A bottom-up transportation network efficiency measuring approach: A case study of taxi efficiency in New York City

Journal of Transport Geography 80 (2019) 102502

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A bottom-up transportation network efficiency measuring approach: A case study of taxi efficiency in New York City

T

⁎

Wei Zhaia,b, Xueyin Baic,1, Zhong-ren Penga,d, , Chaolin Gue a

International Center for Adaptation and Design (iAdapt), School of Landscape Architecture and Planning, College of Design, Construction and Planning, University of Florida, USA b Department of Electrical and Computer Engineering, Herbert Wertheim College of Engineering, University of Florida, USA c School of Landscape Architecture and Planning, College of Design, Construction and Planning, University of Florida, USA d China Institute for Urban Governance, Shanghai Jiao Tong University, Shanghai, China e School of Architecture, Tsinghua University, China

A R T I C LE I N FO

A B S T R A C T

Keywords: Transportation network efficiency OD-level efficiency Citywide efficiency Taxi efficiency Big data

In this paper, we proposed an improved transportation network efficiency (TNE) measurement method, which is called passenger- and speed-weighted efficiency (PSWE). The new method is used to measure both origin-destination-level (OD-level) transportation efficiency and citywide transportation efficiency by integrating with the excess commuting (EC) framework. To show the feasibility of the proposed measurement method, we chose New York City (NYC) as the study area and employed open taxi data. By calculating the efficiency value of the ODlevel, we discovered that the average distance of highly efficient taxi trips is much longer than that of inefficient trips. Then, the OD-level efficiency value is applied to the EC framework by replacing the conventional cost unit (time or distance) with the proposed efficiency impedance (Eimp). The maps of minimized OD flows indicate that taxi trips within Manhattan and to the two airports (LGA and JFK) should be particularly considered if citywide efficiency is expected to be improved.

1. Introduction Transportation efficiency analysis is attracting great attention worldwide because the improvement of efficiency can reduce energy consumption and CO2 emissions (Yin et al., 2015), as well as increase the effectiveness of city operations. In an attempt to measure a city's efficiency, excess commuting (EC) is often adopted in the research area of transportation. However, the EC framework is typically used for citywide efficiency. Moreover, the characteristics of individual trips are ignored in many studies considering time (e.g., White, 1988; Zhou et al., 2018; Schleith and Horner, 2014; Zhou and Murphy, 2019) or distance (e.g., Hamilton and Röell, 1982; Buliung and Kanaroglou, 2002; Horner and Murray, 2002; Ma and Banister, 2006) as the only parameters for the measurement of citywide efficiency. One single factor, such as time or distance, cannot convincingly reflect efficiency. For instance, in highly congested regions, drivers may prefer to take a detour to avoid congestion, which may save time even though the route distance would increase.

Transportation planners aim to amend the inefficient road network to adapt to urban growth. Although the EC-based approaches could show specific flows of each OD pair across the city, improving the roads over every corner of the city is impossible considering the limited government budget. To address the limitations of the EC framework, previous studies on transportation network efficiency (TNE) could help decision makers find the most inefficient routes and OD pairs (e.g., Latora and Marchiori, 2001; Hsu and Shih, 2008; Gastner and Newman, 2006; Nagurney and Qiang, 2007; Qiang and Nagurney, 2008; Dong et al., 2016). More factors are commonly considered in TNE to reflect the comprehensive efficiency of a transport network, so that it can avoid the problems from a single-factor method (Qin et al., 2014). However, TNE-based studies have not examined whether they can be applied to evaluate citywide efficiency. Moreover, the high cost of transportation-related data also makes it difficult to monitor the effectiveness of proposed strategies from planners over time, which makes previous TNE measurement methods impractical in practice. The open taxi data in New York City (NYC) provides us with an

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Corresponding author at: International Center for Adaptation and Design (iAdapt), School of Landscape Architecture and Planning, College of Design, Construction and Planning, University of Florida, USA. E-mail addresses: wei.zhai@ufl.edu (W. Zhai), xueyin.bai@ufl.edu (X. Bai), zpeng@ufl.edu (Z.-r. Peng), [email protected] (C. Gu). 1 Present address: Arch Building, P.O. Box 115,706, Gainesville, FL 32611-5706. https://doi.org/10.1016/j.jtrangeo.2019.102502 Received 16 August 2018; Received in revised form 17 August 2019; Accepted 19 August 2019 0966-6923/ © 2019 Elsevier Ltd. All rights reserved.

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collective transportation line networks by integrating with the passenger system level. In addition, Dong et al. (2016) introduced an approach to quantify TNE by incorporating the population with a distance factor. However, the researchers assume that trips between each OD pair use the same route. The heterogeneity of individuals would be ignored based on this assumption. Representative indicators have also been used in existing TNE-based studies. Costa and Markellos (1997) studied the production efficiency of public transport services and the competitive efficiency of bus operators. However, the efficiency of network operations is not specifically considered. Levinson (2003) developed a comprehensive indicator system to understand all-around transportation network efficiency from five aspects, including flexibility, efficiency, accessibility, productivity, and utilization fairness. Nait-Sidi-Moh et al. (2009) considered passengers' waiting time as a unique indicator of the efficiency of public transportation services. Moreover, the data envelopment analysis was combined with the stochastic frontier analysis to study the input-output efficiency of transportation networks (e.g., Gudmundsson, 2004; Yu and Lin, 2008; Zhao et al., 2011). However, the generated results can be seen as the relative efficiency value in terms of the input-output ratio of the enterprise, instead of road network efficiency, which is more important for planners.

opportunity to overcome the gaps discussed. However, taxi data also has limitations in terms of the capability to represent the total population. For instance, the 2017 Citywide Mobility Survey shows that < 3% of residents in NYC choose a taxi as the primary trip mode (NYC, 2018). Additionally, a great proportion of taxi passengers in NYC are transient tourists since Yellow Taxi serves over 25% of all passengers from airports (NYC-TLC, 2014). Despite the limitations introduced, the method based on taxi data can be generalized to other trip modes given that data set is accessed. In addition, there are still two research questions expected to be addressed in this study: 1) How can TNE be measured based on the open big data, considering the real-world characteristics? 2) Can the proposed TNE measurement be applied to the measurement of citywide efficiency? To answer the abovementioned research questions, this study proposes a distance- and speed-weighted approach to measure OD-level efficiency. Then, we apply it to the measurement of citywide efficiency and show the feasibility of the proposed approach. 2. Literature review 2.1. Transportation network efficiency measurement Researchers and planners commonly employ the EC approach to measure citywide efficiency. In this sense, EC-based studies explore urban transportation efficiency from a systems perspective. Specifically, proposed by Hamilton and Röell (1982), the EC framework represents the additional commute, which is the difference between the real-world commute and the theoretically minimum commute. White (1988) realized the method by using a linear programming algorithm. Then, the excess commuting framework was extended to several conditions. For instance, Horner and Murray (2002) developed a similar index called the ‘commuting potential utilized’ index, which integrates the theoretical maximum commute with the existing EC framework. Similarly, Yang and Ferreira Jr (2008) developed another method to represent the maximum commute, called ‘proportionally matched commuting’. Murphy and Killen (2011) introduced the ‘commuting economy’ index by extending the random commute and improving the ‘commuting potential utilized’ index to the normalized commuting economy. However, in the real world, an individual's travel behavior is associated with his or her own demand and utility because the individual is not aware of the operation of the entire city. Different from EC-based studies that mainly employ travel time or distance as the cost unit, TNE-based studies take more traffic information into account. Latora and Marchiori (2001) introduced the LM network performance to evaluate the efficiency of transportation networks, based on which links should be weighted. This method has been widely used by agencies in practice, such as the Massachusetts Bay Transportation Authority (MBTA) in the Greater Boston region. Hsu and Shih (2008) also adopted the L-M method to analyze the efficiency of the aviation network. Roughgarden and Tardos (2002) employed travel cost as the key factor to assess network efficiency and efficiency loss in proposed scenarios. Wang et al. (2014) examined the efficiency loss of selfish routing based on the proposed approach. Gastner and Newman (2006) developed a distance factor (Euclidean distance/ route distance) to represent the network efficiency between an OD pair. These studies mainly employed network analyses to evaluate the efficiency of a specific OD pair or the structure of a road network. However, they lost sight of other associated factors affecting efficiency in the real world, such as travel demand, travel speed, and so on. To take more factors into consideration, Nagurney and Qiang (2007) proposed a model that integrates travel fees, traffic flows, and travel behavior features to detect the vulnerability of a transportation road network. Qiang and Nagurney (2008) furthered the method to fields beyond transportation network analysis. However, population and passenger volume are not considered in Nagurney and Qiang (2007) or Qiang and Nagurney (2008). To address this gap, Barrena et al. (2015) used hypergraphs to explore the transferability of

2.2. Taxi supply and demand in New York City In NYC, high-volume airports play a significant role in generating and attracting taxi trips (Yazici et al., 2013). Schaller Consulting (2006) found that 35% and 23% of air passengers arriving at LaGuardia (LGA) and John F. Kennedy (JFK) airports preferred to use taxis, respectively. It was found that during an extreme weather event, taxis make short trips more frequently in Manhattan (Kamga et al., 2013). For this reason, taxi shortages are often reported during inclement weather conditions at the JFK airport in NYC (Conway et al., 2012). Yang et al. (2014) found that, compared to taxis, transit is the more likely choice during most of the day except the midnight period in NYC. The pickup decision of a taxi driver is closely correlated with the taxi supply and demand in the city. Both taxi supply excess (e.g., Skok and Martinez, 2010) and shortage (e.g., Da Costa and De Neufville, 2012) could occur. Yang and Gonzales (2014) employed demographic, socioeconomic, and employment data to identify the factors that drive taxi demand. Kamga et al. (2011) examined many factors affecting the taxi supply based on taxi driver interviews. Yazici et al. (2013) developed three travel time reliability measures to quantify the travel time reliability in NYC by using the taxi dataset. A case of taxi shortages in NYC is related to low taxi supplies at JFK airport during inclement weather conditions because taxi drivers prefer picking up passengers in city centers (Conway et al., 2012; Kamga et al., 2011). Although some regulations have been proposed to increase taxi supply, the performances of these regulations are not guaranteed (Santani et al., 2008). In addition, taxi efficiency is analyzed from different aspects, including taxi operations and the routing of vacant taxis (e.g., Gui and Wu, 2018; Rahimi et al., 2018; Dong et al., 2019; Chen et al., 2018). Specifically, in NYC, Phithakkitnukoon et al. (2010) introduced a model to estimate the number of vacant taxis based on the time of the day, day of the week, and weather conditions. Kamga et al. (2012) illustrated how new technologies and policy changes can be employed to improve the efficiency of taxi operations at the JFK airport. Kamga et al. (2011) proposed strategies to provide a better taxi service for JetBlue customers at JFK terminal 5. Yazici et al. (2016) quantified the potential impacts from the pick-up decisions of taxi drivers and then proposed suggestions for the improvement of the JFK airport's ground access. It is clear that there are many insightful studies exploring the taxi demand and supply in NYC, as well as the efficiency of taxi operations. However, few studies concern the efficiency of taxi services in NYC from the perspective of TNE. In addition, regarding the limitations in previous EC-based and TNE-based studies, the purpose of this study is 2

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assumed in Fig. 3:

to advance existing studies one step further by proposing a bottom-up approach, which can be applied to measure taxi efficiency on both an OD-level and a city-level.

(a) Keeping all else the same, if the geometric distance (dgeo) of origin O1 and destination D1 is small and the route distance (droute) is large, then we can define that the distance factor of this OD pair (dgeo/droute) is small. That is, the network design between this OD pair is expected to be improved (see Fig. 3(a)). (b) Assume that the geometric distances of two OD pairs are the same and that the route distances of two OD pairs are also the same. Then, we assume that the speed on the route (O1, D2) is greater than that on the other route (O1, D1) (i.e., v2 > v1). In this situation, the efficiency value of the route (O1, D2) is greater than that of the other route (O1, D1) because it takes less time from O1 to D2 (see Fig. 3(b)). (c) Assume that the travel speeds of two OD pairs are the same (i.e., the distance factors are also the same). Then, we assume that the number of passengers on the route (O1, D2) is greater than that on the other route (O1, D1) (i.e., c2 > c1). In this situation, the efficiency value of the route (O1, D2) is greater than that of the other route (O1, D1) because it serves more passengers (see Fig. 3(c)).

3. Methodology 3.1. Data origins and zonal system Based on the open data from the New York City Taxi & Limousine Commission (NYC-TLC), we can obtain detailed OD information for each taxi. Specifically, pick-up and drop-off dates/times, pick-up and drop-off locations, trip distances, and driver-reported passenger counts are recorded. The Yellow Taxi and Green Taxi are the most popular and recognized taxi companies in NYC. However, Green Taxi drivers can only pick up passengers from the street in northern Manhattan, the Bronx, and Queens. Therefore, Yellow Taxi trips are mainly used for efficiency measurement in this study. The time span of the data analyzed is from January 1, 2016, to January 31, 2016. We did not use the latest data because the coordinates of pick-up locations and drop-off locations have been aggregated into Neighborhood Tabulation Areas (NTAs) since 2017. NTAs are delineated by the city government to project populations (see Fig. 1). To explore the spatiotemporal distribution of taxi efficiency, the first step is to understand the temporal pattern of taxi trips. Taking a closer look at the temporal changes of passenger counts and taxi counts (see Fig. 2), we differentiate the taxi trips on weekdays from those on weekends (including official holidays). On weekdays, there are two striking peaks during 8:00–10:00 am and 17:00–19:00 pm, which are defined as the morning peak hours and evening peak hours, respectively.

Based on the abovementioned assumptions, we propose a measurement model by weighting the distance factor with the number of passengers and the average speed of one trip. The equation for passenger- and speed-weighted efficiency (PSWE) is as follows (Eq. (1)):

e(ni, j) =

n n dgeo c n (i, j) vroute (i, j ) (i, j ) ∙ ∙ n cmax vmax droute (i, j)

(1)

where en(i,j) represents the efficiency value of the n-th trip between the OD pair (i,j), cn(i,j) represents the number of passengers of the n-th trip from region i to region j; cmax represents the maximum capacity of each vehicle; dngeo(i,j) represents the geometric distance of the n-th trip between origin i and destination j; dnroute (i,j) represents the route distance of the n-th trip between origin i and destination j, which is available in the NYC-TLC dataset; and vnroute (i,j) represents the average speed of the

3.2. Assumptions and formulations Before developing the mathematical expression of the measurement method, we first define highly efficient trips. Three scenarios are

Fig. 1. Map of New York City and analysis units. 3

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Fig. 2. Passenger and taxi count over time.

Fig. 3. Examples of highly efficient trips.

one step further by applying OD-level efficiency measurement to the citywide efficiency measurement. Specifically, we employ the EC framework by replacing the cost unit with Eimp and conducted the calculation based on Eq. (3). Based on the preceding introduction, Tmin and Tact are the key parameters for the EC calculation as follows (see Eq. (5)):

n-th trip between origin i and destination j. The maximum speed limit vmax, which is 50 mph, is used to normalize the speed of each trip in this study. The route speed of an individual trip can be calculated from the taxi data. When all trips are calculated based on Eq. (1), we can obtain the average efficiency value of each OD pair by Eq. (2) as follows:

e(i, j) =

1 N(i, j)

N(i, j )

∑

e(ni, j)

n=1

EC = (2)

Min:Z =

1 Mj

(3)

n

i=1 j=1

∑ X(i,j)

(6)

= Dj ∀ j = 1, …, m

(7)

n

∑ X(i,j)

= Oi ∀ i = 1, …, n

j=1

(8)

X (i, j) ≥ 0 ∀ i, j.

(9)

where m represents the origin trips; n represents the destination trips; Oi represents the total trips leaving from region i; Dj represents the total trips arriving at region j; Xij represents the total trips from region i to region j; and cij represents the cost unit from region i to region j. Note that cij could be represented by time, distance and Eimp, respectively. In this sense, apart from Tmin (minimized time), Dmin (minimized distance)

∑ e (i,j) j

m

∑ ∑ c (i,j) X(i,j)

i=1

Given the efficiency value of each OD pair, we can sum up the values based on their destination regions to visualize the efficiency pattern across the city on a zone-level.

Ej (D) =

1 N

n

s. t.

1 e (i, j) + λ

(5)

where Tact represents the actual travel cost. To obtain the minimum cost, namely, Tmin, the linear programming model is commonly adopted. The objective function and constraints of the approach are defined as follows:

where e(i,j) represents the average efficiency value of the OD pair (i,j) and N(i,j) represents the number of trips between the OD pair (i, j). To tie the proposed efficiency measurement to the conventional trip cost unit (time and distance), we introduce a new cost index which is called efficiency impedance (Eimp). It can be calculated based on the efficiency value of each OD pair (see Eq. (3)). In particular, we add a hyperparameter λ to avoid the situation in which e (i,j) is zero. In this study, λ is 0.0001.

Eimp(i, j) =

Tact − Tmin Tact

(4)

Based on Eqs. (1)–(3), we could measure the efficiency value of a specific OD pair. However, the measurement of citywide efficiency has not been considered. We therefore advance the TNE-based approach 4

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Fig. 4. Scatter diagrams of different distances.

OD pairs (top 10%) and that of the most inefficient OD pairs (bottom 10%). Additionally, Fig. 6(a) indicates the spatial distribution of inefficient OD pairs. Fig. 6(b) indicates the spatial distribution of highly efficient OD pairs. Two interesting findings should be highlighted from Table 1 and Fig. 6. First, the route distance of inefficient OD pairs is much shorter than that of highly efficient OD pairs, which also partially challenges the method in Gastner and Newman (2006). Specifically, the result in Table 1 shows that a trip with a longer distance does not mean that its efficiency value is low. However, based on the assumption in Gastner and Newman (2006), a longer trip distance represents a lower efficiency value. Additional evidence to justify the argument is that most inefficient routes are close to the East River (Fig. 6(a)). Taxis must pass through nearby bridges because there is no shortcut to cross the East River. To this end, the efficiency value of one trip could be low, even though the geometric distance of the trip is very short. Admittedly, we cannot conclude that longer trips are all beneficial to citywide efficiency; however, the finding indicates that part of long-distance trips can be more efficient than short-distance trips in some situations. Second, even though the average trip distance of highly efficient OD pairs is greater than that of inefficient ones, the average travel time of highly efficient OD pairs is just slightly greater than that of inefficient ones (see Table 1). It can be explained that the trip with a longer distance could have a higher average speed. Another explanation is that most inefficient trips are generated in highly congested regions such as Manhattan (see Fig. 6(a)); therefore, such trips take more driving time even though their trip distance is short. This can be further demonstrated by the speed ratio distribution map (see Fig. 5(b)), which shows that the average driving speed outside Manhattan is much greater than that within Manhattan. Apart from identifying inefficient pairs, we can use Eq. (4) to obtain the efficiency distribution of NTAs (Fig. 7). For AM peak hours and PM peak hours, taxi drivers heading to Manhattan are prone to experience a relatively inefficient trip. Specifically, the percentage of inefficient NTAs in Fig. 7(a) is relatively less than that in Fig. 7(b) and Fig. 7(c), meaning that the taxi efficiency values of some NTAs in Manhattan in nonpeak hours may be greater than that in peak hours. It shows that taxi efficiency is indeed impacted by the commuting trips in NYC during peak hours, even though many passengers are not going to their job by taxi. Staten Island is isolated from the other boroughs in terms of geography and taxi trips since it is the least populated area in NYC. One piece of evidence is that some NTAs on Staten Island do not contain taxi trips in peak hours (Fig. 7(b) and Fig. 7(c)). In addition, for the 24-h efficiency distribution (see Fig. 7(a)), most NTAs on Staten Island are inefficient because the passenger ratios are relatively low for taxis heading to this borough (Fig. 5(c)). This is additional evidence showing the low population density of Staten Island.

and Eimpmin (minimized efficiency) are additionally calculated in this study. 4. Results 4.1. An examination of the bias in the unweighted method Before applying the proposed approach to measure taxi efficiency in NYC, we first show the necessity of weighing the distance factor. Fig. 4(a) indicates that with an increase in geometric distance, the actual route distance gets much greater than the geometric distance. That is, the distance factor, namely, dngeo(i,j)/dnroute(i,j), is lower if the route distance is longer. It cannot fully reflect the efficiency of a road network if it is certain that the increased distance decreases efficiency. This finding challenges the approach proposed by Gastner and Newman (2006), which only considers the distance factor in the measurement model. For the method introduced in Dong et al. (2016), the route distance between i-th TAZ and j-th TAZ is simplified as the distance between centroids of TAZs. However, the individual person does not travel from a centroid or arrive at a centroid in the real world. The true route distance of each trip may be either smaller or greater than the simplified route distance derived from centroids. We adopt the Google Map API to request the shortest route distance between each OD pair. Fig. 4(b) can be used to demonstrate our argument for the method in Dong et al. (2016). In addition, the driver's response to congestion is not considered since taxi drivers may choose to take a detour if road links are congested. Therefore, this study furthers the work of Gastner and Newman (2006) and Dong et al. (2016) by integrating the number of passengers and the speed of the taxi trip into the distance factor. 4.2. OD-level efficiency analysis In Fig. 5, we display the spatial distribution of key factors for the composed factor in Eq. (1). The distribution of the distance ratio across NYC reveals where taxi drivers have to take a detour. Fig. 5(a) reveals that Manhattan is the main region where drivers are most likely to take a longer detour. Fig. 5(b) indicates the distribution of the average speed ratio (vnroute (i,j)/vmax) when drivers drive to NTAs. Clearly, from the city boundary to the city center (Manhattan), the taxi speed ratio shows a decreasing trend. Taxis can obtain a higher speed if drivers take a detour to avoid congested links in Manhattan. Admittedly, taxi drivers may take unnecessarily long routes to increase their fares, but we assume that drivers are all “upstanding” in this case. Fig. 5(c) shows an even distribution of the passenger ratio (cn(i,j)/ cmax) because the number of passengers in a taxi is not mainly determined by the destination. To further understand the characteristics of the efficiency pattern on an OD-level, Table 1 presents descriptive statistics of the most efficient 5

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Fig. 5. Spatial distribution of each factor.

efficiency between airports and other urban regions should be particularly discussed. Admittedly, the theoretical results cannot be completely implemented in practice, but the spatial pattern of OD flows nevertheless helps planners identify the critical regions to improve citywide efficiency.

4.3. Citywide efficiency analysis Based on Eq. (3), we can convert the efficiency value of each OD pair into Eimp. Then, by applying the EC framework (Eqs. (5)–(9)), we can calculate the citywide efficiency value. To compare the performance with conventional EC methods, we also calculate the time-based EC value and the distance-based EC value. Table 2 shows the citywide efficiency results derived from different cost units. In general, the Eimpbased EC value is close to the values derived from conventional methods. Originally, there were 5720 OD pairs that contained taxi trips in NYC. In the situation in which the citywide efficiency value is maximized (the total cost is minimized), only 436 OD pairs contain taxi trips because OD pairs with a high cost would not be assigned taxi flows in the model. The distribution of minimized OD flows is mapped to show the theoretically most efficient pattern across the city. Fig. 8(a)–(c) indicates how the OD flows should be organized to obtain the highest citywide efficiency value with different cost units. Fig. 8(d) indicates that the data distribution of minimized OD flows is very close with each other. Specifically, when the cost unit is time (Fig. 8(a)) or distance (Fig. 8(b)), the minimized OD flows are more evenly distributed, whereas the Eimp-based map (Fig. 8(c)) indicates significantly more taxi flows in Manhattan. Overall, no matter what the cost unit is in the linear programming model, the critical regions for maximizing citywide efficiency are Manhattan and the two NTAs containing airports (see Fig. 8(a)–(c)). In other words, if the city government aims to maximize citywide efficiency from the perspective of taxi trips, addressing inefficient taxi trips within Manhattan needs more attention. Furthermore, increasing taxi

4.4. Methods evaluation 4.4.1. The relationship between the composed factor and the single factor The correlation relationships between three factors, namely, the distance ratio, the speed ratio, and the passenger ratio, and the composed factor should be further explored. As indicated in Table 3, for all OD pairs, the speed factor is most correlated with the composed factor, meaning that the speed ratio contributes more to the taxi efficiency value of one OD pair. In addition, for high-efficiency OD pairs, the correlation coefficient between the speed factor and the composed factor is the highest. It is not surprising that the passenger ratio is the least correlated factor in all groups considering the relatively random pattern revealed in Fig. 5(c). In contrast to high-efficiency OD pairs, the distance ratio is most correlated with the composed factor for low-efficiency OD pairs. That is, the route choice largely determines the low-efficiency OD pairs. Another interesting finding is that the passenger factor and the speed factor are both negatively correlated with the composed factor. This further demonstrates that the distance factor mainly determines the low-efficiency OD pairs. In other words, the detour may occur more frequently and far more within low-efficiency OD pairs compared to high-efficiency OD pairs. Thus, the road network should be optimized between the OD pair that contains a low distance ratio.

Table 1 Comparison of highly efficient and inefficient OD pairs. Factors

Efficiency Passenger count Passenger ratio Speed Speed ratio Geometric distance Route distance Distance ratio Time

Top 10%

Bottom 10%

N

Min

Max

Mean

SD

Min

Max

Mean

SD

572 572 572 572 572 572 572 572 572

1.76 1.26 0.21 5.59 0.11 0.84 1.02 0.23 1.23

14.80 4.50 0.75 112.61 2.25 26.54 50.04 14.08 62.05

2.79 3.41 0.67 29.67 0.59 9.68 12.32 0.79 25.31

1.13 1.42 0.30 11.06 0.24 3.44 4.38 0.65 7.98

0.01 1.00 0.17 1.42 0.03 0.92 1.13 0.01 1.45

0.56 4.10 0.68 94.00 1.88 10.83 31.02 10.19 61.42

0.41 2.42 0.29 15.20 0.30 2.87 4.81 0.85 20.49

0.10 0.42 0.15 5.74 0.21 2.17 3.79 0.27 12.01

Note: The unit for speed is mph; The unit for geometric distance and route distance is mile; The unit for time is minute. 6

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Fig. 6. Inefficient and highly efficient OD pairs.

citywide efficiency, as the baseline. Then, we can compare the performance of the proposed PSWE method with previous methods in terms of citywide efficiency measurement. Note that we only use the linear programming approach in the EC method introduced in Section 3.2, not intending to only analyze commuting trips. We convert the efficiency value of each OD pair to Eimp by Eq. (3) and then calculate citywide efficiency by Eq. (5)–(9). In particular, the efficiency calculation of each TNE method is different in this study. Specifically, the parameter d in Latora and Marchiori (2001) is presented by the shortest route distance derived from taxi data, and the parameter N is the number of NTAs containing taxi trips. The parameter λ in Nagurney and Qiang (2007) is represented by the shortest route distance between two NTAs, and the parameter d is intuitively the OD demands between NTAs. Then, we replace the cost unit in EC with the OD-level efficiency index proposed by Nagurney and Qiang (2007). The parameter of li in Gastner and Newman (2006) is the route distance in this study, and di is the Euclidean distance between the original location and destination location. For OD-level efficiency measurement in Dong et al. (2016), Ptot is represented by the total number of passengers in NYC; P(i,j) is represented by the number of passengers between the corresponding OD pair; and the distance factor is the same as the distance ratio in PSWE. Table 4 displays the results of citywide efficiency based on the previous TNE methods and the proposed TNE method. Based on

The correlation coefficients between the single factors also reveal interesting patterns. One finding is that the speed factor and the distance factor are negatively correlated in both high-efficiency OD pairs and low-efficiency OD pairs. This reveals that a trip with a lower distance ratio is more likely to have a higher speed ratio. This finding is consistent with the assumptions in Section 3.2 and the findings summarized in Table 1. More specifically, the taxi drivers may choose to take a detour (distance ratio decreases) to gain a high speed (speed ratio increases) when the shortest path is congested with traffic. A surprising finding is that the passenger ratio is negatively correlated with the distance ratio in all groups. This means that if more passengers are in a taxi, the taxi driver may take a longer detour.

4.4.2. Performance comparison with previous methods As we introduced in Section 2.1, there are some TNE methods for OD-level efficiency measurement, but it is difficult to compare the performance in terms of measuring the efficiency value of each OD pair. One fundamental reason is that efficiency is a concept so there is no concrete truth for validation. Therefore, it is not easy to compare the effectiveness of the proposed approach with previous methods of ODlevel efficiency measurement. One solution is to compare the performance of citywide efficiency based on OD-level efficiency measurement methods (e.g., Dong et al., 2016). We use citywide efficiency derived from the EC method, which is the most widely used approach for

Fig. 7. Spatial distribution of NTAs' taxi efficiency. 7

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Table 2 Minimized results of different cost unit. Cost Unit

Actual Value

Minimum Value

EC

Valid OD pairs

Maximum Flow Volume (trips)

Travel Flow Median

Time Distance Eimp

773,457.3 min 154,133.4 km 45,330.23

42,536.48 min 12,658.52 km 3312.24

0.943 0.926 0.934

436 436 436

91,450 87,590 71,250

440 440 625

measuring citywide efficiency compared to the composed factor.

Table 2, there are two EC values available for the baseline depending on which cost unit is used. The difference between the TNE-based citywide efficiency and the EC-based citywide efficiency can be calculated. We use the absolute value of the difference as the criteria. In addition, the single factor for composing PSWE is also considered a cost unit to compute citywide efficiency. The result shows that the PSWE-based citywide efficiency is closest to the EC-based citywide efficiency. Note that even though we show the effectiveness of PSWE in the citywide efficiency measurement, we cannot conclude that it is better than previous methods in terms of the OD-level efficiency measurement. The advantage of PSWE is that it is not only feasible for OD-level efficiency measurement but also for citywide efficiency measurement. Furthermore, the result indicates that the single factor may not be enough for

5. Discussion and conclusion 5.1. Implications for policy and planning 5.1.1. Road network improvement Analogous to previous studies on TNE, identified inefficient OD pairs can help planners prioritize their strategies to optimize road networks with limited resources. Specifically, the most straightforward implication is that OD pairs with high traffic flows and the abnormally low efficiency values should be improved. Fig. 6(a) reveals the necessity of promoting the road network design that connects NTAs along the

Fig. 8. OD flows of the minimized solution. 8

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Table 3 Correlation coefficients between composed factor and single factor.⁎ Pearson Correlation (All OD pairs, N = 5720)

Composed Factor (PSWE) Passenger Ratio Distance Ratio Speed Ratio

Composed Factor (PSWE)

Passenger Ratio

Distance Ratio

0.2468⁎⁎⁎ 0.3216⁎⁎⁎ 0.4570⁎⁎⁎

−0.0047⁎⁎ 0.0112⁎⁎⁎

−0.0185⁎⁎⁎

Composed Factor (PSWE)

Passenger Ratio

Distance Ratio

0.1008⁎⁎⁎ 0.2164⁎⁎⁎ 0.3955⁎⁎⁎

−0.0970⁎⁎ −0.1217⁎⁎

−0.1832⁎⁎⁎

Composed Factor (PSWE)

Passenger Ratio

Distance Ratio

−0.1694⁎⁎⁎ 0.2789⁎⁎⁎ −0.2293⁎⁎⁎

−0.1110⁎⁎ 0.0812⁎⁎

−0.2496⁎⁎⁎

Speed Ratio

Pearson Correlation of High-efficiency OD pairs (Top 10% OD pairs, N = 572)

Composed Factor (PSWE) Passenger Ratio Distance Ratio Speed Ratio

Speed Ratio

Pearson Correlation of Low-efficiency OD pairs (Bottom 10% OD pairs, N = 572)

Composed Factor (PSWE) Passenger Ratio Distance Ratio Speed Ratio ⁎ ⁎⁎

Speed Ratio

10%. 5%. 1% level.

⁎⁎⁎

taxis and subway systems both provide transportation services to the public (Yang and Gonzales, 2014; Wang and Ross, 2019). The factors that influence subway ridership may affect taxi trip generation. For instance, the tendency to take the subway versus a taxi may be affected by the accessibility of subway stations near trip origins. To examine the relationship between taxi demand and subway ridership, we employed the subway station entrance data from January 2016 from The Metropolitan Transportation Authority (MTA). Fig. 9(a) indicates the spatial distribution of subway station ridership. In addition, we map the daily pickups by taxis (see Fig. 9(b)). Particularly, the taxi pickups are the summation of pickups by Yellow Taxi and Green Taxi. Fig. 9(c) shows the relationship between taxi pickups and subway ridership (transformed to log values for the model estimation). It is clear that if subway ridership increases in NTAs, corresponding taxi pickups will increase at a significance level of 0.01. The main inconsistency is NTAs with airports (Fig. 9(b)). Fig. 9(a) shows that there is a low subway ridership in NTAs with airports since the subway system does not go directly to the airport. Then, we correlate subway ridership with NTA-level taxi efficiency presented in Fig. 7(a). It shows that in NTAs with a higher subway ridership, the taxi efficiency value is lower (see Fig. 9(d)). In other words, even though both taxis and subway systems can provide highvolume transportation services to the public, the taxi efficiency value indeed decreases in high-demand NTAs. This shows that regions providing high-volume transportation services are not necessarily efficient in terms of taxi trips. For future subway station planning, planners should consider not only the prediction of travel demand but also the reduction of efficiency.

Table 4 Comparison of performance in terms of citywide efficiency. TNE methods

Previous Methods Latora and Marchiori (2001) Nagurney and Qiang (2007) Gastner and Newman (2006) Dong et al. (2016) Proposed Method Composed Factor (PSWE) Passenger Ratio Distance Ratio Speed Ratio

TNE-based Citywide efficiency

Absolute value of the difference Distance

Time

0.885

0.041

0.158

0.905

0.021

0.038

0.863

0.063

0.080

0.911

0.015

0.032

0.934

0.008

0.009

0.642 0.863 0.765

0.284 0.063 0.161

0.301 0.080 0.178

East River. This is because the more direct routes between the OD pair, the more efficient the road network is. Although the geometric distance between NTAs along the two sides of the East River is short, there is no direct route connecting NTAs so that the drivers have to take a detour to pass the bridge. More broadly, Fig. 6(b) shows that in some cases, highly efficient taxi trips do not mean that the origin and destination must be geographically close. In this sense, planners should reconsider the conventional EC approach that simply minimizes the distance (or time). Another significant upshot of this study is that Manhattan is the most inefficient region in NYC both in AM peak hours and PM peak hours (Fig. 7(b) and (c)), even though many taxi passengers could be tourists and the trip purpose is not going to a job.

5.1.3. Taxi and ride-hailing services in NYC It is evident that most taxi trips in NYC are concentrated in Manhattan, meaning that NTAs outside Manhattan face a lack of supply. In response to that, NYC introduced Green Taxis in addition to Yellow Taxis. Recently, with the development of ride-hailing apps, Uber and Lyft have been introduced in NYC to address the supply shortage. In particular, the spatial dependency between taxis and ride-hailing

5.1.2. Taxi and Subway systems in NYC Taxi demand is closely related to subway ridership in NYC because 9

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Fig. 9. Subway ridership and its relationship with a taxi.

5.1.4. Airport and tourism industry in NYC The taxi is the major transport mode in airports for dispatching tourists because tourists prefer to take a taxi from the airport to their New York hotels or tourist attractions (La Croix et al., 1992). Additionally, it is evident that two major NTAs with high-demand taxi pickups are regions containing airports (Fig. 9(b)). Hence, the results indicate that the tourism industry in New York City has an impact on taxi demand and efficiency. Specifically, NYC had approximately 12 million more visitors in 2016 than in 2010 (NYC, 2018). In contrast, the population only increased from 8.18 million in 2010 to 8.54 million in 2016. Hence, a large percentage of taxi trips are not generated by local residents but by tourists. Therefore, the growing tourism industry in NYC raises an interesting question for local transportation planners - how should transportation planners optimize the operation of airport taxis to meet the demand of the growing tourism industry? Fig. 8 shows an ideal and most efficient pattern to maximize citywide efficiency, providing a big picture for decision makers in terms of which OD pairs would be important to focus on. Clearly, the airports are two critical locations for maximizing citywide efficiency. However, the introduced approach does not particularly consider the locations associated with tourism, such as tourist attractions, hotels, etc. Hence, to better adapt to the growing tourism industry in NYC, future research on taxi efficiency in NYC should particularly take the demand of tourists into consideration.

service has been examined (Correa et al., 2017). To show the tendency of ride-hailing services and taxis, we displayed the supply and demand of ride-hailing services and taxis from 2010 to 2018 (see Fig. 10(a) and (b)). It is clear that the growth of ridehailing trips is exponential. An interesting finding is that the curve of Yellow Taxi shows a decreasing trend since 2015 in terms of daily trips, whereas the total vehicles in supply remain stable during the same period. Thus, ride-hailing services such as Uber and Lyft do help provide more supplies for NYC in terms of vehicles and trips. However, the total number of trips and vehicles can hardly reflect the spatial correlation between conventional taxis and ride-hailing services in NYC. We therefore map the share of pickups by Yellow Taxi, Green Taxi and ridehailing service based on the 2017 data from NYC-TLC (see Fig. 10(c)–(e)). Intuitively, Fig. 10(c) shows that passengers in Manhattan are more likely to take Yellow Taxi. Fig. 10(d) indicates that Green Taxi serves more passengers in the Bronx. Part of the reason is that Green Taxi drivers are not allowed to pick up passengers from the street in southern Manhattan. Fig. 10(e) shows that there are more demands for ride-hailing services in Brooklyn. In summary, the newly introduced ride-hailing services partially address the supply shortage in NYC. However, a follow-up question for decision makers is: Will the growing number of vehicles make the city more congested in the future? Based on Fig. 10(b), if the number of ride-hailing vehicles continues to grow, the congestion and parking problems this growth brings may outweigh the benefit it generates. Hence, decision makers should balance the growth of ride-hailing vehicles and the travel demand in NYC with policy intervention.

5.2. Conclusion and limitations In summary, we proposed an improved TNE measurement, which is called PSWE, to measure taxi efficiency in NYC. The approach 10

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Fig. 10. Taxi and Ride-hailing in NYC.

However, for transportation engineers, they may be more concerned about specific road segments. In the future work, the real-time traffic volumes in road segments could be integrated with the existing framework to specify travel efficiency of each road segment.

integrates the average speed of each trip and the number of passengers with the conventional distance factor. Then, we demonstrated that Eimp derived from OD-level efficiency can be an alternative cost unit to time (or distance) in the EC framework. In this way, the bottom-up approach can be applied to the OD-level efficiency measurement and citywide efficiency measurement. We also show the patterns of minimized taxi OD flows based on different cost units: time, distance and Eimp. The maps provide practical insights into the spatial distribution of the highest citywide efficiency value, which is otherwise missed in previous studies on the same topic. We are not intending to replace the conventional cost units in the EC framework because we cannot demonstrate that the result of Eimp-based citywide efficiency outperforms that of the EC-based citywide efficiency. It is worth noting that the proposed PSWE can be generalized to other trip modes as long as related datasets can be accessed. Admittedly, despite the contributions of this study, there are some potential improvements in our future work. First, it would be more insightful to integrate the taxi ‘big data’ with the household trip survey data. If possible, passengers can be interviewed when they are taking a taxi. This could help collect much richer information like socioeconomic characteristics of passengers, so that the inefficient trips can be explained in a more explicit way. Second, the interpretation of taxi efficiency would be greatly improved if the waiting time of passengers can be estimated. Waiting time is necessary because some taxis are running without passengers, which is indeed a loss of efficiency. Although the additional information may increase the difficulty of modeling TNE, it is nevertheless believed to be worth the effort because it provides a broader scope to understand taxi efficiency. Third, the proposed approach can identify specific inefficient OD pairs, suggesting improvements of road networks within the identified OD pairs.

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