Modified Betweenness-Based Measure For Traffic

Modified Betweenness-Based Measure For Traffic Flow Prediction Of Urban Road

Pengyao Ye School of Transportation and Logistics, Southwest Jiaotong University National United Engineering Laboratory of Integrated and Intelligent Transportation 111 the Second Ring Road North, Chengdu, Sichuan, China 610031 Tel: +86-180-3087-9310; Email: [email protected] Bo Wu School of Transportation and Logistics, Southwest Jiaotong University National United Engineering Laboratory of Integrated and Intelligent Transportation 111 the Second Ring Road North, Chengdu, Sichuan, China 610031 Tel: +86-135-1814-6925; Email: [email protected] Wenbo Fan, Corresponding Author School of Transportation and Logistics, Southwest Jiaotong University National United Engineering Laboratory of Integrated and Intelligent Transportation 111 the Second Ring Road North, Chengdu, Sichuan, China 610031 Tel: +86-136-5808-2981; Email: [email protected] Word count:

4262 words text + 10 tables/figures x 250 words (each) =6,722 words

TRR Paper number: 16-5817

Submission Date: February 28, 2016

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ABSTRACT The conventional network structure measure, betweenness centrality, has been used to predict roadway traffic flow; however, the prediction capability is limited by its static nature without consideration of the variable travel demand on roadway network. With the objective to explicitly address the effects of travel pattern (e.g., origin-destination (OD) distribution) on urban roadway traffic flow prediction, the paper proposes a modified measure integrating the betweenness centrality index and the traditional travel demand metrics (i.e., the OD demand and ratios of total demand). In the case study, roadway networks of two cities, i.e., San Francisco (USA) and Nanjing (China) are selected to demonstrate the effectiveness of the proposed method. Taxi GPS trace data in the two cities are retrieved and applied to calibrate and validate the proposed measure. Correlation analyses are conducted to compare the predictions of the conventional and the modified betweenness measures against the observed taxi traffic flows. The results show that compared to the traditional approach, the modified betweenness measure produces the prediction with better correlations with the observed taxi traffic flows in both case studies. More accurate prediction for the future year traffic flow can be expected by applying the new modified measure. Keywords: Traffic flow, Betweenness, Roadway network, Origin-destination distribution, Taxi globe position system trace

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1 INTRODUCTION The distribution of traffic flow in roadway network depends on network structure (1-4) (e.g., topological characteristics) among other factors (e.g., travel demand characteristics). As one of the network structure measures, betweenness centrality (BC) has been applied to quantitively correlate network structure with roadway traffic flow, and accordingly makes prediction for future (1,2,5). The concept of BC is defined as the percentage of all shortest paths between vertices that pass through the node/link of interest, indicating the centrality of the node/link in the network (6). The theoretical basis for BC-based traffic flow prediction is the assumption that travelers are most likely to choose the shortest paths between origin and destination (OD) and thus node/link with higher value of BC implies more attraction for travel demand and ultimately tends to have larger volume of traffic flow (1,2,5). Nevertheless, as Kazerani and Winter (7) indicated, the BC-based traffic flow prediction approach neglects the variable characteristics of traffic flows that depends on demand-side factors. It is demonstrated that the BC-based approach is limited to predict traffic flow in a significantly varying context, such as urban roadways with tidal flows (8-10). Thus, efforts have been expended to modify the traditional BC-based method, e.g., combining the BC index with geographic information (9) and taking spatial distribution of human activities into account (10). With the objective to explicitly address the effects of travel pattern (e.g., origin-destination (OD) distribution) in urban roadway traffic flow prediction, the paper proposes a modified measure integrating the BC index and traditional travel demand metrics (e.g., OD demand ratios). Two case studies in San Francisco (USA) and Nanjing (China) are given to illustrate the better correlation of the modified centrality measure (as compared to the conventional BC index) and the observed link traffic flows. The paper is organized as follows: Next section presents a literature review. Section 3 describes the methodologies used to modify the BC measure. In Section 4, two case studies are conducted in San Francisco (USA) and Nanjing (China) based on real taxi trace data. The final section summarizes conclusions and points out future research directions. 2 LITERATURE REVIEW As a fundamental concept in network analysis, centrality measures the natures of network from different aspects. Centrality determines the relative structure importance of a node in network (5,12-14). In many fields, such as molecular biology, urban structure, and transportation, researchers often use centrality to reflect topological characteristics of nodes in network (4,15-20). Hillier (21) found that closeness centrality can be linked with lots of phenomena, including crime rates, pedestrian and vehicular flows, and human wayfinding capacity. Therefore some researchers studied the behaviors of pedestrian and cyclist and attempted to estimate bicycle volumes with centrality (22-25). Centrality also was used to distinguish and quantitatively describe the road network patterns (26,27). Vital road usually attracts high traffic flow. This is an implicit sense and accords with centrality concept. Hence, many researchers focused on the relationships of centrality and traffic flow, expecting to get an ideal measure to characterize and predict traffic flow (1-4,6,18,19,28). Results of these studies reported that traffic flow is significantly correlated to morphological characteristics of urban roads. Correlation coefficient between betweenness centrality and traffic flow could reach up to 0.8 and even higher (1-3). But they either lacked real data as support or were restricted to a small region. Doubts emerged about the ability of betweenness as a predictor. Kazerani and Winter (7) stressed that traffic demands are not evenly distributed in urban road network and traffic is a

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dynamic system, which conflict with betweenness. In addition, because of the bounded rationality of human behavior, route choices of travelers are limited by their cognitions about road network, and people tend to choose the familiar routes rather than the shortest routes (29,30). Those also suggest that betweenness is not a competent predictor. And Song et al (10) demonstrated that through real data analysis, they pointed out the gap between betweenness centrality and actual flow. For the limitations of conventional betweenness, some researches tried to modify or combine it with factors reflecting the traffic demand distribution. Kazerani and Winter (11) proposed a modified version of betweenness centrality by considering people’s specific traffic demands in different times of the day, but unfortunately it was in a fictive network. Leung et al (9) introduced location information of restaurants and combined it with betweenness to get a centrality-based methodology to predict traffic flow with the support of real data. Song et al (10) modified betweenness taking account of spatial heterogeneity of human activities and distancedelay law. 3 METHODOLOGY 3.1 Modified Betweenness Centrality Given a graph G (V , E ) , where V is the set of vertices and E is the set of edges. The BC of node v is defined as (5):

C B (v) 

 st (v) stvV  st



(1)

where

 st =number of the shortest paths from s V to t V ; and  st (v) =number of such paths passing through v V .

Note that when the above-defined BC is applied to roadway network, nodes (s, t) are treated indistinctively without consideration of their travel demand generation and existing travel pattern between them, which may vary significantly among nodes (e.g., nodes in central business district and those in suburban area). Thus, BC-based traffic flow prediction only reflects the effects of topological features of the roadway network but neglects the demand-side influences driven by socioeconomic factors associated with the nodes. This is one of the major limitations of the conventional BC-based traffic flow prediction. To overcome the limitation, it is intuitive to introduce the demand-side factor into BC models via linearly weighted aggregation, which meets the observation that each link traffic flow is the sum of all OD demand via routes passing the link. In this way, the BC factor of each link becomes capable of reflecting the diversity of link traffic flow as a result of the heterogeneous traffic demand between different OD pairs. The demand-side influences that determinate traffic flows in roadway network can be represented by demand distribution between OD pairs, which is a classical index used in travel survey and transportation planning and thus the data can be readily obtained. To explicitly address the demand-side influence, the paper modifies the traditional BC by introducing OD demand ratios. We define st ,ts as the standardized OD demand ratios of total demands:

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 st   ts 

M st  M ts Max ( M ij  M ji )

(2)

i jV

where M= OD demand distribution matrix; M st = produced and attracted trips between nodes, s  V and t V ; and

M ts =attracted trips between nodes, s  V and t V .

 st or  ts can be used as weighed attributes of a given node pair. Substituting equation (2) into equation (1) and adapting the ranges of nodes (s, t), we get a modified BC definition, C (v ) :

C(v) 



s tV

st

 st (v)  st

(3)

In equation (3), the adaption of ranges of nodes (s, t) makes this modified BC measure C (v ) able to contain the influences of traffic demands of v to others. And the above-modified BC

measure (equation (3)) can be computed by using adapted Brandes algorithm (31, 32), of which the details are omitted in this paper. 3.2 Topology of Roadway Network To reduce the computation efforts of the above-modified BC measure in real roadway network, we apply the following steps to simply the roadway networks without loss of topological characteristics: 1. Roadway networks are treated as undirected networks, i.e., each link has a two-way connection (9, 10). One-way links are not considered in the study. 2. Multilane roadways are treated as single links, and the connection between adjacent links is guaranteed without need to identify turning lanes. 3. Ramps are integrated into the connected roadway links, and thus interchange can be represented in a simple topological form as shown in Figure 1. 4. Following the work by Leung et al. (9), the intermediate joints of roadway links are excluded to keep two adjacent intersections having one connection link. 5. The simplified network is then topologized by representing actual roadway links as vertices and intersections/interchanges as edges, as illustrated in Figure 2 (33). 3.3 OD Demand and Traffic Flow Estimation Based on Taxi Trajectory Data Each taxi GPS trip consists of multiple trace points as shown in Figure 3, where the starting and ending points (denoted by ‘a’ and ‘g’ dots, respectively) are identified as the origin and destination (i.e., O and D points) of the trip and dots with other grayscales are trace points during this trip. Nevertheless, the raw GPS data cannot be directly applied to retrieve travel information because of the difference between taxi driving behaviors (e.g., detouring and waiting for customers) and normal passenger cars as well as misreporting data. Therefore, before OD and flow estimation, we

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need to manage the GPS data in the following steps: First, as for representing real travel demand, GPS records should exclude the detouring trips of taxi, of which empty occupancy can be identified as the filter criterion. Second, misreporting records should be also removed by identifying data with very short distance (e.g., less than 1 miles) or time (e.g., less than 10 mins). Third, the trace points of different GPS trips can be located to the nearest links in roadway network (as illustrated in Figure 3), and by summing all related trace points of different GPS trips in the link, we extract taxi OD pairs from the probe taxies’ trajectory data to represent the OD demand of taxi trips, and accumulate taxi counts on each street segment to obtain the link taxi traffic flow. 4 CASE STUDIES 4.1 Experimental Network Based on the spatial coverage of available taxi GPS data (34), we choose the study areas of San Francisco and Nanjing as shown in Figures 4-5. Figure 4 shows a part of roadway network in central San Francisco (approximately 67 square kilometers), containing 10,357 street segments (links) and 6,453 nodes. The roadway network of Nanjing in Figure 5 contains 3,224 links and 2,156 nodes in an area of 106 square kilometers. Other statistical descriptions of the two experimental networks are given in Table 1 including average link length, total length, and connection degree of nodes (indicating how many other nodes one node connects in the network). 4.2 Correlation Analysis and Discussion Following the above-given methods, we prepare and obtain about 500 taxis’ GPS records for San Francisco during May 22 to Jun 9, 2008 and 7,500 for Nanjing in Sept. 1 and 2, 2010. After OD demand and link traffic flow estimation of taxi trips, the modified BC measure of each link is calculated and a correlation analysis is applied to explore the relationship of the modified BC measure and traffic flow. Because there is a delay from traffic demands occurring to relevant traffic flows spreading on the network, traffic flows in short period can’t match to the traffic demands. Hence, the paper analyzes traffic flow and OD distribution by the day. In this study, we use taxi data to illustrate the correlation of the proposed centrality measure (i.e., the modified BC) and the link taxi traffic flow, given the easy availability of taxi GPS data. In the future, the modified BC will be examined using all types of vehicle data (including the OD demand and link traffic flow), when available. The paper compares the modified BC with three basic centrality measures (i.e., degree, betweenness, and closeness) (15) by conducting Pearson and Spearman correlation analyses. The correlation analysis of the modified BC and link taxi traffic flow includes the following three steps: (i) extracting taxi OD demand matrix and link taxi traffic flow data from the probe taxies’ GPS records, which have been processed to eliminate error records or noise data (e.g., drifting GPS points); (ii) computing the modified BC values on each link according to equation (3) with the input of the obtained OD demand matrix; and (iii) conducting Pearson and Spearman correlation analyses on the modified BC values (obtained in step ii) and the link taxi traffic flows (step i), respectively. Generally, Pearson correlation coefficient (P value) measures the linear relationship between two variables (i.e., the modified BC factor and link taxi traffic flow in our case), giving a value in the range of +1 and −1, where 1 is total positive correlation, and −1 total negative correlation (35). Spearman correlation coefficient (S value) assesses the monotonic relationship

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between two variables (36,37). Thus, a combination of Pearson and Spearman correlation analyses is used to examine the linear and nonlinear relationship between the modified BC and the link taxi traffic flow. For instance, a correlation with both high P value and S value indicates that a linear function exists between the two variables; and a correlation with a low P value and high S value denotes a monotonic nonlinear function. Tables 2 and Table 3 summarize the correlation analysis results of the four centrality measures, i.e., the modified BC (MBC), the conventional betweenness centrality (BC), the degree (De), and the closeness (Clo) for the two cases, respectively. Results in Table 2 and Table 3 show that in both cities, modified BC measure C ( v ) has greater correlations (i.e., higher P value and S value) with the observed link taxi traffic flow than the above three basic centrality measures, implying better capability of characterizing the distribution of traffic flows. In addition, it is observed that the correlation coefficients of C ( v ) fluctuate slightly during the study periods and remain relatively high (more than 0.65) for both cities. The results suggest that modified measure C ( v ) can adapt to changes of dynamic traffic and reliably reflect the characteristics of traffic flow. It is observed that the modified BC has generally high S values but relatively low P values against the link taxi traffic flow for both the two case studies. It is implied that a monotonic nonlinear function may exist between the modified BC and the link taxi traffic flow. It’s also remarkable that performances of three basic centrality measures differ widely as Table 2 and Table 3 show. The main reason is inconformity of urban network structure and traffic demand distribution (10). Most local regions of San Francisco network are similar to grid, that is, the network is homogeneous. While its traffic demands irregularly distribute, so that the distribution of its flows is inhomogeneous. Conventional betweenness centrality can’t adapt to that. Conversely, the modified BC measure C ( v ) expresses its ability and universality as a good predictor in cities with different structure types. Figure 6 shows the scatter diagrams of C ( v ) (in Y-axis) and the observed taxi traffic flows (X-axis) for the two cities, where each dot represents one street segment in road network with some traffic flow value and C ( v ) . Because lots of dots are with same flow value but mapping different C ( v ) values, plots in Figure 6 seem messy. Therefore C ( v ) values are aggregated and averaged according to flow values to get scatter diagrams again (shown in Figure 7). Obviously, there is a rough monotonic relationship between link taxi traffic flow and link’s C ( v ) according to Figure 7. 5 CONCLUSIONS AND FUTURE WORK This paper introduces a new betweenness-based modified measure to explicitly address the effects of network structure and travel demand pattern on urban traffic flow prediction. The modified measure is proposed by combining conventional BC with traffic demand, which can be extracted with taxi GPS data. Then correlation analyses are conducted in two case studies of modified BC measure and the basic centrality measures against the observed link taxi traffic flows. The results show that the proposed centrality measure (i.e., the modified BC) incorporated with the taxi OD demand appears to have a higher correlation with the link taxi traffic flow, as oppose to the conventional BC without the demand-side factor. In the future, the modified BC will be examined using all types of vehicle data (including the OD demand and link traffic flow), when available. Moreover, this study considers only daily volumes, which are not time dependent, and thus may have limited implication for dynamic application. In the future, the daily OD demand and link

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traffic flow can be disaggregated into different time intervals (e.g., morning peak hours and midday hours). In the future, the betweenness centrality can also be examined with the consideration of network heterogeneity in terms of the link length, capacity, speed limits, etc., which often reflect the diverse activity demands on the adjacent lands. In practice, traffic flow prediction based on the modified BC can be done in two steps: first, using the traffic survey data to calibrate the regressive traffic flow model as a function of the modified BC factor; and second, substituting the forecasted OD demand data (e.g., at different times of day) into the obtained regressive model and predicting the link traffic flow for the future roadway network. Accordingly, dynamic traffic control strategies can be made in advance of the peak traffic flows, so as to deal with potential traffic congestions by limiting the inflows of bottlenecks or altering them to other routes in less congested area. In conclusion, the new modified measure C ( v ) proposed in this paper extends the applicability of conventional BC concept in traffic flow prediction, but there still are three limitations in this study, which are the major directions of our future research. The first is to use larger-scale traffic data (including OD demand and link traffic flows) of all vehicle types to examine the modified BC measure; the second is to disaggregate traffic flows and demands into different time intervals (e.g., morning peak hours and midday hours) to enhance its implication for dynamic application; the third is to consider other possible factors (such as link length, road capacity and routes choosing behavior) for further modification. ACKNOWLEDGEMENT This research was supported by the National Natural Science Foundation of China (51308462) and Fundamental Research Funds for the Central Universities (2682015CX042). REFERENCES 1. Hillier, B., A. Penn, J. Hanson, T. Grajewski, and J. Xu. Natural Movement: or Configuration and Attraction in Urban Pedestrian Movement. Environment and Planning B: Planning and Design, Vol. 20, No. 1, 1993, pp. 29-66. 2. Penn, A., B. Hillier, D. Banister, and J. Xu. Configurational Modeling of Urban Movement Networks. Environment and Planning B: Planning and Design, Vol. 25, No. 1, 1998, pp. 59-84. 3. Jiang, B. Ranking Spaces for Predicting Human Movement in an Urban Environment. International Journal of Geographical Information Science, Vol. 23, No. 7, 2009, pp. 823837. 4. Crucitti, P., V. Latora, and S. Porta. Centrality in Networks of Urban Streets. Chaos, Vol. 16, No. 1, 2006. 5. Jiang, B., and C. Liu. Street-based Topological Representations and Analyses for Predicting Traffic Flow in GIS. International Journal of Geographical Information Science, Vol. 23, No. 9, 2009, pp. 1119-1137. 6. Freeman, L.C. A Set of Measures of Centrality Based on Betweenness. Sociometry, Vol. 40, No. 1, 1977, pp. 35-41. 7. Kazerani, A., and S. Winter. Can Betweenness Centrality Explain Traffic Flow? Presented at 12th AGILE International Conference on Geographic Information Science, Hannover, Germany, 2009. 8. Porta, S., V. Latora, F. Wang, E. Strano, A. Cardillo, and S. Scellato. Street Centrality and Densities of Retail and Services in Bologna, Italy. Environment and Planning B: Planning

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LIST OF TABLES TABLE 1 Experimental Roadway Networks TABLE 2 Correlation Coefficients of 4 Centrality Measures in San Francisco TABLE 3 Correlation Coefficients of 4 Centrality Measures in Nanjing LIST OF FIGURES FIGURE 1 Illustration of a simplified interchange. FIGURE 2 Topologization of roadway network. FIGURE 3 One example trip and its trace record points. FIGURE 4 Roadway network in the study area of San Francisco. FIGURE 5 Roadway network in the study area of Nanjing. FIGURE 6 Scatter diagrams of C(v) and traffic flow. Left plot is of San Francisco on May 25, and the right is of Nanjing on Sep 2. The unit of flow is vehicle/day. FIGURE 7 Scatter diagrams of average C(v) aggregated and traffic flow. Left plot is of San Francisco on May 25, and the right is of Nanjing on Sep 2. The unit of flow is vehicle/day.  

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  TABLE 1 Experimental Roadway Networks Network San Francisco Nanjing 

Area (km2)

Node

Segment

Average Length (m)

Total Length (km)

Average Degree

67

6453

10357

112

1164.8

3.21

106

2156

3224

210

676.6

2.99



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  TABLE 2 Correlation Coefficients of 4 Centrality Measures in San Francisco Dates 5-22 5-23 5-24 5-25 5-26 5-27 5-28 5-29 5-30 5-31 6-01 6-02 6-03 6-04 6-05 6-06 6-07 6-08 6-09 

MBC 0.670 0.666 0.701 0.705 0.686 0.665 0.653 0.667 0.689 0.701 0.707 0.679 0.678 0.662 0.675 0.685 0.718 0.709 0.695

Pearson’ r BC 0.190 0.182 0.191 0.191 0.209 0.197 0.182 0.186 0.190 0.188 0.200 0.198 0.190 0.178 0.188 0.184 0.196 0.195 0.188 

(P value) De 0.227 0.229 0.236 0.233 0.233 0.233 0.228 0.229 0.245 0.245 0.244 0.238 0.225 0.219 0.226 0.225 0.235 0.231 0.221

Clo 0.158 0.153 0.160 0.172 0.179 0.150 0.150 0.151 0.164 0.164 0.178 0.154 0.151 0.150 0.149 0.147 0.155 0.163 0.145

MBC 0.784 0.788 0.790 0.794 0.770 0.760 0.776 0.787 0.807 0.807 0.800 0.773 0.774 0.785 0.779 0.792 0.807 0.804 0.755

Spearman's rho (S value) BC De Clo 0.383 0.343 0.313 0.383 0.335 0.310 0.385 0.343 0.300 0.384 0.344 0.310 0.389 0.341 0.324 0.379 0.325 0.296 0.383 0.331 0.308 0.385 0.339 0.301 0.394 0.346 0.301 0.394 0.346 0.301 0.387 0.340 0.326 0.395 0.340 0.296 0.384 0.343 0.300 0.382 0.337 0.306 0.380 0.334 0.299 0.382 0.339 0.302 0.394 0.035 0.309 0.387 0.342 0.310 0.370 0.327 0.293

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  TABLE 3 Correlation Coefficients of 4 Centrality Measures in Nanjing Dates 9-01 9-02  

MBC 0.735 0.737

Pearson’ r BC 0.427 0.429 

(P value) De Clo 0.251 0.263 0.261 0.274

MBC 0.892 0.892

Spearman's rho (S value) BC De Clo 0.500 0.369 0.509 0.500 0.372 0.509

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(a)

(b) FIGURE 1 Illustration of a simplified interchange. Plot (a) is the original representation of an interchange, and (b) is the simplified representation.

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(a)

(b) Topology of the simple network. FIGURE 2 Topologization of roadway network. Plot (a) is the simple network with 5 roadway links and 5 intersections, and (b) is the topology of the simple network.

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FIGURE 3 One example trip and its trace record points.

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FIGURE 4 Roadway network in the study area of San Francisco.

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FIGURE 5 Roadway network in the study area of Nanjing.

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(a)

(b) FIGURE 6 Scatter diagrams of C(v) and traffic flow. Plot (a) is of San Francisco on May 25, and (b) is of Nanjing on Sep 2. The unit of flow is vehicle/day.

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(a)

(b) FIGURE 7 Scatter diagrams of average C(v) aggregated and traffic flow. Plot (a) is of San Francisco on May 25, and (b) is of Nanjing on Sep 2. The unit of flow is vehicle/day.