031.720.86 (0.86)1.28 (1.28)Speed/km/h7.8310.637.308.067.12 (7.20)8.62 (6.94)SimilarTravel time/min11.2414.9212.9915.1712.31 (13.68)14.99 (18.53)Distance/km2.172.942.292.882.24 (2.27)2.90 (2.83)Speed/km/h5.604.107.656.696.99 (6.94)6.17 (7.82)DifferentTravel time/min15.2814.9417.8518.6817.07 (16.40)17.74 (19.22)Distance/km3.105.844.888.594.58 (3.40)8.11 (6.52)Speed/km/h7.275.058.697.488.36 (8.62)7.05 (7.00)Note. The data outside the brackets is on the weekday, and the data inside the brackets is on the weekend.When the activity types are considered, the average absolute residual value of the commuting time is 11.85 minutes. The average absolute value of the distance residual is 1.87 km. The average absolute value of the travel speed residual is 7.16 km/h. The absolute standard deviations of the residual values for each index are 14.46, 3.77, and 7.70, respectively. The average absolute value of the travel time residual for the other travel is 11.21 minutes. The average absolute value of the residual for route distance is 2.62 km. The average absolute value of the residual for travel speed is 7.60 km/h. The absolute standard deviations of the residual values for each index are 14.86, 5.52, and 7.52. The difference in commuting travel time is slightly more significant than that in noncommuting. However, the differences in route distance and travel speed are minor compared to noncommuting. When path difference is considered, in the same path pairs, the travel time of commuting activities is greater than that of noncommuting activities, and the difference between route distance and travel speed is smaller than that of noncommuting activities. In similar and different path pairs, the difference of each index of commuting activity is smaller than that of noncommuting activity.


#### 3.1.4. Other Comparisons for Deviation Quantification

This section will analyze the residents’ choice of the shortest path for actual travel under different conditions.(1) Whether to Commute. 268 commuter and 1132 noncommuter travel routes were obtained during the working day. More commuters do not drive directly from home to work (including school pickup, entertainment, and other activities). These trips are not defined as commuting in travel behavior identification, so the scale is different in the number of commuting and noncommuting routes.The shortest path selection ratio of the two travel modes is shown in Table8, and the deviation between the actual path and the shortest path is shown in Table 9. The research results show that the proportion of residents choosing the shortest path in the process of commuting is smaller than that of noncommuting because people think that the familiar path is more able to let them reach the workplace within a particular time [5]. However, the route selected by commuters takes an average of 4–7 minutes longer than the shortest path, with an absolute deviation of about 10 minutes. The difference between the two in the distance of travel is slight, generally about 1 km. Since the probability of choosing the shortest path for noncommuter travel is greater, the difference between noncommuter travel and the shortest paths is smaller than that between commuter travel and the shortest paths. No matter what kind of travel mode, the proportion of residents choosing the shortest time path is higher than that of residents choosing the shortest distance path, and the two shortest paths overlap to a large extent. More than 80% of the shortest distance path is consistent with the shortest time path.Table 8
Shortest path selection proportions for commuters and noncommuters on a working day.
TypeShortest distance pathShortest time pathSum (%)Commuters31.34% (80.95%)42.16% (61.06%)47.76Noncommuters44.17% (85.80%)49.47% (76.61%)55.74Note. The proportion that is simultaneously another shortest path is given in the parentheses.Table 9
The deviation between the actual and the shortest paths for commuters/noncommuters on a working day.
Sample groupTravel time/minTravel distance/kmResidualAbsolute residualStandard deviationResidualAbsolute residualStandard deviationRP & SDP′4.47/0.2410.24/6.6110.80/8.720.66/0.591.25/1.092.05/2.60RP & STP′7.14/2.2710.35/6.3110.81/8.57−0.18/0.151.16/1.082.63/3.16(2) Whether OD is Fixed. The fixed OD trip refers to the trip with the exact origin and destination, and at least two trips with the same OD exist in one day.According to statistics, there are 584 fixed OD travel routes and 814 nonfixed OD travel routes on weekdays. There are 634 fixed OD travel paths and 828 nonfixed OD travel paths on the weekend. The selection of the shortest path is shown in Table10. The research results show that, in the case of fixed OD and the weekday, the proportion of residents choosing the shortest distance or time path is smaller than that of non-fixed OD and the rest day. On the rest day, the proportion of residents choosing the shortest path is significantly higher than that on a working day, regardless of whether OD is fixed or not. When distinguishing whether the OD is fixed or not, the total proportion of residents choosing the shortest path for the fixed OD trip is slightly higher than that for the nonfixed OD trip.Table 10
The proportion of shortest path selection for fixed and nonfixed OD trips.
TypeDateShortest distance pathShortest time pathSum (%)Fixed ODMonday40.24% (85.96%)47.09% (73.82%)52.57Saturday46.06% (61.99%)52.37% (55.42%)69.87Nonfixed ODMonday43.73% (85.11%)48.65% (76.26%)55.28Saturday46.86% (73.71%)53.26% (65.08%)65.58Note. The proportion that is simultaneously another shortest path is given in the parentheses.To some extent, whether the OD is fixed or not indicates the driver’s familiarity with the route. Meanwhile, the fixed OD trip can also indicate the importance of the trip, and the commuting process is an important part. The results show that residents are more likely to choose the shortest path when they are not working. Moreover, choosing the shortest path in an entirely nonworking state (rest day) is higher compared to the situation in a partial nonworking state (nonfixed OD travel on the weekday). This phenomenon shows the residents’ trust paradox on the shortest path. In the case of relatively urgent commuting, people tend to choose a more familiar path rather than the shortest path to ensure the timely arrival of the destination. However, in other nonemergency travel situations, people tend to choose the shortest path to obtain a shorter travel distance or time.When the deviation between the actual travel path and the shortest path is investigated under the condition that the OD is fixed or not, as shown in Tables11 and 12, the trends of the working day and rest day are generally the same. However, there is a slight difference in the specific value. The unified trend is that the deviation between the average travel time, the distance of nonfixed OD trips, and the shortest path is generally more significant than fixed OD trips. This shows that although there is a significant probability to choose the shortest path for the nonfixed OD trip, the deviation caused by the part that does not choose the shortest path is greater than the part that does not choose the shortest path in the fixed OD trip. The difference is as follows: the deviation of the rest day is more significant than that of the working day. On the weekday, compared with the shortest distance and time paths, the average travel time of residents consumes 1 and 3 minutes more, and the average distance is 0.80 and 0.25 km more. On the rest day, compared with the shortest distance and time paths, the average travel time of residents is 4.44 and 6.34 minutes longer, and the average distance is 1.04 and 0.49 km longer.Table 11
The deviation between the actual and the shortest paths of the fixed/nonfixed OD trips on weekdays.
Sample groupTravel time/minTravel distance/kmResidualAbsolute residualStandard deviationResidualAbsolute residualStandard deviationRP & SDP′0.89/1.028.66/6.3110.63/8.100.32/0.801.19/1.072.90/2.24RP & STP′0.34/2.990.35/6.221.30/8.28−0.15/0.250.24/0.991.32/2.39Table 12
The deviation between the actual and the shortest paths of the fixed/nonfixed OD trips on the weekend.
Sample groupTravel time/minTravel distance/kmResidualAbsolute residualStandard deviationResidualAbsolute residualStandard deviationRP & SDP′1.83/4.448.09/8.4011.36/10.090.82/1.041.15/1.301.76/2.35RP & STP′4.26/6.347.54/8.419.73/10.870.23/0.491.08/1.141.91/2.10


### 3.2. Comparisons between the Weekday and the Weekend

#### 3.2.1. Travel Characteristics Description of Private Cars

Figure8 shows the travel time distribution of private cars trips in Chongqing. The results showed that the proportion of trips within 15 minutes accounted for 34.62% on the weekdays. The mean travel time was 26.62 minutes, and the standard deviation was 20.15. The travel time distribution of the weekend is very similar to that of the weekday. The proportion of trips within 15 minutes accounted for 33.65%. The mean travel time was 27.20 minutes, and the standard deviation was 19.90.Figure 8
Histogram of travel time. (a) The weekday; (b) the weekend.
(a)(b)Figure9 shows the distribution of travel distance of private cars in Chongqing. The results show that, on the weekday, the proportion of trips within 22 km accounts for 84.76%. The mean travel distance is 12.13 km, and the standard deviation is 12.11. The proportion of the rest day at critical time points is higher than that of the working day. The proportion of trips within 22 km is 87.57%. The mean travel distance is 11.36 km, and the standard deviation is 11.40.Figure 9
Histogram of travel distance. (a) The weekday; (b) the weekend.
(a)(b)Regarding the number of trips, the maximum trip frequency on the weekday is 2, accounting for 34.53%. It is the same as the result of the weekend. However, it accounts for 28.17% of all trips, which is less than that of the weekday. For samples with travel times ranging from 2 to 10, the distributions for the weekday and weekends conform to the asymptotic exponential distribution, as shown in Figure10. When comparing the trip number of the same private cars on two days, the number of trips on the weekday is less than that on the rest day. Moreover, when the number of trips is large (e.g., 4–7), the frequency of the rest day is greater than that of the working day. As shown in Table 13, the trip number of 66.32% of residents on the rest day is no less than that of the weekday.Figure 10
Trip number distributions and fits on the weekday and weekends.Table 13
Comparison of the trips number between the weekday and weekend.
TypeWeekday < weekendWeekday = weekendWeekday > weekendCount1385397Proportion47.92%18.40%33.68%


#### 3.2.2. Classification Comparisons for Date

(1) Driving Preference. In a driver’s private car travel, the total number of trips on a day is b, among which a is the shortest path (the shortest time or distance), and then there is the proportion of the shortest path choice of the driver’s private car travel.(4)ω=ab.19.79% (weekday) and 13.16% (weekend) of the drivers in Chongqing did not choose the shortest path. The proportion of choosing the shortest path for all trips is 23.39% (weekday) and 17.89% (weekend). More details are shown in Figure11.Figure 11
Interval distribution of the shortest path selection for the overall drivers.In order to more accurately characterize the influence of different dates on the driver’s shortest path selection, this section screened the overlapped samples for two days and obtained a total of 286 valid identical samples. The proportion interval distribution of shortest path selection is shown in Figure12. The percentage of those who did not choose the shortest path is 17.13% (weekday) and 12.24% (weekend). The proportion of choosing the shortest path for all trips is 23.78% (weekday) and 15.03% (weekend).Figure 12
Interval distribution of the shortest path selection for the same drivers.(2) Segmented Travel Time. The shortest path selection varies for various times and dates, as shown in Figure 13. With the increase in travel time, the proportion of private cars choosing the shortest path decreases gradually. Among the shortest path choices, the proportion of private cars choosing the shortest time (ST) path in different time intervals is slightly higher than that of the shortest distance (SD) path. When the travel time exceeds 80 minutes, private cars do not use the shortest path to a large extent. When dividing the dates, the proportion of private car trips taking the shortest path on the weekend is slightly higher than that on weekdays. Table 14 shows that the proportion of private cars choosing the shortest path for residents in different periods also shows similar characteristics. However, when the travel time is significant, the sample size is limited, and the proportion of the shortest path selection may be significant.Figure 13
A global selection of different time intervals for the shortest paths.Table 14
Segment selection of different time intervals for the shortest paths.
IntervalShortest distance pathShortest time pathWeekdayWeekendWeekdayWeekend0∼100.68280.66320.70150.750010∼200.48330.53740.53470.604320∼300.36460.40670.44440.518730∼400.34090.35890.43750.459340∼500.28870.39020.36080.406550∼600.20830.26190.30560.285760∼700.15560.30000.15560.280070∼800.15380.28570.26920.250080∼900.15790.33330.21050.400090∼1000.50000.20000.37500.2000100∼1100.16670.28570.00000.2857110∼1200.00000.25000.25000.0000(3) Segmented Travel Distance. Figure 14 shows that the proportion of private cars choosing the shortest path gradually decreases with the increase in travel distance. Among the shortest path choices, the proportion of private cars choosing the shortest time (ST) path at different distances is slightly higher than that of those choosing the shortest distance (SD) path. When the travel distance is more than 54 kilometers, the proportion of private cars choosing the shortest path is deficient. When dividing the date, the proportion of private cars taking the shortest path on the rest day is slightly higher than that on weekdays in most of the cases. Correspondingly, Table 15 shows that the proportion of private cars choosing the shortest path at different distances also shows similar characteristics. Similar to travel time, when the distance is considerable, the sample size is limited, and the proportion of the shortest path may be significant.Figure 14
A global selection of different distance intervals for the shortest paths.Table 15
Segment selection of different distance intervals for the shortest paths.
IntervalShortest distance pathShortest time pathWeekdayWeekendWeekdayWeekend0∼60.59880.59180.60670.66336∼120.41310.41970.46100.479312∼180.23880.32570.37310.399118∼240.30000.35350.37270.494924∼300.23530.45610.42650.491230∼360.45710.39390.31430.575836∼420.26670.23810.40000.190542∼480.18750.21740.37500.304348∼540.44440.50000.33330.400054∼600.16670.33330.50000.166760∼660.00000.55560.40000.555666∼720.40000.50000.40000.000072∼780.20000.00000.60001.0000


## 3.1. Comparisons between Travel Path and the Shortest Path

### 3.1.1. General Results

Excluding a small number of circular routes (of the exact origins) or trips with apparent detour behavior, 1398 effective paths in the working day and 1462 effective paths in the rest day were finally obtained to compare the deviations between the selected path and the shortest path. Table4 shows the situation of sampled residents in Chongqing who choose the shortest route to travel. On Monday, 46.72% of Chongqing residents chose the shortest distance route, and 68.81% was the shortest time route. The shortest time path takes up 52.87%, among which 60.93% is also the shortest distance path. On Saturday, 46.51% of residents chose the shortest distance route, and 68.68% is also the shortest time route. The shortest time path takes up 52.94%, of which 60.85% is also the shortest distance path. According to the summary, the proportion of Chongqing residents choosing the shortest route (including the shortest time and the shortest distance) to travel on the weekday is 67.44%. On the weekend, 67.51% chose the shortest path, which was similar to the percentage on the weekday.Table 4
The proportion of residents choosing the shortest path in Chongqing.
DayData descriptionShortest distance path (%)Shortest time path (%)Monday391 residents’ 2860 private car trips46.7252.87Saturday46.5152.94Compared with Chongqing, the existing studies of cities worldwide have shown a smaller proportion of shortest path selection, and only the research of Minneapolis-St. Paul described the deviation between the commuters’ actual path and the shortest path. Next, the study will analyze the deviation between the actual travel path and the shortest path for Chongqing residents.


### 3.1.2. Deviation between Travel Path and the Shortest Path

The shortest distance path, the shortest time path, and the recommended path that coincide with the actual travel path provided by Baidu Maps can be compared with the actual path data. The statistical description results are shown in Table5. The research results showed that the actual travel route selected by residents on the weekday consumed 3.37 and 5.41 minutes (residual) more on average. The average distance was 1.39 and 0.78 kilometers (residual), more than the shortest distance and time paths. Nevertheless, the deviation reached about 9 min and 2 km (absolute residual). Travelers saved 2 minutes on average after choosing the shortest time path compared with the shortest distance path but traveled 0.62 km more.Table 5
The statistical description of the deviation between the actual and shortest paths.
Sample groupSample sizeTravel time/minTravel distance/kmResidualAbsolute residualStandard deviationResidualAbsolute residualStandard deviationRP/SDP1398 (1462)3.37 (5.64)8.97 (10.01)11.35 (13.22)1.39 (1.69)1.95 (2.05)3.51 (4.05)RP/STP1398 (1462)5.41 (7.70)9.03 (10.11)11.38 (13.63)0.78 (1.08)1.80 (1.08)3.46 (1.84)SDP/STP1398 (1462)2.03 (2.06)2.02 (2.06)4.96 (5.61)−0.62 (−0.55)0.64 (0.62)1.90 (2.01)RP/RRP824 (1021)2.23 (4.51)6.82 (7.85)8.65 (10.03)0.16 (0.43)0.84 (0.93)2.32 (1.79)RRP/SDP824 (1021)−1.33 (−1.18)1.68 (2.00)5.25 (6.12)0.44 (0.53)0.44 (0.55)1.30 (1.56)RRP/STP824 (1021)0.31 (0.91)0.33 (1.00)2.40 (2.72)0.07 (−0.06)0.12 (0.43)0.69 (1.48)RP/SDP′824 (1021)0.90 (3.29)7.21 (8.26)9.11 (10.66)0.61 (0.94)1.12 (1.24)2.54 (2.11)RP/STP′824 (1021)2.54 (5.42)6.77 (8.03)8.34 (10.39)0.24 (0.37)0.92 (1.12)2.07 (2.02)Note. RP is the actual path; SDP is the shortest distance path; STP is the shortest time path; RRP is the recommended path that overlaps with the actual path; ' stands for deviation correction. The data outside the brackets are on the weekday, and the data inside the brackets are on the weekend. The same is below.However, we note that there is a deviation between the indexes of the actual path and the recommended path of the Baidu Maps which coincides with the actual path, so this deviation is used to correct the error between the actual path and the shortest path. Compared with the shortest distance and time paths, the actual travel route selected by the residents consumes 0.90 and 2.54 minutes more on average, and the average distance is 0.61 and 0.24 km more. Compared with the working day, the indicators of the rest day are more deviated. On the weekend, compared with the shortest distance and time paths, the actual travel route selected by residents consumed 3.33 and 5.42 minutes more on average, and the average distance was 0.96 and 0.37 km more. Although many Chinese urban residents still do not choose the shortest path, the deviation between the actual path and the shortest path is slight. Based on the residual error, the actual travel time of the selected path takes no more than 6 minutes on average, and the travel distance is no more than 1 km. Taking the absolute residual value as the benchmark, we found that the selected path takes no more than 9 minutes on average, and the travel distance is no more than 2 km.


### 3.1.3. Deviation between Similar Route Pairs

This section uses the same OD paths of the same resident to conduct a preliminary comparative analysis of the travel paths. The path similarity is shown in Table6. There are 655 trips (45.64% of the total trips) with the fixed OD involving 259 residents (66.24% of the residents), and 205 of them are commuter routes (31.29% of the fixed OD trips) in the working day. The commuters usually have a relatively fixed OD and route. They account for a considerable proportion, and their route choices tend to have a certain regularity and may be optimized by some measures. Thus, uncovering the similarity of commuter routes is of importance to design more targeted measures. In the total path of the rest day, there were 743 trips (49.90% of the total trips) with the fixed OD, involving 259 residents (67.62% of the residents). The weekend does not differentiate between activity types.Table 6
Trip paths similarity of residents in Chongqing.
SimilaritySameSimilarDifferentActivity typeCommuterOtherCommuterOtherCommuterOtherCount/pairs4311827713387Sum/pairs161 (154)98 (112)120 (132)Note. The data outside the brackets is on the weekday, and the data inside the brackets is on the weekend.Table7 shows the comparative analysis of the residuals of three indexes of travel time, distance, and travel speed of different path pairs. The average absolute value of travel time residual of all samples is 11.34 (weekend is 12.04) minutes, and the average absolute value of travel distance residual is 2.40 (weekend is 2.10) km. Moreover, the average absolute value of the travel speed residual is 7.48 (weekend is 7.60) km/h. The absolute standard deviations of the residual values corresponding to each index are 14.74 (16.48), 5.11 (4.25), and 7.57 (7.23). The differences of each index of the same and similar path pairs are less than the whole. However, the difference between different paths is greater than the whole.Table 7
Absolute residual values and standard deviations of trip indicators for the path pairs.
Activity typeCommutingOtherWholePair typeResidualAbsoluteStandard deviationAbsoluteStandard deviationAbsoluteStandard deviationSameTravel time/min9.4213.526.5110.916.48 (7.11)9.69 (9.83)Distance/km0.730.681.031.720.86 (0.86)1.28 (1.28)Speed/km/h7.8310.637.308.067.12 (7.20)8.62 (6.94)SimilarTravel time/min11.2414.9212.9915.1712.31 (13.68)14.99 (18.53)Distance/km2.172.942.292.882.24 (2.27)2.90 (2.83)Speed/km/h5.604.107.656.696.99 (6.94)6.17 (7.82)DifferentTravel time/min15.2814.9417.8518.6817.07 (16.40)17.74 (19.22)Distance/km3.105.844.888.594.58 (3.40)8.11 (6.52)Speed/km/h7.275.058.697.488.36 (8.62)7.05 (7.00)Note. The data outside the brackets is on the weekday, and the data inside the brackets is on the weekend.When the activity types are considered, the average absolute residual value of the commuting time is 11.85 minutes. The average absolute value of the distance residual is 1.87 km. The average absolute value of the travel speed residual is 7.16 km/h. The absolute standard deviations of the residual values for each index are 14.46, 3.77, and 7.70, respectively. The average absolute value of the travel time residual for the other travel is 11.21 minutes. The average absolute value of the residual for route distance is 2.62 km. The average absolute value of the residual for travel speed is 7.60 km/h. The absolute standard deviations of the residual values for each index are 14.86, 5.52, and 7.52. The difference in commuting travel time is slightly more significant than that in noncommuting. However, the differences in route distance and travel speed are minor compared to noncommuting. When path difference is considered, in the same path pairs, the travel time of commuting activities is greater than that of noncommuting activities, and the difference between route distance and travel speed is smaller than that of noncommuting activities. In similar and different path pairs, the difference of each index of commuting activity is smaller than that of noncommuting activity.


### 3.1.4. Other Comparisons for Deviation Quantification

This section will analyze the residents’ choice of the shortest path for actual travel under different conditions.(1) Whether to Commute. 268 commuter and 1132 noncommuter travel routes were obtained during the working day. More commuters do not drive directly from home to work (including school pickup, entertainment, and other activities). These trips are not defined as commuting in travel behavior identification, so the scale is different in the number of commuting and noncommuting routes.The shortest path selection ratio of the two travel modes is shown in Table8, and the deviation between the actual path and the shortest path is shown in Table 9. The research results show that the proportion of residents choosing the shortest path in the process of commuting is smaller than that of noncommuting because people think that the familiar path is more able to let them reach the workplace within a particular time [5]. However, the route selected by commuters takes an average of 4–7 minutes longer than the shortest path, with an absolute deviation of about 10 minutes. The difference between the two in the distance of travel is slight, generally about 1 km. Since the probability of choosing the shortest path for noncommuter travel is greater, the difference between noncommuter travel and the shortest paths is smaller than that between commuter travel and the shortest paths. No matter what kind of travel mode, the proportion of residents choosing the shortest time path is higher than that of residents choosing the shortest distance path, and the two shortest paths overlap to a large extent. More than 80% of the shortest distance path is consistent with the shortest time path.Table 8
Shortest path selection proportions for commuters and noncommuters on a working day.
TypeShortest distance pathShortest time pathSum (%)Commuters31.34% (80.95%)42.16% (61.06%)47.76Noncommuters44.17% (85.80%)49.47% (76.61%)55.74Note. The proportion that is simultaneously another shortest path is given in the parentheses.Table 9
The deviation between the actual and the shortest paths for commuters/noncommuters on a working day.
Sample groupTravel time/minTravel distance/kmResidualAbsolute residualStandard deviationResidualAbsolute residualStandard deviationRP & SDP′4.47/0.2410.24/6.6110.80/8.720.66/0.591.25/1.092.05/2.60RP & STP′7.14/2.2710.35/6.3110.81/8.57−0.18/0.151.16/1.082.63/3.16(2) Whether OD is Fixed. The fixed OD trip refers to the trip with the exact origin and destination, and at least two trips with the same OD exist in one day.According to statistics, there are 584 fixed OD travel routes and 814 nonfixed OD travel routes on weekdays. There are 634 fixed OD travel paths and 828 nonfixed OD travel paths on the weekend. The selection of the shortest path is shown in Table10. The research results show that, in the case of fixed OD and the weekday, the proportion of residents choosing the shortest distance or time path is smaller than that of non-fixed OD and the rest day. On the rest day, the proportion of residents choosing the shortest path is significantly higher than that on a working day, regardless of whether OD is fixed or not. When distinguishing whether the OD is fixed or not, the total proportion of residents choosing the shortest path for the fixed OD trip is slightly higher than that for the nonfixed OD trip.Table 10
The proportion of shortest path selection for fixed and nonfixed OD trips.
TypeDateShortest distance pathShortest time pathSum (%)Fixed ODMonday40.24% (85.96%)47.09% (73.82%)52.57Saturday46.06% (61.99%)52.37% (55.42%)69.87Nonfixed ODMonday43.73% (85.11%)48.65% (76.26%)55.28Saturday46.86% (73.71%)53.26% (65.08%)65.58Note. The proportion that is simultaneously another shortest path is given in the parentheses.To some extent, whether the OD is fixed or not indicates the driver’s familiarity with the route. Meanwhile, the fixed OD trip can also indicate the importance of the trip, and the commuting process is an important part. The results show that residents are more likely to choose the shortest path when they are not working. Moreover, choosing the shortest path in an entirely nonworking state (rest day) is higher compared to the situation in a partial nonworking state (nonfixed OD travel on the weekday). This phenomenon shows the residents’ trust paradox on the shortest path. In the case of relatively urgent commuting, people tend to choose a more familiar path rather than the shortest path to ensure the timely arrival of the destination. However, in other nonemergency travel situations, people tend to choose the shortest path to obtain a shorter travel distance or time.When the deviation between the actual travel path and the shortest path is investigated under the condition that the OD is fixed or not, as shown in Tables11 and 12, the trends of the working day and rest day are generally the same. However, there is a slight difference in the specific value. The unified trend is that the deviation between the average travel time, the distance of nonfixed OD trips, and the shortest path is generally more significant than fixed OD trips. This shows that although there is a significant probability to choose the shortest path for the nonfixed OD trip, the deviation caused by the part that does not choose the shortest path is greater than the part that does not choose the shortest path in the fixed OD trip. The difference is as follows: the deviation of the rest day is more significant than that of the working day. On the weekday, compared with the shortest distance and time paths, the average travel time of residents consumes 1 and 3 minutes more, and the average distance is 0.80 and 0.25 km more. On the rest day, compared with the shortest distance and time paths, the average travel time of residents is 4.44 and 6.34 minutes longer, and the average distance is 1.04 and 0.49 km longer.Table 11
The deviation between the actual and the shortest paths of the fixed/nonfixed OD trips on weekdays.
Sample groupTravel time/minTravel distance/kmResidualAbsolute residualStandard deviationResidualAbsolute residualStandard deviationRP & SDP′0.89/1.028.66/6.3110.63/8.100.32/0.801.19/1.072.90/2.24RP & STP′0.34/2.990.35/6.221.30/8.28−0.15/0.250.24/0.991.32/2.39Table 12
The deviation between the actual and the shortest paths of the fixed/nonfixed OD trips on the weekend.
Sample groupTravel time/minTravel distance/kmResidualAbsolute residualStandard deviationResidualAbsolute residualStandard deviationRP & SDP′1.83/4.448.09/8.4011.36/10.090.82/1.041.15/1.301.76/2.35RP & STP′4.26/6.347.54/8.419.73/10.870.23/0.491.08/1.141.91/2.10


## 3.1.1. General Results

Excluding a small number of circular routes (of the exact origins) or trips with apparent detour behavior, 1398 effective paths in the working day and 1462 effective paths in the rest day were finally obtained to compare the deviations between the selected path and the shortest path. Table4 shows the situation of sampled residents in Chongqing who choose the shortest route to travel. On Monday, 46.72% of Chongqing residents chose the shortest distance route, and 68.81% was the shortest time route. The shortest time path takes up 52.87%, among which 60.93% is also the shortest distance path. On Saturday, 46.51% of residents chose the shortest distance route, and 68.68% is also the shortest time route. The shortest time path takes up 52.94%, of which 60.85% is also the shortest distance path. According to the summary, the proportion of Chongqing residents choosing the shortest route (including the shortest time and the shortest distance) to travel on the weekday is 67.44%. On the weekend, 67.51% chose the shortest path, which was similar to the percentage on the weekday.Table 4
The proportion of residents choosing the shortest path in Chongqing.
DayData descriptionShortest distance path (%)Shortest time path (%)Monday391 residents’ 2860 private car trips46.7252.87Saturday46.5152.94Compared with Chongqing, the existing studies of cities worldwide have shown a smaller proportion of shortest path selection, and only the research of Minneapolis-St. Paul described the deviation between the commuters’ actual path and the shortest path. Next, the study will analyze the deviation between the actual travel path and the shortest path for Chongqing residents.


## 3.1.2. Deviation between Travel Path and the Shortest Path

The shortest distance path, the shortest time path, and the recommended path that coincide with the actual travel path provided by Baidu Maps can be compared with the actual path data. The statistical description results are shown in Table5. The research results showed that the actual travel route selected by residents on the weekday consumed 3.37 and 5.41 minutes (residual) more on average. The average distance was 1.39 and 0.78 kilometers (residual), more than the shortest distance and time paths. Nevertheless, the deviation reached about 9 min and 2 km (absolute residual). Travelers saved 2 minutes on average after choosing the shortest time path compared with the shortest distance path but traveled 0.62 km more.Table 5
The statistical description of the deviation between the actual and shortest paths.
Sample groupSample sizeTravel time/minTravel distance/kmResidualAbsolute residualStandard deviationResidualAbsolute residualStandard deviationRP/SDP1398 (1462)3.37 (5.64)8.97 (10.01)11.35 (13.22)1.39 (1.69)1.95 (2.05)3.51 (4.05)RP/STP1398 (1462)5.41 (7.70)9.03 (10.11)11.38 (13.63)0.78 (1.08)1.80 (1.08)3.46 (1.84)SDP/STP1398 (1462)2.03 (2.06)2.02 (2.06)4.96 (5.61)−0.62 (−0.55)0.64 (0.62)1.90 (2.01)RP/RRP824 (1021)2.23 (4.51)6.82 (7.85)8.65 (10.03)0.16 (0.43)0.84 (0.93)2.32 (1.79)RRP/SDP824 (1021)−1.33 (−1.18)1.68 (2.00)5.25 (6.12)0.44 (0.53)0.44 (0.55)1.30 (1.56)RRP/STP824 (1021)0.31 (0.91)0.33 (1.00)2.40 (2.72)0.07 (−0.06)0.12 (0.43)0.69 (1.48)RP/SDP′824 (1021)0.90 (3.29)7.21 (8.26)9.11 (10.66)0.61 (0.94)1.12 (1.24)2.54 (2.11)RP/STP′824 (1021)2.54 (5.42)6.77 (8.03)8.34 (10.39)0.24 (0.37)0.92 (1.12)2.07 (2.02)Note. RP is the actual path; SDP is the shortest distance path; STP is the shortest time path; RRP is the recommended path that overlaps with the actual path; ' stands for deviation correction. The data outside the brackets are on the weekday, and the data inside the brackets are on the weekend. The same is below.However, we note that there is a deviation between the indexes of the actual path and the recommended path of the Baidu Maps which coincides with the actual path, so this deviation is used to correct the error between the actual path and the shortest path. Compared with the shortest distance and time paths, the actual travel route selected by the residents consumes 0.90 and 2.54 minutes more on average, and the average distance is 0.61 and 0.24 km more. Compared with the working day, the indicators of the rest day are more deviated. On the weekend, compared with the shortest distance and time paths, the actual travel route selected by residents consumed 3.33 and 5.42 minutes more on average, and the average distance was 0.96 and 0.37 km more. Although many Chinese urban residents still do not choose the shortest path, the deviation between the actual path and the shortest path is slight. Based on the residual error, the actual travel time of the selected path takes no more than 6 minutes on average, and the travel distance is no more than 1 km. Taking the absolute residual value as the benchmark, we found that the selected path takes no more than 9 minutes on average, and the travel distance is no more than 2 km.


## 3.1.3. Deviation between Similar Route Pairs

This section uses the same OD paths of the same resident to conduct a preliminary comparative analysis of the travel paths. The path similarity is shown in Table6. There are 655 trips (45.64% of the total trips) with the fixed OD involving 259 residents (66.24% of the residents), and 205 of them are commuter routes (31.29% of the fixed OD trips) in the working day. The commuters usually have a relatively fixed OD and route. They account for a considerable proportion, and their route choices tend to have a certain regularity and may be optimized by some measures. Thus, uncovering the similarity of commuter routes is of importance to design more targeted measures. In the total path of the rest day, there were 743 trips (49.90% of the total trips) with the fixed OD, involving 259 residents (67.62% of the residents). The weekend does not differentiate between activity types.Table 6
Trip paths similarity of residents in Chongqing.
SimilaritySameSimilarDifferentActivity typeCommuterOtherCommuterOtherCommuterOtherCount/pairs4311827713387Sum/pairs161 (154)98 (112)120 (132)Note. The data outside the brackets is on the weekday, and the data inside the brackets is on the weekend.Table7 shows the comparative analysis of the residuals of three indexes of travel time, distance, and travel speed of different path pairs. The average absolute value of travel time residual of all samples is 11.34 (weekend is 12.04) minutes, and the average absolute value of travel distance residual is 2.40 (weekend is 2.10) km. Moreover, the average absolute value of the travel speed residual is 7.48 (weekend is 7.60) km/h. The absolute standard deviations of the residual values corresponding to each index are 14.74 (16.48), 5.11 (4.25), and 7.57 (7.23). The differences of each index of the same and similar path pairs are less than the whole. However, the difference between different paths is greater than the whole.Table 7
Absolute residual values and standard deviations of trip indicators for the path pairs.
Activity typeCommutingOtherWholePair typeResidualAbsoluteStandard deviationAbsoluteStandard deviationAbsoluteStandard deviationSameTravel time/min9.4213.526.5110.916.48 (7.11)9.69 (9.83)Distance/km0.730.681.031.720.86 (0.86)1.28 (1.28)Speed/km/h7.8310.637.308.067.12 (7.20)8.62 (6.94)SimilarTravel time/min11.2414.9212.9915.1712.31 (13.68)14.99 (18.53)Distance/km2.172.942.292.882.24 (2.27)2.90 (2.83)Speed/km/h5.604.107.656.696.99 (6.94)6.17 (7.82)DifferentTravel time/min15.2814.9417.8518.6817.07 (16.40)17.74 (19.22)Distance/km3.105.844.888.594.58 (3.40)8.11 (6.52)Speed/km/h7.275.058.697.488.36 (8.62)7.05 (7.00)Note. The data outside the brackets is on the weekday, and the data inside the brackets is on the weekend.When the activity types are considered, the average absolute residual value of the commuting time is 11.85 minutes. The average absolute value of the distance residual is 1.87 km. The average absolute value of the travel speed residual is 7.16 km/h. The absolute standard deviations of the residual values for each index are 14.46, 3.77, and 7.70, respectively. The average absolute value of the travel time residual for the other travel is 11.21 minutes. The average absolute value of the residual for route distance is 2.62 km. The average absolute value of the residual for travel speed is 7.60 km/h. The absolute standard deviations of the residual values for each index are 14.86, 5.52, and 7.52. The difference in commuting travel time is slightly more significant than that in noncommuting. However, the differences in route distance and travel speed are minor compared to noncommuting. When path difference is considered, in the same path pairs, the travel time of commuting activities is greater than that of noncommuting activities, and the difference between route distance and travel speed is smaller than that of noncommuting activities. In similar and different path pairs, the difference of each index of commuting activity is smaller than that of noncommuting activity.


## 3.1.4. Other Comparisons for Deviation Quantification

This section will analyze the residents’ choice of the shortest path for actual travel under different conditions.(1) Whether to Commute. 268 commuter and 1132 noncommuter travel routes were obtained during the working day. More commuters do not drive directly from home to work (including school pickup, entertainment, and other activities). These trips are not defined as commuting in travel behavior identification, so the scale is different in the number of commuting and noncommuting routes.The shortest path selection ratio of the two travel modes is shown in Table8, and the deviation between the actual path and the shortest path is shown in Table 9. The research results show that the proportion of residents choosing the shortest path in the process of commuting is smaller than that of noncommuting because people think that the familiar path is more able to let them reach the workplace within a particular time [5]. However, the route selected by commuters takes an average of 4–7 minutes longer than the shortest path, with an absolute deviation of about 10 minutes. The difference between the two in the distance of travel is slight, generally about 1 km. Since the probability of choosing the shortest path for noncommuter travel is greater, the difference between noncommuter travel and the shortest paths is smaller than that between commuter travel and the shortest paths. No matter what kind of travel mode, the proportion of residents choosing the shortest time path is higher than that of residents choosing the shortest distance path, and the two shortest paths overlap to a large extent. More than 80% of the shortest distance path is consistent with the shortest time path.Table 8
Shortest path selection proportions for commuters and noncommuters on a working day.
TypeShortest distance pathShortest time pathSum (%)Commuters31.34% (80.95%)42.16% (61.06%)47.76Noncommuters44.17% (85.80%)49.47% (76.61%)55.74Note. The proportion that is simultaneously another shortest path is given in the parentheses.Table 9
The deviation between the actual and the shortest paths for commuters/noncommuters on a working day.
Sample groupTravel time/minTravel distance/kmResidualAbsolute residualStandard deviationResidualAbsolute residualStandard deviationRP & SDP′4.47/0.2410.24/6.6110.80/8.720.66/0.591.25/1.092.05/2.60RP & STP′7.14/2.2710.35/6.3110.81/8.57−0.18/0.151.16/1.082.63/3.16(2) Whether OD is Fixed. The fixed OD trip refers to the trip with the exact origin and destination, and at least two trips with the same OD exist in one day.According to statistics, there are 584 fixed OD travel routes and 814 nonfixed OD travel routes on weekdays. There are 634 fixed OD travel paths and 828 nonfixed OD travel paths on the weekend. The selection of the shortest path is shown in Table10. The research results show that, in the case of fixed OD and the weekday, the proportion of residents choosing the shortest distance or time path is smaller than that of non-fixed OD and the rest day. On the rest day, the proportion of residents choosing the shortest path is significantly higher than that on a working day, regardless of whether OD is fixed or not. When distinguishing whether the OD is fixed or not, the total proportion of residents choosing the shortest path for the fixed OD trip is slightly higher than that for the nonfixed OD trip.Table 10
The proportion of shortest path selection for fixed and nonfixed OD trips.
TypeDateShortest distance pathShortest time pathSum (%)Fixed ODMonday40.24% (85.96%)47.09% (73.82%)52.57Saturday46.06% (61.99%)52.37% (55.42%)69.87Nonfixed ODMonday43.73% (85.11%)48.65% (76.26%)55.28Saturday46.86% (73.71%)53.26% (65.08%)65.58Note. The proportion that is simultaneously another shortest path is given in the parentheses.To some extent, whether the OD is fixed or not indicates the driver’s familiarity with the route. Meanwhile, the fixed OD trip can also indicate the importance of the trip, and the commuting process is an important part. The results show that residents are more likely to choose the shortest path when they are not working. Moreover, choosing the shortest path in an entirely nonworking state (rest day) is higher compared to the situation in a partial nonworking state (nonfixed OD travel on the weekday). This phenomenon shows the residents’ trust paradox on the shortest path. In the case of relatively urgent commuting, people tend to choose a more familiar path rather than the shortest path to ensure the timely arrival of the destination. However, in other nonemergency travel situations, people tend to choose the shortest path to obtain a shorter travel distance or time.When the deviation between the actual travel path and the shortest path is investigated under the condition that the OD is fixed or not, as shown in Tables11 and 12, the trends of the working day and rest day are generally the same. However, there is a slight difference in the specific value. The unified trend is that the deviation between the average travel time, the distance of nonfixed OD trips, and the shortest path is generally more significant than fixed OD trips. This shows that although there is a significant probability to choose the shortest path for the nonfixed OD trip, the deviation caused by the part that does not choose the shortest path is greater than the part that does not choose the shortest path in the fixed OD trip. The difference is as follows: the deviation of the rest day is more significant than that of the working day. On the weekday, compared with the shortest distance and time paths, the average travel time of residents consumes 1 and 3 minutes more, and the average distance is 0.80 and 0.25 km more. On the rest day, compared with the shortest distance and time paths, the average travel time of residents is 4.44 and 6.34 minutes longer, and the average distance is 1.04 and 0.49 km longer.Table 11
The deviation between the actual and the shortest paths of the fixed/nonfixed OD trips on weekdays.
Sample groupTravel time/minTravel distance/kmResidualAbsolute residualStandard deviationResidualAbsolute residualStandard deviationRP & SDP′0.89/1.028.66/6.3110.63/8.100.32/0.801.19/1.072.90/2.24RP & STP′0.34/2.990.35/6.221.30/8.28−0.15/0.250.24/0.991.32/2.39Table 12
The deviation between the actual and the shortest paths of the fixed/nonfixed OD trips on the weekend.
Sample groupTravel time/minTravel distance/kmResidualAbsolute residualStandard deviationResidualAbsolute residualStandard deviationRP & SDP′1.83/4.448.09/8.4011.36/10.090.82/1.041.15/1.301.76/2.35RP & STP′4.26/6.347.54/8.419.73/10.870.23/0.491.08/1.141.91/2.10


## 3.2. Comparisons between the Weekday and the Weekend

### 3.2.1. Travel Characteristics Description of Private Cars

Figure8 shows the travel time distribution of private cars trips in Chongqing. The results showed that the proportion of trips within 15 minutes accounted for 34.62% on the weekdays. The mean travel time was 26.62 minutes, and the standard deviation was 20.15. The travel time distribution of the weekend is very similar to that of the weekday. The proportion of trips within 15 minutes accounted for 33.65%. The mean travel time was 27.20 minutes, and the standard deviation was 19.90.Figure 8
Histogram of travel time. (a) The weekday; (b) the weekend.
(a)(b)Figure9 shows the distribution of travel distance of private cars in Chongqing. The results show that, on the weekday, the proportion of trips within 22 km accounts for 84.76%. The mean travel distance is 12.13 km, and the standard deviation is 12.11. The proportion of the rest day at critical time points is higher than that of the working day. The proportion of trips within 22 km is 87.57%. The mean travel distance is 11.36 km, and the standard deviation is 11.40.Figure 9
Histogram of travel distance. (a) The weekday; (b) the weekend.
(a)(b)Regarding the number of trips, the maximum trip frequency on the weekday is 2, accounting for 34.53%. It is the same as the result of the weekend. However, it accounts for 28.17% of all trips, which is less than that of the weekday. For samples with travel times ranging from 2 to 10, the distributions for the weekday and weekends conform to the asymptotic exponential distribution, as shown in Figure10. When comparing the trip number of the same private cars on two days, the number of trips on the weekday is less than that on the rest day. Moreover, when the number of trips is large (e.g., 4–7), the frequency of the rest day is greater than that of the working day. As shown in Table 13, the trip number of 66.32% of residents on the rest day is no less than that of the weekday.Figure 10
Trip number distributions and fits on the weekday and weekends.Table 13
Comparison of the trips number between the weekday and weekend.
TypeWeekday < weekendWeekday = weekendWeekday > weekendCount1385397Proportion47.92%18.40%33.68%


### 3.2.2. Classification Comparisons for Date

(1) Driving Preference. In a driver’s private car travel, the total number of trips on a day is b, among which a is the shortest path (the shortest time or distance), and then there is the proportion of the shortest path choice of the driver’s private car travel.(4)ω=ab.19.79% (weekday) and 13.16% (weekend) of the drivers in Chongqing did not choose the shortest path. The proportion of choosing the shortest path for all trips is 23.39% (weekday) and 17.89% (weekend). More details are shown in Figure11.Figure 11
Interval distribution of the shortest path selection for the overall drivers.In order to more accurately characterize the influence of different dates on the driver’s shortest path selection, this section screened the overlapped samples for two days and obtained a total of 286 valid identical samples. The proportion interval distribution of shortest path selection is shown in Figure12. The percentage of those who did not choose the shortest path is 17.13% (weekday) and 12.24% (weekend). The proportion of choosing the shortest path for all trips is 23.78% (weekday) and 15.03% (weekend).Figure 12
Interval distribution of the shortest path selection for the same drivers.(2) Segmented Travel Time. The shortest path selection varies for various times and dates, as shown in Figure 13. With the increase in travel time, the proportion of private cars choosing the shortest path decreases gradually. Among the shortest path choices, the proportion of private cars choosing the shortest time (ST) path in different time intervals is slightly higher than that of the shortest distance (SD) path. When the travel time exceeds 80 minutes, private cars do not use the shortest path to a large extent. When dividing the dates, the proportion of private car trips taking the shortest path on the weekend is slightly higher than that on weekdays. Table 14 shows that the proportion of private cars choosing the shortest path for residents in different periods also shows similar characteristics. However, when the travel time is significant, the sample size is limited, and the proportion of the shortest path selection may be significant.Figure 13
A global selection of different time intervals for the shortest paths.Table 14
Segment selection of different time intervals for the shortest paths.
IntervalShortest distance pathShortest time pathWeekdayWeekendWeekdayWeekend0∼100.68280.66320.70150.750010∼200.48330.53740.53470.604320∼300.36460.40670.44440.518730∼400.34090.35890.43750.459340∼500.28870.39020.36080.406550∼600.20830.26190.30560.285760∼700.15560.30000.15560.280070∼800.15380.28570.26920.250080∼900.15790.33330.21050.400090∼1000.50000.20000.37500.2000100∼1100.16670.28570.00000.2857110∼1200.00000.25000.25000.0000(3) Segmented Travel Distance. Figure 14 shows that the proportion of private cars choosing the shortest path gradually decreases with the increase in travel distance. Among the shortest path choices, the proportion of private cars choosing the shortest time (ST) path at different distances is slightly higher than that of those choosing the shortest distance (SD) path. When the travel distance is more than 54 kilometers, the proportion of private cars choosing the shortest path is deficient. When dividing the date, the proportion of private cars taking the shortest path on the rest day is slightly higher than that on weekdays in most of the cases. Correspondingly, Table 15 shows that the proportion of private cars choosing the shortest path at different distances also shows similar characteristics. Similar to travel time, when the distance is considerable, the sample size is limited, and the proportion of the shortest path may be significant.Figure 14
A global selection of different distance intervals for the shortest paths.Table 15
Segment selection of different distance intervals for the shortest paths.
IntervalShortest distance pathShortest time pathWeekdayWeekendWeekdayWeekend0∼60.59880.59180.60670.66336∼120.41310.41970.46100.479312∼180.23880.32570.37310.399118∼240.30000.35350.37270.494924∼300.23530.45610.42650.491230∼360.45710.39390.31430.575836∼420.26670.23810.40000.190542∼480.18750.21740.37500.304348∼540.44440.50000.33330.400054∼600.16670.33330.50000.166760∼660.00000.55560.40000.555666∼720.40000.50000.40000.000072∼780.20000.00000.60001.0000


## 3.2.1. Travel Characteristics Description of Private Cars

Figure8 shows the travel time distribution of private cars trips in Chongqing. The results showed that the proportion of trips within 15 minutes accounted for 34.62% on the weekdays. The mean travel time was 26.62 minutes, and the standard deviation was 20.15. The travel time distribution of the weekend is very similar to that of the weekday. The proportion of trips within 15 minutes accounted for 33.65%. The mean travel time was 27.20 minutes, and the standard deviation was 19.90.Figure 8
Histogram of travel time. (a) The weekday; (b) the weekend.
(a)(b)Figure9 shows the distribution of travel distance of private cars in Chongqing. The results show that, on the weekday, the proportion of trips within 22 km accounts for 84.76%. The mean travel distance is 12.13 km, and the standard deviation is 12.11. The proportion of the rest day at critical time points is higher than that of the working day. The proportion of trips within 22 km is 87.57%. The mean travel distance is 11.36 km, and the standard deviation is 11.40.Figure 9
Histogram of travel distance. (a) The weekday; (b) the weekend.
(a)(b)Regarding the number of trips, the maximum trip frequency on the weekday is 2, accounting for 34.53%. It is the same as the result of the weekend. However, it accounts for 28.17% of all trips, which is less than that of the weekday. For samples with travel times ranging from 2 to 10, the distributions for the weekday and weekends conform to the asymptotic exponential distribution, as shown in Figure10. When comparing the trip number of the same private cars on two days, the number of trips on the weekday is less than that on the rest day. Moreover, when the number of trips is large (e.g., 4–7), the frequency of the rest day is greater than that of the working day. As shown in Table 13, the trip number of 66.32% of residents on the rest day is no less than that of the weekday.Figure 10
Trip number distributions and fits on the weekday and weekends.Table 13
Comparison of the trips number between the weekday and weekend.
TypeWeekday < weekendWeekday = weekendWeekday > weekendCount1385397Proportion47.92%18.40%33.68%


## 3.2.2. Classification Comparisons for Date

(1) Driving Preference. In a driver’s private car travel, the total number of trips on a day is b, among which a is the shortest path (the shortest time or distance), and then there is the proportion of the shortest path choice of the driver’s private car travel.(4)ω=ab.19.79% (weekday) and 13.16% (weekend) of the drivers in Chongqing did not choose the shortest path. The proportion of choosing the shortest path for all trips is 23.39% (weekday) and 17.89% (weekend). More details are shown in Figure11.Figure 11
Interval distribution of the shortest path selection for the overall drivers.In order to more accurately characterize the influence of different dates on the driver’s shortest path selection, this section screened the overlapped samples for two days and obtained a total of 286 valid identical samples. The proportion interval distribution of shortest path selection is shown in Figure12. The percentage of those who did not choose the shortest path is 17.13% (weekday) and 12.24% (weekend). The proportion of choosing the shortest path for all trips is 23.78% (weekday) and 15.03% (weekend).Figure 12
Interval distribution of the shortest path selection for the same drivers.(2) Segmented Travel Time. The shortest path selection varies for various times and dates, as shown in Figure 13. With the increase in travel time, the proportion of private cars choosing the shortest path decreases gradually. Among the shortest path choices, the proportion of private cars choosing the shortest time (ST) path in different time intervals is slightly higher than that of the shortest distance (SD) path. When the travel time exceeds 80 minutes, private cars do not use the shortest path to a large extent. When dividing the dates, the proportion of private car trips taking the shortest path on the weekend is slightly higher than that on weekdays. Table 14 shows that the proportion of private cars choosing the shortest path for residents in different periods also shows similar characteristics. However, when the travel time is significant, the sample size is limited, and the proportion of the shortest path selection may be significant.Figure 13
A global selection of different time intervals for the shortest paths.Table 14
Segment selection of different time intervals for the shortest paths.
IntervalShortest distance pathShortest time pathWeekdayWeekendWeekdayWeekend0∼100.68280.66320.70150.750010∼200.48330.53740.53470.604320∼300.36460.40670.44440.518730∼400.34090.35890.43750.459340∼500.28870.39020.36080.406550∼600.20830.26190.30560.285760∼700.15560.30000.15560.280070∼800.15380.28570.26920.250080∼900.15790.33330.21050.400090∼1000.50000.20000.37500.2000100∼1100.16670.28570.00000.2857110∼1200.00000.25000.25000.0000(3) Segmented Travel Distance. Figure 14 shows that the proportion of private cars choosing the shortest path gradually decreases with the increase in travel distance. Among the shortest path choices, the proportion of private cars choosing the shortest time (ST) path at different distances is slightly higher than that of those choosing the shortest distance (SD) path. When the travel distance is more than 54 kilometers, the proportion of private cars choosing the shortest path is deficient. When dividing the date, the proportion of private cars taking the shortest path on the rest day is slightly higher than that on weekdays in most of the cases. Correspondingly, Table 15 shows that the proportion of private cars choosing the shortest path at different distances also shows similar characteristics. Similar to travel time, when the distance is considerable, the sample size is limited, and the proportion of the shortest path may be significant.Figure 14
A global selection of different distance intervals for the shortest paths.Table 15
Segment selection of different distance intervals for the shortest paths.
IntervalShortest distance pathShortest time pathWeekdayWeekendWeekdayWeekend0∼60.59880.59180.60670.66336∼120.41310.41970.46100.479312∼180.23880.32570.37310.399118∼240.30000.35350.37270.494924∼300.23530.45610.42650.491230∼360.45710.39390.31430.575836∼420.26670.23810.40000.190542∼480.18750.21740.37500.304348∼540.44440.50000.33330.400054∼600.16670.33330.50000.166760∼660.00000.55560.40000.555666∼720.40000.50000.40000.000072∼780.20000.00000.60001.0000


## 4. Conclusions and Discussions

The study proposed a deviation analysis method between actual and shortest paths based on private car trajectory data and the digital map. First of all, according to the definition of travel, the rules of private car travel are defined, and they may vary in different cities. Travel is divided according to these rules. The travel paths of private cars are generated based on GIS technology, and the essential travel characteristics of private cars are described and analyzed. Baidu Maps’ path planning function collects the shortest path (distance and time) data based on the private car travel paths. Finally, the difference and deviation between the private car travel path and the shortest path in a Chinese city (Chongqing) are compared and analyzed. Then we found the difference between the weekday and weekends on the shortest path selection. The proposed method in the study is also validated in practice.The conclusions mainly include the following:(1)
Many trips of residents in Chongqing, China, did not choose the shortest path. Only about 67% of the trips chose the shortest path (distance and time), which is significantly higher than residents in other countries. However, the deviation between the actual and shortest paths is relatively minor. Based on the residual error, the actual travel time of the selected path takes no more than 6 minutes on average compared to the shortest time path, and the travel distance is no more than 1 km compared to the shortest distance path. Taking the absolute residual value as the benchmark, the actual travel time of the selected path takes no more than 9 minutes on average, and the travel distance is no more than 2 km. Path selection and deviation vary in travel modes, OD attributes, drivers’ preferences, travel time, and distance.(2)
The results show that the distributions of residents’ private car trips on the weekdays and the weekends are very similar in terms of travel time, distance, and trip count. The path selection difference and deviation of the weekend are slightly higher than those on weekdays. In the case of relatively urgent conditions, people tend to choose a more familiar path rather than the shortest path to ensure the timely arrival of the destination. However, in other nonemergency travel situations, people choose the shortest path to obtain a shorter travel distance or time.(3)
The proposed analysis method on the deviation quantification between the actual and shortest paths is proved to be feasible in the way of a case study. More related studies may analyze the similar question via the proposed method in the future.Compared with Chongqing, the existing studies of cities worldwide have shown a smaller proportion of shortest path selection, and only the research of Minneapolis-St. Paul described the deviation between the commuters’ actual path and the shortest path. The existing studies in different parts of the world did not report the travel distance or time preference for shortest path selection. A higher shortest path selection proportion is partly because Chongqing, China, is a mountain city; private car drivers may be more likely to choose the shortest path than the plain city due to the terrain limitation. The empirical study on the shortest path selection in different cities worldwide is currently limited. In the theoretical aspect, the study is beneficial to quantify the perception error in stochastic traffic assignment [18] and handle the stochastic assignment paradox better [19]. In the practice aspect, the study’s findings are helpful to understand the relationship between the actual route selection and the recommended optimal paths. Travel information plays a crucial role in transport management [20, 21]. The findings provide valuable references for customized interventions concerning promoting route guidance. The travel information service mode should vary with the drivers’ preference and travel purpose during traffic management. For example, the managers or system should first evaluate the robustness and stability of the selected familiar route for commuters and then consider more efficient alternative recommendations. When the management provides better service, the drivers tend to follow and rely on the management.Traveler heterogeneity and bounded rationality are helpful to better understand route choice behavior [22, 23]; however, we failed to collect the socioeconomic attributes of the private car drivers because of privacy. Thus, we focus on analyzing the shortest route selection proportion, its clarified characteristics, and deviations in the study. Meanwhile, private car drivers in Chongqing, China, may be more likely to choose the shortest path than the plain city due to the terrain. We will undertake the plain city analysis on the question to enrich the route selection study further and consider more socioeconomic and psychological factors, especially the differences between different age groups [24].



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