Encapsulating Urban Traffic Rhythms into Road Networks Junjie Wang +, Dong Wei +, Kun He, Hang Gong, Pu Wang * School of Traffic and Transportation Engineering, Central South University, Changsha, Hunan, 410000, P.R. China + These authors contributed equally to this work * Corresponding Author Email: wangpu@csu.edu.cn Page 1 / 16
Supplementary Information Here, we briefly introduce the data and method used for generating transient ODs to maintain the completeness of the paper. This part is an abbreviation of Part II of the Supplementary Information with reference [1]. For more detailed information and analysis on transient ODs, please refer to [1]. PART 1. Mobile Phone Data and Road GIS Data The San Francisco Bay area mobile phone data were collected by a US mobile phone operator, having temporal and spatial records for nearly half a million customers. Each time a person uses a phone (call/text message/web browsing) the time and the mobile phone tower providing the service is recorded. In the three week observational period, we totally collect 374 million location records. A voronoi lattice is used to estimate the service area of a mobile phone tower [2, 3]. It provides the rough region where a mobile phone user can be located by the phone usage (Fig. S1a). In the Boston area mobile phone data, the coordinates of the recorded locations are estimated by a standard triangulation algorithm. In the three weeks observational period, more than 200,000 distinct locations are recorded, this data is aggregated at the census tract level to define the location of a phone user (Fig. S1b). We further find that a large majority of driver sources are located within dense mobile phone grids or small enough census tracts, thus providing accurate spatial resolution for the purpose of this study. Users privacy is protected by using anonymized user IDs. In addition, the spatial resolution of the voronoi lattice or the census tract provides sufficiently large areas to prevent personal location identification at an individual level. Furthermore, no individual trajectory is shown in our results. In both areas the selected mobile phone users have at least one location recorded between 9:00 p.m. to 7:00 a.m., allowing for the definition of home location in connection with a tower s service area or a census tract. Consequently, we select 356,670 Bay Area users and 683,001 Boston Area users, which represent 6.56% and 19.35% of the population in the two metropolitan areas respectively. We measure Page 2 / 16
the population in each census tract of the two areas, finding that the distributions of population can be approximated by two Gaussian distributions (Fig. S1c & d). The road networks, which include both highways and arterial roads, are provided by NAVTEQ, a commercial provider of geographical information systems data [4]. The data incorporate the attributes of roads needed for the computations presented in this work, in particular the road capacity. The road network in the Bay area contains 21,880 road segments and 11,096 intersections, while the road network in the Boston area contains 21,905 road segments and 9,643 intersections. For each road segment, the speed limit sl (miles/hr), the number of lanes l and the direction are extracted from the database. According to 2000 Highway Capacity Manual [5] and Reference [6], we estimate the capacity C of a road segment as follows: (1) when the speed limit of a road segment sl 45, it is defined as an arterial road: C=1,900 l q (vehicles/hour) (S1) for simplicity, the effective green time-to-cycle length ratio q is selected to be 0.5. (2) when the speed limit of a road segment 45<sl<60, it is defined as a highway: C=(1,000+20 sl) l (vehicles/hour) (S2) (3) when the speed limit of a road segment sl 60, it is defined as a freeway: C=(1,700+10 sl) l (vehicles/hour) (S3) Page 3 / 16
Figure S1 Human mobility and population data. (a) In the Bay area, 892 mobile phone towers (blue dots) are used by the carrier. The towers servicing areas are defined by a voronoi tessellation (blue polygons). The census tracts are represented by the light grey polygons. (b) Red polygons show the 750 census tracts in the Boston area. Mobile phone users coordinates were estimated by a standard triangulation algorithm, which resulted in more than 200,000 distinct locations with a 100m 100m spatial resolution (black dots). (c), (d) The distribution of population in the Bay area and Boston area census tracts. Two Gaussian distributions: and were plotted to guide the eyes. The maps in (a), (b) were generated using TransCAD 5.0 and ArcGIS. Page 4 / 16
Part 2. Estimation of the Transient ODs The major challenge when estimating travel demands with mobile phone data is embedded in the sparse and irregular records [7], in which user displacements (consecutive different recorded locations) are usually observed between a long period (i.e. the first location is observed at 8:00am and next location is observed at 6:00pm). To more accurately extract users travel demands between zones (mobile phone towers service areas for the Bay area and the census tracts for the Boston area), we only record displacements occurring within a short time window. However, the time window we select must be long enough in order to ensure that enough travel demand information is extracted. In our modelling framework, we set the time window to one hour and define a trip as a displacement occurring within one hour in each time period (i.e. Morning Period, Noon & Afternoon Period, etc). Fig. S2a illustrates a mobile user s time and location records, using the presented approach; in this example two trips are detected. Changes of locations C->D are not defined as a trip, because they do not occur within a one-hour time window. In this study, zones were defined by towers servicing areas in the Bay area and census tracts in the Boston area. The different zone definitions were resulted from the different features of location records in the two mobile phone datasets. The defined zones were only used in the process of generating the t-ods. All measurements regarding the dynamical driver sources (Fig. 1c-f) were based on the census tracts for both Bay area and Boston area. We next count the number of trips between zone i and zone j in a specific time period: (S4) where is the total number of selected users and is the total number of trips that user made between zone i and zone j in the observational period. One may note that the extracted distribution of travel demands did not take the population distribution into account. To avoid the bias caused by the Page 5 / 16
unevenly distributed mobile phone user market share, we define the down-scale ratio ( ) or the up-scale ratio ( ) as follows: (S5) where and are the population and the number of selected mobile phone users in zone i (the population of each Bay area zone was estimated based on the proportion of the zone area in each census tract). The measured distributions are shown in Fig. S2c. Note that in some regions the actual number of mobile phone users staying there may be larger than the number of residents registered by census. For both areas, they are relatively broad, thus it is necessary to adjust the number of trips by up-scaling or down-scaling the mobile phone users (Eq. S6). After this process, the total number of trips generated by residents in a zone is proportional with its actual population: (S6) where is the total number of users in the zone and is the total number of trips that user made between zone i and zone j during the three weeks of study. People use different transportation modes throughout their trips. Possible transportation modes include car (drive alone), carpool, public transportation, bicycle and walk. We define a user is a vehicle user if he/she uses car to commute. We calculate the vehicle using rate ( ) in a zone as follows: (S7) where and are the probabilities that residents in zone i drive alone or share a car. The average carpool size is 2.25 in California and 2.16 in Massachusetts (8). As shown in Fig. S2d, is low in downtown and high in the suburb areas. Using the calculated for each zone, we randomly assign the transportation mode (vehicle or non-vehicle) to the users living in each zone. We then filter the trips that are not made by vehicles and calculate the total number of trips generated by vehicles : Page 6 / 16
(S8) where user n is a vehicle user, is the number of users in zone. The average number of daily trips per person is about 4 in the US [9]. This generates about 22 million trips in the Bay area and 14 million trips in the Boston area. Based on the daily distribution of traffic volume obtained from [10], we estimate the average hourly trip production in the four time periods (Fig. S2e). Next, we upscale the obtained distribution of travel demands with the hourly trip production for the entire population, thus finally defining the estimated t-od. t- (S9) where is the number of zones. To assign trips to the road networks, we map each t-od pair from zone based t-od to intersection-based t-od. We find the road intersections within a zone and randomly select one intersection to be the origin or destination in the intersection-based t-od (Fig. S2b). In very few cases no intersection is found in a zone. In such cases we assign a trip s origin or destination to a randomly chosen intersection in the nearest neighbouring zone. We generate four 11,096 11,096 intersection based t-od from the four 892 892 zone based t-od in the Bay Area (the Bay Area road network contains 11,096 intersections). For the Boston Area, we generate four 9,643 9,643 intersection based t-od from the four 750 750 zone based t-od (the Boston road network contains 9,643 intersections). In conclusion, we selected census tracts as the Boston area zones because the mobile phone tower information was not available. The Bay Area t-ods were generated in the mobile phone tower resolution to avoid errors introduced by converting the tower-based trips to census tract-based trips. In the process of generating the zone-based t-ods, different zone definitions were used to adapt better to the data formats. After converting the zone based t-ods to intersection-based t-ods, only census tract definition was used to locate the dynamical driver sources in the Bay area and the Boston area. Page 7 / 16
Figure S2 Methodology to generate t-ods. (a) Illustration of trip definition from a mobile phone user s billing record. Black lines represent phone usage records; for each record, the time and the associated towers (A-D) routing the service were recorded. (b) Illustration of a mobile phone user s OD and t-od. Road segments in Boston are depicted by grey lines. A driver drives from zone A (origin) to zone D (destination); however, he/she may only be detected by phone records at zone B (transient origin) and zone C (transient destination). The thick red line indicates the predicted route from the observed t-od, whereas the thick yellow line represents the missing segment of the route. (c) The blue curve corresponds to the distribution of up-scaling/down-scaling ratios in the Bay area. The red curve corresponds to that of the Boston area. (d) Vehicle usage rates by geographical area in the Boston area. The vehicle usage in each Bay area mobile phone tower s servicing area was estimated based on the proportion of the servicing area in each census tract. (e) The average hourly total trip productions for the four time periods. For each time period, the hourly total trip productions were assigned as the average. The maps in (b), (d) were generated using TransCAD 5.0 and ArcGIS. Page 8 / 16
PART 3. Supplementary Figures Figure S3 Distributions of and. Comparison of the distributions of and, is much smaller than ; validating vehicle origins of a road segment during a specific time period has been confined to a much smaller scale than drivers home locations. Figure S4 Properties of road segments in different groups. Properties of road segments in the whole road network (group I), the giant road cluster (group II), the remaining 1,000 road segments (group III), and the remaining 500 road segments (group IV) were analyzed. (a) The distribution of extra travel time in the Bay area. (b) The distribution of traffic flow in the Bay area. (b) The distribution of in the Bay area. (d), (e), (f) Same as (a), (b), (c) but for the Boston area. Page 9 / 16
Figure S5 The largest road cluster size and properties of remaining road segments in the noon/afternoon period and the evening period. Identical to Figure 2, but indicates the noon/afternoon period and the evening period. Page 10 / 16
Figure S6 The effects of congestion mitigation for different scales of targeted road clusters (Bay area). (a) The change of total extra travel time with the reduction of speed limit for different scales of targeted road clusters. (b) The change of total travel time with the reduction of speed limit for different scales of targeted road clusters. (c) The change in the number of congested road segments with the reduction of speed limit for different scales of targeted road clusters. (d), (e), (f) Same as (a), (b), (c) but indicated cases of increased capacity for different scales of targeted road clusters. Figure S7 The effects of congestion mitigation for different scales of targeted road clusters (Boston area). (a)-(f) Same with Figure S6, but for the Boston area Page 11 / 16
PART 4. Results for Weekdays and Weekends As Fig. S8 shows, the number of major dynamical driver sources followed similar exponential distributions during the weekdays and weekend days, and the distribution of total extra travel time of each census tract also follows similar power laws. These results show very tiny differences with the results depicted in Fig. 1 (where weekday and weekend records were not separated). Figure S8 Distributions of and. (a) The weekday follows an exponential distribution ( ) for the Bay area (Boston area). (b) The weekend follows an exponential distribution ( ) for the Bay area (Boston area). (c) The weekday extra travel time follows a power-law distribution ( ) for the Bay area (Boston area). (d) The weekend follows a power-law distribution ( ) for the Bay area (Boston area). ( for all fits) Page 12 / 16
We observed slightly different spatial distributions of the congested driver sources in weekdays and weekend days, suggesting that more detailed travel demand information can lead to more accurate estimation of congested driver sources (Fig. S9). Figure S9 Sources of traffic congestion in the Bay area and Boston area. The color of a census tract represents the total extra travel time experienced by drivers whose trips originated from that census tract during one of the peak morning hours. We defined the top 2% census tracts with the largest as congested driver sources and highlighted those using yellow polygons. (a) Weekday results in the Bay area. (b) Weekend morning in the Bay area. (c) Weekday results in the Boston area. (d) Weekend results in the Boston area. We also measured the size of the largest road cluster with the fraction of removed road segments for the morning, noon & afternoon and evening periods of the weekdays and weekend days. The properties of the remaining road segments show very similar patterns with the results shown in Fig. 2 and Fig. S5. Page 13 / 16
Figure S10 Locating the road segments used extensively by drivers from congested driver sources. Same with Fig. 2 and Fig. S5, but for the weekday and weekend cases. The top five road clusters targeted at different time periods of weekdays and weekend days were shown in Fig. S11 and Fig. S12 for the Bay area and the Boston area. We observed slightly different spatial distributions of targeted road clusters in different time periods and different types of days. The fundamental findings are well preserved when using weekday data and weekend data, indicating that our modeling framework and results show enough generality. Page 14 / 16
Figure S11 Spatial distribution of targeted road clusters in the Bay area when 500 road segments remain. (a), (b), (c) The weekday results. (d), (e), (f) The weekend results. Figure S12 Spatial distribution of targeted road clusters in the Boston area when 500 road segments remain. (a), (b), (c) The weekday results. (d), (e), (f) The weekend results. Page 15 / 16
REFERENCES: 1. Wang, P. et al. Understanding road usage patterns in urban areas. Scientific Reports 2, 01001 (2012). 2. Fu, T., Yin, X. & Zhang, Y. Voronoi algorithm model and the realization of its program. Computer Simulation 23, 89-91 (2006). 3. Song, C., Qu, Z., Blumm, N. & Barabási, A.-L. Limits of predictability in human mobility. Science 327, 1018-1021 (2010). 4. Navteq official website. http://www.navteq.com/ 5. Transportation Research Board. Highway capacity manual: 2000 (Transportation Research Board, Washington, D.C. 2000). 6. Villalobos, J. R. et al. Logistics capacity study of the guaymas-tucson corridor (A report to the Arizona Department of Transportation, 2005). 7. Candia, J. et al. Uncovering individual and collective human dynamics from mobile phone records. J. Phys. A 41, 224015 (2008). 8. State averages for private vehicle occupancy, carpool size and vehicles per 100 workers. http://www.nctr.usf.edu/clearinghouse/censusavo.htm 9. National household travel survey daily travel quick facts. http://www.bts.gov/programs/national_household_travel_survey/daily_travel.html 10. Seto, Y. W., Holt, A., Rivard, T. & Bhatia, R. Spatial distribution of traffic induced noise exposures in a US city: an analytic tool for assessing the health impacts of urban planning decisions. International Journal of Health Geographics 6, 24 (2007). Page 16 / 16