Estimating cycleway capacity and bicycle equivalent unit for electric bicycles

Transportation Research Part A 77 (2015) 225–248

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Transportation Research Part A journal homepage: www.elsevier.com/locate/tra

Estimating cycleway capacity and bicycle equivalent unit for electric bicycles Sheng Jin a,⇑, Xiaobo Qu b, Dan Zhou a, Cheng Xu c,d, Dongfang Ma a,⇑, Dianhai Wang a a

College of Civil Engineering and Architecture, Zhejiang University, Hangzhou 310058, China Griffith School of Engineering, Griffith University, Gold Coast 4222, Australia c Zhejiang Police College, Hangzhou 310053, China d College of Transportation, Jilin University, Changchun 130022, China b

a r t i c l e

i n f o

Article history: Received 18 November 2014 Received in revised form 22 March 2015 Accepted 21 April 2015 Available online 16 May 2015 Keywords: Electric bicycle Regular bicycle Capacity Bicycle equivalent unit Speed–density relationship

a b s t r a c t With the rapid increase of electric bicycles (E-bikes) in China, the heterogeneous bicycle traffic flow comprising regular bicycles and E-bikes using shared cycleway creates issues in terms of efficiency as well as safety. Capacity and bicycle equivalent units (BEUs) for E-bikes are two most important parameters for the planning, design, operation, and management of bicycle facilities. In this paper, eight traffic flow fundamental diagrams are developed for one-way cycleway capacity estimation, and a novel BEU estimation model is also proposed. Eleven datasets from different shared cycleway sections with different cycleway widths were collected in Hangzhou, China for estimation and evaluation purposes. The results indicate that, with around 70% share of E-bikes, the mean estimated capacity is 2348 bicycle/h/m. The effects on the capacity of the proportions of E-bikes, gender of cyclists, age of cyclists, and cyclists carrying things were also analyzed. The results implied that the estimated capacity is independent of a cyclist’s gender and age, but increases with the proportion of E-bikes. According to this study, the mean BEU for the E-bike is 0.66, and the converted capacities of pure regular bicycles and pure E-bikes are 1800 and 2727 bicycle/h/m, respectively. These findings can be used to propose practical countermeasures to improve the capacity of heterogeneous bicycle traffic flow on shared cycleway. Ó 2015 Elsevier Ltd. All rights reserved.

1. Introduction Non-motorized traffic trips form one of the main trip modes in developing countries, especially in Southeast Asian countries such as China, Indian, and Vietnam. The average proportion of trips using non-motorized traffic is very large in most southern Chinese cities. In recent years, because of its low-cost, convenience, and relative energy-efficiency, the electric bicycle (E-bike) has quickly become one of the main non-motorized travel modes in China (Weinert et al., 2007a, 2007b; Rose, 2012). E-bike ownership in China reached approximately 200 million in 2013 (Xinhua News, 2013). There are several reasons for the quick development of E-bikes in China. First, compared with the price of a typical car (around CNY 100,000–150,000 or $16,393–24,590), which is equivalent to four times the average annual household income of city residents, the price of an E-bike is much lower (below CNY 2000 or $328, 1/15 of the average annual household income). Second, in the southern Chinese cities of Guangzhou, Dongguan, and Shenzhen, motorcycles and mopeds are ⇑ Corresponding authors. Tel.: +86 571 88208704; fax: +86 571 88208685. E-mail addresses: [email protected] (S. Jin), [email protected] (D. Ma). http://dx.doi.org/10.1016/j.tra.2015.04.013 0965-8564/Ó 2015 Elsevier Ltd. All rights reserved.

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completely banned from certain downtown districts. There are also bans in place in small areas of Shanghai, Hangzhou, and Beijing. E-bikes represent the best alternative to motorcycles. Third, E-bikes currently are under the same classification as regular bicycles and hence operating one does not require a driver license. Fourth, according to the Electric Bicycles General Technical Requirements issued by the Standardization Administration of China (1999), ‘‘the maximum speed of Electric bicycles should not be greater than 20 km/h and the total weight of the vehicle should not exceed 40 kg’’. In reality, most E-bike riders do not follow these rules which are not easy to enforce. Last, in terms of modal share, as the public bus service has a low level of service and large delays, they have been shown to have only about a 22% share in Hangzhou (Zhang et al., 2014). Therefore, due to low prices, there being no need for a license, and inefficient public transport, the E-bike travel mode looks likely to continue for a long term. With the increasing use of E-bikes along with regular bicycles, a public bike-sharing system offering flexible short-term public bicycle access, targeting daily mobility and allowing users to access shared bikes at multiple stations (Shaheen et al., 2010) is also growing in many Chinese metropolises and tourism cities. For example, the public bike sharing system in Hangzhou had 2674 stations and 65,000 bicycles at the end of February 2012 (Zhang et al., 2014). Due to the fact that bicycles and E-bikes are under the same classification and management, heterogeneous traffic comprising E-bikes and slower-moving regular bicycles sharing non-motorized facilities is and will continue to be very common in many Chinese cities. This heterogeneous traffic brings about issues in terms of efficiency and safety. The size and speed differences between these two modes will inevitably lead to more complicated characteristics and a higher risk of traffic collisions. Due to such challenges, the planning, design, and management of shared bicycle facilities need to take into account the mixed bicycle traffic flow and new criteria and standards should be proposed accordingly. In this study, we defines ‘‘cycleway’’ as the non-motorized facilities which regular bicycles and E-bikes share. Different with ‘‘bicycle path’’ in Highway Capacity Manual (2000), where the bicycle paths are defined as exclusive off-street bicycle paths or shared off-street paths, cycleway is adjacent to highway traffic lanes, mostly one-way, has one or more bicycle lanes, and some of them separated with motorized vehicles by physical barriers. Based on the above reasons, the efficiency of bicycle facilities shared between regular bicycles and E-bikes is an important topic for analysis and improvement. Unfortunately, to the best of our knowledge, little if not none research has ever focused on cycleway capacity and the equivalent units of E-bikes, especially under conditions of heterogeneous bicycle traffic flow. Accordingly, in this paper, we focus on estimating the capacity of a shared one-way cycleway under heterogeneous bicycle traffic flow, and the bicycle equivalent unit (BEU) for E-bikes. These two parameters, which vary according to traffic conditions (e.g., volume, speed, proportion of E-bikes), road geometries (e.g., lane width, gradient) driver characteristics (e.g., age, gender), and weather conditions, must be considered under these different conditions. The purpose of this paper is to accurately estimate the capacity and the BEU for E-bikes, and comprehensively analyze the factors that influence them, based on a large amount of field survey data collected from Hangzhou, China. We believe that the findings offer some effective countermeasures for improving the planning and management of non-motorized vehicle facilities. The rest of the paper is organized into five sections. The next section briefly describes the development of E-bikes and reviews the literature. Section 3 explains how the field data were collected and analyzed. Section 4 proposes a method of capacity estimation and analyzes the factors that influence capacity. Section 5 presents the estimation method and the results for the BEU for E-bikes. Section 6 concludes the paper with a summary of our findings. 2. Literature review Bicycles, as an inexpensive and convenient trip mode, have become a significant mode of transportation in the past decade and are being used more widely in many developed countries, such as the United States and the countries of the European Union (Nosal and Miranda-Moreno, 2014; Ruiz and Bernabé, 2014; Fernández-Heredia et al., 2014). Though the use of bicycles in China has decreased significantly since 1995 due to the rapid motorization and expansion of urban regions (Zhang et al., 2014), with the development of E-bikes and public bike-sharing schemes, the government has been gradually realizing the potential benefits of bicycles and is proposing to plan new cycleway systems, to build bicycle corridors and to improve the level of service for bicycle facilities in many Chinese cities. Therefore, research into the efficiency and safety of bicycles and bicycling facilities has long been an important topic. 2.1. Development of bicycles and E-bikes The development of bicycles and E-bikes, which form one of the primary trip modes in developing countries, especially China, is the key pathway to understanding and researching the motorization and transformation of this travel mode. Zhang et al. (2014) examined four phases of bicycle evolution in China, from initial entry and slow growth (1900s to 1978), to rapid growth (1978–1995), to bicycle use reduction (1995–2002), and finally to policy diversification (2002 to the present). They also explored two bicycle innovations, the E-bike and public bike sharing (the shared use of a bicycle fleet), and describing their characteristics in details. Weinert et al. (2007a, 2007b) examined how and why E-bikes have developed so quickly in China, with particular focus on the key technical, economic, and political factors involved. Their case study provided important insights for policy makers in China and abroad, on how timely regulatory policy could change the purchasing choices of millions and create a new mode of transportation.

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In our opinion, research related to bicycles and E-bikes can be classified into four categories: safety, environmental impacts, traffic characteristics, and operating efficiency. In terms of bicycle safety, many researchers refer to illegal bicycling behavior, vehicle–bicycle collisions, bicycle accidents, and injuries to cyclists (Wu et al., 2012; Rasanen and Summala, 1998; Kim et al., 2007; Nordbacka et al., 2014). Bai et al. (2013) compared the risk-taking behavior of the riders of E-bikes and bicycles and their effects on safety at signalized intersections. The related risk factors of injuries caused by E-bikes and bicycle crashes were explored by Hu et al. (2014), and they proposed that age, road user category, traffic rule violations, crash mode, impact type, and vehicle type were all related to the severity of injuries caused by E-bike/bicycle crashes. In terms of environmental impacts, as E-bike use grows, leading to pollution from their batteries and emissions from their use of grid electricity, primarily generated by coal power plants, research has referred to the environmental impacts of alternative modes, compared E-bike emissions with those of alternative modes, and looked at the market potential and factors that influence E-bike adoption (Asian Development Bank, 2009; Cherry et al., 2009). In terms of bicycle traffic characteristics, bicycle travel behavior, fundamental diagrams of bicycle traffic flow (speed–flow–density relationships), and heterogeneous bicycle speed characteristics have been studied (Allen et al., 1998a,b). A statistical analysis has indicated that the mean operating speed of E-bikes is 21.86 km/h, 7.05 km/h faster, or 47.6% higher, than that of bicycles (Lin et al., 2008). In terms of operating efficiency, capacity and equivalent units are two important topics that will be summarized in details below.

2.2. Cycleway capacity Capacity is one of the most significant parameters used for highway planning, design, operation evaluation, and management. The capacity of a cycleway section can be defined similarly to the capacity of a freeway or multi-lane highway section, as proposed in the Highway Capacity Manual (HCM 2000) (Transportation Research Board, 2000). Therefore, the capacity of a cycleway section is defined as the maximum hourly rate at which bicycles can reasonably be expected to traverse a point or uniform section of a lane or roadway during a given time period under prevailing roadway, traffic, and control conditions. Related research on the cycleway capacity focuses on two aspects. One is the capacity under uninterrupted-flow conditions, which is the main research object of this paper. The other is the capacity under interrupted-flow conditions, especially the saturation flow rate or capacity of bicycles and the effect of bicycles on the motorized vehicle capacity at signalized intersections (Allen et al., 1998a, 1998b; Raksuntorn and Khan, 2003; Wang et al., 2011a, 2011b). Due to capacity rarely being observed on bicycle facilities in the United States, measures of capacity are based on sparse data, generally from Europe, Asian countries, or simulations (Transportation Research Board, 2000). The American Association of State Highway and Transportation Officials (AASHTO, 1991) recommends that separated bicycle path be 3.0 m wide, with a minimum width of 2.4 m in low-volume conditions, where a standard width for a bicycle lane is approximately 1.2 m. Meanwhile, the Ministry of Housing and Urban–Rural Development of China (MOHURD, 2012) recommends that a standard width for a bicycle lane be 1.0 m, and that a cycleway must contain two lanes and be not less than 2.5 m wide. It can be seen from the above descriptions that the criteria for the capacity of a bicycle facility in the United States and China both depend on the number of effective lanes used by bicycles. Unlike in the case of motor vehicles, cycling behavior is non-lane-based and very complicated (Jin et al., 2011a, 2011b, 2012). The total width of the bicycle facility (cycleway) is far more important than the number of effective bicycle lanes. Meanwhile, based on historical reasons, cycleway tends to come in many different widths in the downtown areas of Chinese cities. Accordingly, the analysis and comparison of capacities in different locations and traffic conditions are restricted by the different widths of cycleway. In order to remedy this shortcoming, we use bicycles/h/m as a common unit of cycleway capacity. To the best of our knowledge, Table 1 summarizes the estimated capacity results in different countries.

Table 1 Reported results for cycleway capacity.

a b

Author/organization

Country

Capacity (bicycles/h/m)

TRB (2000) NSRA (1977) MOHURD (2012)

United States Sweden China

Homburger (1976) Navin (1994) Botma (1995) Liu et al. (1993) Wei et al. (1993)

United States Canada Holland China China

Li (1995) Wei et al. (1997) Bai et al. (2010)

China China China

1333a 1250a 1600–1800a with physical separation 1400–1600a without physical separationa 2600a 4000a 3200a 1800–2100a 2549a with physical separation 2227a without physical separation 2000a 2344a with physical separation 2000–2700b

Capacity with pure regular bicycles. Capacity with pure E-bikes.

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From the table, it can be seen that the design capacities of cycleway or bicycle paths in the United States, Sweden, and China are all less than those estimated using field survey data. The capacity for a single 1 to 1.2 m bicycle lane differs greatly across different studies, which may be due to differences with respect to calibration methods, bicycle facilities, characteristics of cyclists, and travel purposes. Majority of the estimated capacity results fall between 1300 and 2700 bicycles/h/m (Allen et al., 1998a, 1998b). As described above, most of the previous research focuses on the cycleway capacity for regular bicycles. However, little research has been conducted regarding the cycleway capacity when there is a mixture of regular bicycles and E-bikes. Meanwhile, how the cycleway width, proportion of E-bikes, and characteristics of cyclists affect capacity needs to be modeled, analyzed, calibrated, and validated. 2.3. Equivalent units for bicycles or E-bikes In order to describe different types of vehicles according to a unified standard, the term passenger car equivalent (PCE) was introduced in the 1965 Highway Capacity Manual (Transportation Research Board, 1965). Since 1965, PCE values have been used directly for the estimation and calculation of volume and capacity under various traffic conditions, and the passenger car has been used as the basic vehicle for converting other types of vehicles into PCEs. Introducing the term PCE into the analysis of non-motorized vehicles, bicycles, motorcycles, and E-bikes can also be converted into PCEs. Many studies have been done calculating the PCE values for other types of motor vehicles, and the factors that influence PCEs (Elefteriadou et al., 1997; Webster and Elefteriadou, 1999; Al-Kaisy et al., 2002). However, little research has focused on the PCE for bicycles, especially in developed countries, which do not typically have saturated conditions of bicycle traffic flow for data collection. Table 2 shows the PCEs for bicycles and motorcycles and the BEUs for E-bikes and motorcycles, using field data from some East or South Asian countries that have higher proportions of bicycles and E-bikes than developed countries. From Table 2, it can be seen that the equivalent unit values vary under different traffic conditions. Chen et al. (2012) conclude that the BEUs for mopeds vary under different proportions of mopeds and traffic conditions. The results show that the BEU values tend to increase with an increase in traffic density and the proportion of mopeds, and decrease with an increase in bicycle lane width. 3. Field data collection 3.1. Site characteristics Field data collection is very important for the estimation of cycleway capacity and BEUs. The data quality determines the estimation results and whether the conclusions are correct or not. In this paper, field surveys were designed for collecting characteristics of cyclists (e.g. age, gender) for regular bicycles and E-bikes, and heterogeneous traffic flow parameters (e.g. volume, speed, density, and bicycle type). Eleven cycleway sections from nine roads in Hangzhou, China, a city that is a very famous and beautiful tourist destination, with a population of 8.84 million as of 2013, were selected for the data collection. In China, the cycleway is mostly located on both sides of the road. Therefore, every cycleway used for data collection in this paper was one-way. The cycleway sections are located in the downtown area of Hangzhou, as shown in Fig. 1.

Table 2 Reported results of equivalent units for bicycles or E-bikes. Authors

Location

Passenger car equivalent units (PCEUs) for bicycles or motorcycles CRITEMEB (1998) China Wang et al. (2008) Tianjin & Shenyang, China

Cao and Sano (2012)

Hanoi, Vietnam

Bicycle equivalent units (BEUs) for E-bikes or motorcycles Cao and Sano (2012) Hanoi, Vietnam Chen et al. (2012)a Shanghai, China

Ye et al. (2012) a

Nanjing, China

Equivalent units 0.20 0.28 0.33 0.24 0.22 0.41 0.29

For For For For For For For

bicycles in any situation interrupted through bicycles at intersections interrupted left-turning bicycles at intersections uninterrupted bicycles without physical separation uninterrupted bicycles with physical separation uninterrupted bicycles without physical separation uninterrupted motorcycles without physical separation

0.71 0.64 0.69 0.78 0.88 0.88 0.74 0.96 1.00 1.23

For For For For For For For For For For

motorcycles without physical separation mopeds (percentage between 0.25 and 0.5) mopeds (percentage between 0.5 and 0.75) mopeds (percentage between 0.25 and 0.5) mopeds (percentage between 0.5 and 0.75) mopeds (percentage between 0.75 and 1.0) mopeds (percentage between 0.25 and 0.5) mopeds (percentage between 0.5 and 0.75) mopeds (percentage between 0.75 and 1.0) E-bikes with physical separation

The equivalent unit values proposed above are the means of four survey locations.

under under under under under under under under

free flow free flow stable flow stable flow stable flow forced flow forced flow forced flow

S. Jin et al. / Transportation Research Part A 77 (2015) 225–248

229

Fig. 1. Field survey locations.

All of the sites are located in the middle of road links, away from intersections, so as to minimize the effects of traffic signals and pedestrians. All of the cycleway have zero gradient and are separated from the motorized vehicle lanes by physical barriers. Hence, bicycles are not interrupted by pedestrians or motorized vehicles. In this regard, adjustment factors for lateral motorized vehicles, pedestrians, and traffic signals can be neglected in estimating and analyzing the cycleway capacity. Due to the reconstruction of old cycleway and differences in road planning and design standards, the cycleway in Hangzhou cover a wide range of widths, which provides a chance to analyze the effect of width on the cycleway capacity. 3.2. Video data collection One camera was set up on the side of the cycleway to take videos to collect data on the bicycles’ and E-bikes’ operating behavior (see Fig. 2). Cameras were carefully placed so that the cyclists would be unaware they were being observed. The survey days were sunny, with no occurrence of crashes, and poor weather conditions (such as rain and extreme temperatures) were avoided. The bicycle data collection was conducted on weekdays during peak and off-peak hours (i.e., 7:00– 9:00 a.m., 11:00 a.m.–1:00 p.m., and 4:30–6:30 p.m.). The traffic volume is high during morning and evening peak hours on weekdays at all the eleven sites. Both over-saturated and under-saturated flows of a mixture of regular bicycles and E-bikes were observed during the survey periods. White lines were used to mark the detection area (‘‘virtual detector’’). Cameras were set so as to capture details of the cyclists’ behavior, especially their head positions and bicycle movements. Using video-processing technology, we were able to obtain the moment when a bicycle crossed the marked white lines. Then, the traffic flow parameters of the heterogeneous bicycle (such as volume, speed, and density) could be calculated automatically. Table 3 shows the definitions of the other variables. For every bicycle, these variables were coded manually. In Table 3, gender and age are easy to understand. ‘‘Bicycle type’’ consists of three categories: regular bicycle, bicycle-style E-bike (BSEB) and scooter-style E-bike (SSEB). More information about the two types of E-bikes, BSEB and SSEB, can be found in related references (e.g. Zhang et al., 2014). ‘‘Carrying something’’ means that the cyclist was carrying something (such as a person or other objects) beyond the size of his/her bicycle or E-bike, affecting other cyclists. Though it is illegal for cyclists to carry things in China, our survey data also show that around 11% of the cyclists were carrying something, which could have a negative influence on the cycleway capacity.

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(1) Jiaogong Road A

(2) Jiaogong Road B

(3) Hedong Road

(4) Hushu Road

(5) Wensan Road

(6) Xueyuan Road

(7) Wener Road

(8) Dongxin Road

(9) Tianmushan Road A

(10) Tianmushan Road B

(11) Moganshan Road

Fig. 2. Photos of the camera view of the eleven sites.

Table 3 Definitions of variables. Variables

Descriptions

Bicycle type Gender Age Carrying something

Bicycle: 1, bicycle-style E-bike (BSEB): 2, scooter-style E-bike (SSEB): 3 Male: 1, female: 0 Young: <40, middle-aged: [40, 60], elderly > 60 Person: 1, luggage: 2

3.3. Data analysis 3.3.1. Data characteristics The sample data characteristics of these eleven sites are listed in Table 4. There were nearly 40,000 observations (the mean across all sites was about 3600) collected for analysis and calibration. From the table, it can be seen that the widths of the eleven cycleway sections vary from 2.27 to 4.60 m. Based on the definition of 1–1.2 m per bicycle lane in China and other countries, the widest cycleway section (Moganshan Road) includes about four lanes in a single direction. The large variety of cycleway widths provides us with the chance to analyze the effect of road characteristics on capacity, which has never been considered in previous studies. The proportions of different bicycle types and the characteristics of the cyclists in each sub-group are presented in Table 4. The overall proportion of E-bikes (including BSEBs and SSEBs) is more than half (70.1%), and varies across sites from 56.3% to 87.2%. The results imply that E-bikes are one of the most important travel modes for commuters in Hangzhou. Much higher proportions of SSEBs were observed than BSEBs (53.7% vs. 16.4%). This is likely due to SSEBs having a larger battery capacity, more load, higher speeds, and better stability than BSEBs. In addition, the proportion of male cyclists was found to be more than that of females (64.6% vs. 35.4%), and the proportion of young cyclists was greater than those of the other two age groups (67.3% vs. 26.5% (middle-aged) and 6.2% (elderly)). The higher proportions of male and young cyclists are probably due to E-bikes being used at peak times for work purposes and because the income levels of cyclists are typically lower, respectively. Due to the low service level of public transport in

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S. Jin et al. / Transportation Research Part A 77 (2015) 225–248 Table 4 Statistical description of field survey data. Bicycle typea

Genderb

Age groupc

Carrying somethingd

2943

RB BS SS

31.4% 18.3% 50.3%

M F

63.8% 36.2%

Y M E

80.3% 15.4% 4.3%

P O N

8.7% 4.2% 87.1%

2.43

2944

RB BS SS

32.5% 17.0% 50.5%

M F

64.1% 35.9%

Y M E

66.4% 29.4% 4.2%

P O N

8.5% 4.9% 86.6%

HD

2.76

2176

RB BS SS

40.9% 13.8% 45.3%

M F

58.3% 41.7%

Y M E

52.9% 28.5% 18.6%

P O N

5.1% 6.2% 88.7%

Hushu Road

HS

2.93

3604

RB BS SS

29.7% 16.1% 54.2%

M F

59.7% 40.3%

Y M E

62.2% 30.4% 7.4%

P O N

3.5% 2.3% 94.2%

Wensan Road

WS

3.01

3252

RB BS SS

43.7% 18.8% 37.5%

M F

66.3% 33.7%

Y M E

75.6% 18.5% 5.9%

P O N

7.5% 3.5% 89.0%

Xueyuan Road

XY

3.45

2571

RB BS SS

33.7% 19.1% 47.2%

M F

66.2% 33.8%

Y M E

59.5% 33.1% 7.4%

P O N

8.9% 2.7% 88.4%

Wener Road

WE

3.52

2885

RB BS SS

41.3% 12.8% 45.9%

M F

66.1% 33.9%

Y M E

71.3% 25.1% 3.6%

P O N

2.9% 3.3% 93.9%

Dongxin Road

DX

3.65

3364

RB BS SS

22.9% 18.2% 58.9%

M F

58.8% 41.2%

Y M E

67.2% 28.2% 4.6%

P O N

9.1% 2.4% 88.5%

Tianmushan Road A

TMS-A

3.97

2222

RB BS SS

26.1% 13.9% 60.0%

M F

80.0% 20.0%

Y M E

69.8% 24.8% 5.4%

P O N

2.2% 8.9% 89.0%

Tianmushan Road B

TMS-B

4.50

4704

RB BS SS

31.4% 16.2% 52.4%

M F

68.2% 31.8%

Y M E

71.8% 20.0% 8.2%

P O N

2.6% 5.7% 91.8%

Moganshan Road

MGS

4.60

9155

RB BS SS

19.2% 15.9% 64.9%

M F

63.4% 36.6%

Y M E

63.6% 31.8% 4.6%

P O N

8.3% 5.3% 86.4%

Overall

–

–

39,820

RB BS SS

29.9% 16.4% 53.7%

M F

64.6% 35.4%

Y M E

67.3% 26.5% 6.2%

P O N

6.4% 4.5% 89.1%

Survey site

Abbr.

Cycleway width (m)

Jiaogong Road A

JG-A

2.27

Jiaogong Road B

JG-B

Hedong Road

Sample size

a

Bicycle type is divided into three categories: RB for regular bicycles, BS for bicycle-style E-bikes, and SS for scooter-style E-bikes. M indicates male and F female cyclists. c Age group is divided into three categories: Y indicates young (<40), M middle-aged (40–60), and E elderly (>60) cyclists. Due to the small proportion of teenagers (<20, less than 3%), the young group includes teenagers. d Carrying something is divided into three categories: P indicates carrying a person, O carrying one or more objects, and N carrying nothing. b

Hangzhou, and the fact that only one subway line is in operation, more people choose E-bikes, which are more convenient and inexpensive than other travel modes. Another interesting result is that the proportion of cyclists carrying things is large, averaging up to 10.9%, although this is illegal in China and will increase the number of bicycle-related accidents. Due to the high power of E-bikes, some will be used for freight, or for picking children up from school, which could have a large lateral effect on other bicycles and decrease cycleway capacity.

3.3.2. Descriptive statistics (1) Bicycle sizes The sizes of different types of bicycles greatly influence the parameters that in turn affect heterogeneous bicycle traffic flow, such as speed, density, and capacity. Some bicycle parks in the downtown areas of Hangzhou near to the above sites were surveyed, resulting in a total sample of 522 bicycles including 124 RBs, 156 BSEBs, and 242 SSEBs. The statistical results for their width and length are shown in Table 5. Based on the statistical results, there is no significant difference in width between BSEBs and SSEBs (65.2 cm vs. 68.5 cm), but a large difference in width between SSEBs and RBs (57.2 cm vs. 68.5 cm). Bicycle length also differs by bicycle type, with

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Table 5 External sizes of the three bicycle types. Bicycle type

RB BSEB SSEB a

Sample size

124 156 242

Bicycle width (cm)

Bicycle length (m)

Mean

SDa

Mean

SD

57.2 65.2 68.5

6.1 6.5 7.7

1.71 1.68 1.82

0.10 0.09 0.11

SD = Standard deviation.

the SSEBs longer than the BSESs and RBs (1.82 m vs. 1.68 m and 1.71 m). Their larger sizes mean that SSEBs occupy more space on the cycleway. Therefore, we conjecture that the type of bicycle may influence the characteristics of bicycle traffic flow. (2) Bicycle speed Speed is an important traffic parameter for capacity and BEU estimation. Fig. 3 presents the means and standard deviations of bicycles in different subcategories. It can be seen that (a) the average speeds of RBs, BSEBs, and SSEBs across all sites are 13.48, 16.48, and 17.22 km/h, respectively, with a large difference between regular bicycles and E-bikes; (b) the standard deviations of the speeds of E-bikes are larger than those of regular bicycles; (c) male cyclists exhibit higher speeds than females (16.33 vs. 15.11 km/h); (d) the average speeds of different age groups are less significantly different (young: 15.90 km/h; middle-aged: 16.29 km/h; elderly: 14.64 km/h); (e) cyclists exhibit approximately similar average speeds whether or not they are carrying something (15.96 vs. 15.91 km/h). In order to compare the average speeds across subcategories, a T-test was conducted to determine whether there were significant differences between two different subcategories. Table 6 shows the T-test results for different factors. Bicycle type was found to be significantly associated with average speed. The average speeds of the BSEBs and SSEBs are significantly different from those of the RBs, but the speed differences between the BSEBs and SSEBs are not significant at sites 1, 2, 4, and 5. It can easily be seen that speed is related to gender, and that the average speed values of the male cyclists are higher than those of the females. Age is also found to be significantly associated with average speed. The average speed values of elderly cyclists are significantly different to those of young or middle-aged cyclists. This is in line with the general fact that female and elderly cyclists act more cautiously than male and young or middle-aged cyclists, as shown by other studies (Bernhoft and Carstensen, 2008; Wang et al., 2015). The T-test results for the speed difference between cyclists who carrying things and those who not show that this behavior has less influence on average speed (only three sites show significant differences). The large dynamic performance of E-bikes may be part of the reason for the high speed of cyclists carrying extra items. 4. Estimation of cycleway capacity 4.1. Methodology Highway capacity estimation is of great significance for highway operation and management. There are two main ways to estimate capacity. One is to collect the time headway between vehicles in saturated conditions. Then, the capacity is the reciprocal of the saturated time headway. The other method is to calibrate a relationship (also known as the fundamental diagram of traffic flow) between the three traffic flow variables: speed, volume, and density (Rakha and Crowther, 2002; Yao et al., 2009; Zhou et al., 2015). Typically, speed–density relationship models are considered in the calibration process and only a single-regime function is developed for this calibration. Then, the density–volume relationship can be obtained using the fundamental formula q = kv. In this approach, the maximum point of the density–volume relationship function is estimated as the capacity. Due to the staggered driving behavior of bicycle traffic flow, it is almost impossible to define the time headway between two consecutive bicycles. Meanwhile, several researchers have demonstrated that bicycle traffic flow presents similar volume–speed–density relationships to vehicle traffic flow (Gould and Karner, 2009; Zhang et al., 2013). Therefore, in this paper, we use the second method to estimate the capacity of the shared bicycle facility. The main process is to select an appropriate speed–density relationship model. Many such models have been proposed in the last eighty years, beginning with Greenshields’ linear model (Greenshields, 1935). Every model has its advantages and disadvantages, making it difficult to choose the most appropriate speed–density model to fit heterogeneous bicycle traffic flow. In order to estimate the capacity accurately and comprehensively, eight well-known speed–density relationship models were chosen. Details of the models are shown in Table 7, in which v and k are the speed and density of a mixture of bicycle types in a given time interval, vf is the free-flow speed, kj is the jam density, vm and km are the speed-at-capacity and density-at-capacity, vb is the average travel speed under stop and go conditions, n and m are parameters to be calibrated, h1 is a scale parameter describing how the curve is stretched out over the whole density range, and h2 is a parameter that controls the lopsidedness of the curve. For more information about these models, refer to the references shown in Table 7. Existing single-regime speed–density models usually calibrated by the least square method (LSM). Recently, a weighted least square method (WLSM) also proposed for improving LSM (Qu et al., 2015). In Table 7, most of the formulae are

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(a) Speeds under different bicycle types

(b) Speeds under different cyclist’s genders

(c) Speeds under different cyclist’s age groups Fig. 3. Statistical results for bicycle speeds under different subcategories.

nonlinear, and the traditional method of least squares cannot be used in parameter calibration directly. Therefore, a nonlinear least squares fitting method (Levenberg–Marquardt, LM) is proposed for calibrating the model parameters. The LM method is the most widely used nonlinear least squares algorithm, and combines the advantages of the gradient method and Newton’s method. When k is small, the step is equal to Newton’s method step; when k is large, the step is equal to the step of the gradient method (Nocedal and Wright, 2006).

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(d) Speeds according to whether carrying something Fig. 3 (continued)

Table 6 T-test results for speed according to different subcategories. Sites

JG-A JG-B HD HS WS XY WE DX TMS-A TMS-B MGS

Bicycle type

Gender

Age

SSEB vs. BSEB

SSEB vs. RB

BSEB vs. RB

Male vs. female

Young vs. middle-aged

Young vs. elderly

Middle-aged vs. elderly

Carrying vs. not

Carrying

H

P-value

H

P-value

H

P-value

H

P-value

H

P-value

H

P-value

H

P-value

H

P-value

0 0 1 0 0 1 1 1 1 1 1

0.865 0.682 0.012 0.054 0.608 0.003 0.002 0.011 0.010 0.001 0.004

1 1 1 1 1 1 1 1 1 1 1

<0.001 <0.001 <0.001 <0.001 <0.001 <0.001 <0.001 <0.001 <0.001 <0.001 <0.001

1 1 1 1 1 1 1 1 1 1 1

<0.001 <0.001 <0.001 <0.001 <0.001 <0.001 <0.001 <0.001 <0.001 <0.001 <0.001

1 1 1 1 1 1 1 1 1 1 1

<0.001 <0.001 <0.001 <0.001 <0.001 <0.001 <0.001 <0.001 <0.001 <0.001 <0.001

0 0 1 1 1 1 1 0 0 1 0

0.717 0.112 0.018 0.001 0.001 0.001 0.029 0.437 0.132 0.002 0.094

1 1 1 0 1 1 1 1 1 1 1

0.049 0.043 0.046 0.854 0.007 0.003 0.004 0.001 0.002 0.001 0.011

1 1 1 1 1 1 1 1 1 1 1

0.041 0.040 0.001 0.049 0.002 0.002 0.012 0.003 0.001 0.002 0.001

0 1 0 0 1 0 0 0 1 0 0

0.681 0.003 0.882 0.132 0.001 0.145 0.242 0.148 0.028 0.314 0.590

Table 7 Single-regime speed–density models proposed for capacity estimation. Name

Abbreviation

Function

Parameters

Greenshields (1935)

GS

Greenberg (1959)

GB

Underwood (1961)

UW

vf , k j vm, kj vf , k m vf , k j vf , k m vf, kj, n

Newell (1961)

NL

Northwestern (Drake and May, 1967)

NW

Pipes-Munjal (Pipes, 1967)

PM

v ¼ v f ð1  k=kj Þ v ¼ v m log kj =k v ¼ v f expðk=km Þ n h io v ¼ v f 1  exp  vk ð1k  k1 Þ h i v ¼ v f exp  12 ðk=km Þ2   v ¼ v f 1  ðk=kj Þn

MacNicholas (2008)

MN

v ¼ vf

Logistic (Wang et al., 2011a, 2011b)

f



n

n

kj k knj þmkn

j



vf, kj, n, m

v f v b

v ¼ v b þ f1þexp ½ðkk

LG

m Þ=h1 g

h2

vf, vb, km, h1, h2

For equation x = f(p), given f() and observation vector x, the main steps of the LM algorithm are as follows:

e0 ¼ kx  f ðp0 Þk, where k :¼ 0; k0 ¼ 103 ; m ¼ 10. þ kk I, then establish the equation N k dk ¼ J Tk ek .

Step 1: Set initial value p0 and stop control constant e, and calculate J Tk J k

Step 2: Calculate the Jacobi Matrix Jk, and N k ¼ Step 3: Solve the above equation for dk . r If kx  f ðpk þ dk Þk < ek , then pkþ1 ¼ pk þ dk , else if kdk k < e, stop iteration, output; else kkþ1 ¼ kk =m, return to Step 2. s If kx  f ðpk þ dk Þk P ek , then kkþ1 ¼ mkk , solve the function again and get dk , return to Step 1.

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Using these three steps, we can complete the calibration and obtain the parameters that minimize the model error. 4.2. Results The raw bicycle traffic flow data needs to be calculated before the capacity can be estimated. Based on a simple calculation, we can obtain the bicycle traffic parameters in one time interval. To estimate the cycleway capacity, traffic volume of each sample is calculated over 15 s and converted into an equivalent rate of flow in bicycles per hour. Therefore, we obtain the vector Xi = [q(i), k(i), u(i), pe(i), pm(i), py(i), pc(i)], where q(i), k(i), and u(i) are the volume per meter (bicycles/h/m), average speed (km/h), and density (bicycles/km/m) in the ith time interval, respectively; pe(i), pm(i), py(i), and pc(i) are the proportions of E-bikes, male cyclists, young cyclists, and cyclists carrying something out of all bicycles in the ith time interval, respectively. Because BSEBs have similar sizes and speeds to SSEBs, and occur in low proportions, we do not distinguish between these two types of E-bike in our capacity estimation. The proportion of E-bikes thus includes both BSEBs and SSEBs. Because the total width of the bicycle facility is far more important than the number of effective bicycle lanes, in order to compare the capacity at different sites, we use bicycle/h/m as the standard unit for describing the volume or capacity of a cycleway. Fig. 4 depicts the results obtained from fitting the field data from all of eleven survey sites, using the eight speed–density relationship models. They show the speed–density and flow–density relationships. Gray circles indicate measured field data points, and the different colored lines represent the eight model curves obtained using the least-squares fitting algorithm. As can be seen from the figures, the eight different models fit the measured field data very well. Table 8 presents the calibrated model parameters, fitting errors, and estimated capacities. Free flow speed is the key parameter for the proposed eight speed–density relationship models. It can be seen that the average free flow speed is about 20 km/h, which is close to the speed limit for E-bikes in China (Standardization Administration of China, 2012). The results of the calibrated parameters exhibit a small standard deviation, varying over a small range for different survey sites and fitting models. The relative fitting errors of the eight speed–density models vary from 10.8% to 34.6%, and the mean is 20.1%. Except for the Greenberg model with a relative error of 27.2%, all of the speed–density models have fitting errors close to 20%. From the results of the calibrated parameters and errors, there is no evidence to suggest which speed–density model has the most effective and stable performance and should be used for capacity estimation. Therefore, in this paper, we present all of the estimated results from the eight models and use the mean of the estimated results as the final estimated capacity of the shared cycleway. From Table 8, it can be seen that the estimated capacity values vary from 1606 to 3023 bicycles/h/m under different datasets and models, averaging at 2348 bicycles/h/m with an approximate average proportion of E-bikes of 70%. Compared with the recommended cycleway capacities, of 1300 bicycles/h/m in the United States (Transportation Research Board, 2000) and 1600–1800 bicycles/h/m in China (MOHURD, 2012), the estimated capacities from the field data are higher. We conjecture that the difference is due to three reasons: (a) cyclists’ urgent commuting requirement at peak hours, (b) the impact of larger proportion of E-bikes with higher speeds, and (c) the larger proportion of young cyclists with better cycling skills. 4.3. Discussions For further analysis, the effects of the time interval, cycleway width, bicycle type, and characteristics of the cyclists on the estimated cycleway capacity were discussed. 4.3.1. Sampling time interval The time interval is a significant parameter in data collection. Different time intervals will lead to different estimation results. The HCM (Transportation Research Board, 2000) suggests that the analysis period should typically be 15 min for bicycle planning and design procedures and policies, and agency resources, which has been established similarly to the vehicular analysis period. However, little research has used the 15 min time interval to analyze bicycles or motorcycles (Cao and Sano, 2012). There are several reasons for this. One is that 15 min is too long for bicycle capacity estimation, and bicycle traffic flow cannot be observed under continuous saturated conditions over a 15 min interval. Another reason is that it is impossible to collect bicycle traffic data during 15 min that include a wide range of proportions of E-bikes, male cyclists and young cyclists so as to calibrate and validate the effects of these proportions. Furthermore, it is easy to obtain bicycle traffic parameters in 15 min by combining traffic parameters for 15 s. Fig. 5 shows the estimated capacities under different sampling time intervals from 8 to 30 s. Fig. 5(a) and (b) corresponds to Jiaogong Road A and Hushu Road, respectively. The figures show that all of the estimated capacities under different density–speed relationships decrease linearly with the increase of the time interval, and the correlation coefficients of the linear regression models are larger than 0.9. Therefore, the sampling time interval of the field survey data has a great effect on the estimated capacity results. Unfortunately, little research has discussed how to choose an appropriate sampling time interval for the collection of traffic parameters (volume, speed, and density). Based on the experiential observation of bicycle traffic flow from the videos and the variations of the fitted curves seen in Fig. 5, we have found that saturated conditions of bicycle traffic flow are rarely observed when the sampling time interval

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(a) Site 1

(b) Site 2

(c) Site 3

(d) Site 4 Fig. 4. Field data and fitted curves for speed–density and flow–density relationships.

S. Jin et al. / Transportation Research Part A 77 (2015) 225–248

(e) Site 5

(f) Site 6

(g) Site 7

(h) Site 8 Fig. 4 (continued)

237

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(i) Site 9

(g) Site 10

(k) Site 11 Fig. 4 (continued)

exceeds 20 s, and the variations in the estimated capacity values in Fig. 5 are smooth with time intervals from 10 to 20 s. Therefore, for the sake of simplicity, we have used 15 s as the time interval for capacity estimation in this paper. Further research will focus on how to determine the optimal sampling time interval for bicycle capacity estimation.

4.3.2. Cycleway width For bicycle capacity estimation, the cycleway width is of significance and needs to be discussed. Differences in the cycleway widths may limit comparisons of capacity across different sites. Lan and Chang (2003) developed traffic volume–density relationships for motorcycles in the mixed traffic flow conditions with passenger cars in 2.5-m and 3.7-m lanes. Wang et al. (2008) calculated bicycle conversion factors using datasets from six cycleway sections, three without physical separation (cycleway widths refer to 1.8 m, 2.8 m, and 2.8 m, respectively) and three with (cycleway widths refer to 5.0 m, 6.1 m, and 7.0 m, respectively). Cao and Sano (2012) collected three types of road segments, with two lanes, three lanes, and four lanes (7 m, 10.5 m, and 14 m), for road capacity estimations for mixed vehicle types with motorcycles. Chen et al. (2012) collected three cycleway datasets (2.2 m, 3.0 m, and 3.5 m) to calculate BEUs for mopeds. Most of the previous research used two or three datasets to calibrate and validate their models. However, comparisons of different datasets with different cycleway widths and the effects of cycleway widths have not been mentioned in previous research, which may be due to the lack of variety of datasets collected from different types of cycleway.

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S. Jin et al. / Transportation Research Part A 77 (2015) 225–248 Table 8 Results of parameter calibration, fitting error, and estimated capacity. Sites JG-A

Overall JG-B

HD

HS

WS

XY

WE

DX

TMS-A

TMS-B

MGS

Mean

SD

Estimated free flow speed (km/h) GS 18.0 18.0 GB – – UW 18.3 18.5 NL 17.0 17.2 NW 17.1 17.3 PM 18.0 20.7 MN 17.9 20.7 LG 17.9 19.6 Overall 17.7 18.9

17.1 – 17.2 16.6 16.6 17.3 17.3 17.3 17.1

18.5 – 18.7 17.9 18.0 18.3 18.1 18.0 18.2

19.6 – 19.9 19.2 19.2 19.7 19.4 19.4 19.5

19.8 – 19.8 19.4 19.5 19.5 19.5 19.5 19.6

22.5 – 22.9 21.6 21.6 26.0 26.0 23.3 23.4

20.6 – 20.7 20.0 20.1 20.4 20.2 20.1 20.3

19.3 – 19.3 19.0 19.0 19.1 19.0 19.0 19.1

21.5 – 21.7 20.9 20.9 21.4 21.3 21.2 21.3

22.7 – 23.0 21.4 21.6 23.4 23.4 23.0 22.6

19.8 – 20.0 19.1 19.2 20.3 20.3 19.8 19.8

1.9 – 1.9 1.8 1.8 2.5 2.6 2.0 2.1

Fitting errors GS 17.0% GB 25.6% UW 17.8% NL 17.2% NW 17.2% PM 17.0% MN 17.0% LG 17.6% Overall 18.3%

19.8% 28.9% 19.8% 20.2% 20.0% 19.9% 19.9% 19.7% 21.0%

19.0% 27.5% 19.8% 18.6% 18.9% 19.1% 18.6% 18.6% 20.0%

26.5% 33.6% 25.7% 25.3% 26.4% 26.2% 25.2% 24.6% 26.7%

16.1% 27.8% 16.2% 15.9% 15.9% 15.9% 15.9% 15.9% 17.5%

18.1% 23.4% 18.1% 18.5% 18.4% 18.6% 18.6% 18.3% 19.0%

24.4% 34.6% 24.9% 24.2% 24.4% 24.4% 24.2% 24.4% 25.7%

20.0% 28.6% 20.1% 19.8% 19.8% 19.9% 19.8% 19.8% 21.0%

16.0% 27.4% 16.1% 16.5% 16.4% 16.1% 16.0% 15.9% 17.6%

10.8% 16.6% 10.8% 11.1% 10.9% 10.8% 10.8% 10.8% 11.6%

19.0% 27.2% 19.1% 19.1% 19.1% 19.2% 19.0% 18.9% 20.1%

4.3% 4.8% 4.1% 4.1% 4.2% 4.3% 4.2% 4.0% 4.3%

Estimated capacity (bicycles/h/m) GS 2445 2707 2364 GB 2422 2268 1969 UW 2678 2602 2842 NL 2251 2606 2091 NW 2369 2796 2146 PM 2444 1979 2364 MN 2429 1979 2364 LG 2638 2947 2821 Overall 2459 2486 2370

2379 2163 2631 2190 2290 2382 2260 2261 2320

2358 2145 2241 1914 2119 2322 2028 2041 2146

2977 2230 2373 2161 2241 2266 2234 2777 2407

1786 2577 1889 1606 1714 2067 2067 2543 2031

2585 2295 2994 2317 2407 2546 2446 2595 2523

2527 2096 2369 1924 1935 1999 2021 2322 2149

2332 2478 2841 1951 2075 2261 2292 2556 2348

2827 2268 2426 2423 2532 3023 3023 2208 2591

2481 2265 2535 2130 2239 2332 2286 2519 2348

312 176 316 276 294 292 296 282 281

21.6% 25.5% 21.1% 22.9% 22.2% 23.1% 23.1% 22.0% 22.7%

Fortunately, eleven cycleway sections with different widths (ranging from 2.27 to 4.6 m) were selected for the capacity estimation in this paper. Fig. 6 presents the relationships between the total cycleway capacities estimated by the eight proposed speed–density relationships and the cycleway widths. The results show that the total capacity increases with the width of the shared cycleway and the relationship is linear. The correlation coefficients from the linear regression results of the eight models are all more than 0.7. Similar conclusions were presented by the HCM (Transportation Research Board, 2000) and Chandra and Kumar (2003). In order to compare the capacities at different sites, the total cycleway capacity needs to be converted into the capacity per meter. For statistical analysis purposes, Table 9 shows the means and standard deviations of the capacity per meter from the eleven datasets, the linear regression models between the cycleway capacity per meter (Cb) and the cycleway width (w), the correlation coefficient (R2), and the P-values. The P-values were calculated to test the hypothesis of no correlation between the cycleway widths and their capacities. Each P-value is the probability of getting a correlation as large as the observed value by random chance, when the true correlation is zero. If the P-value is small, say less than 0.05, then the correlation is significant. From Table 9, it can be seen that the R2 is small and all of the P-values are larger than 0.05. The results show that there is no significant correlation between the cycleway capacity per meter and the cycleway width. Therefore, the capacity of cycleway per meter is independent of its width, and we can compare the estimated capacities at different sites. In the following description, the cycleway capacity is defined in bicycles/h/m, which makes comparison easier. 4.3.3. Characteristics of cyclists Cycleway capacity may vary with factors such as bicycle types, characteristics of cyclists (e.g., gender, age, income, and character), or weather conditions, which have been demonstrated to affect the motorized vehicle capacities of highway. Much research has focused on the effects of vehicle types, weather conditions, and driver characteristics on highway capacity (Transportation Research Board, 2000). In this study, four factors are believed to affect estimated capacity, the proportions of E-bikes, male cyclists, young cyclists, and cyclists who carrying something. Bicycle traffic flow data were divided into two groups to analyze each factors (pe, pm, py, or pc). One group refers to the sample data in which the proportion of the factor was less than the mean, and in the other group the proportion was more than the mean. The means used to divide the sample were calculated from Table 4: 70% for pe, 65% for pm, 67% for py, and 11% for pc. Therefore, for each factor, two estimated capacities are obtained for each site using the methodology presented in Section 4.1.

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(a) Jiaogong Road A

(b) Hushu Road Fig. 5. Linear regression of time interval against estimated capacity.

Fig. 7 shows the results for the estimated capacity using the four different factors for classification, where (a), (b), (c), and (d) represent the capacity differences based on different proportions of E-bikes, male cyclists, young cyclists, and cyclists who carrying something, respectively. From the figure, it can be seen that the estimated capacities vary with different factors and sites. The results identify several significant factors in capacity estimation. T-test was used to study quantitatively the influence of these four factors on the estimated cycleway capacity. The results of the T-test for the four factors are shown in Table 10. The P-values (significantly less than 0.05) and H values indicate that two factors, the proportion of E-bikes and the proportion of cyclists who carrying something, lead to statistically significant differences in the estimated capacity. However, the results fail to support the gender and age of the cyclists as having a significant effect on the estimated cycleway capacity. Estimated capacity was found to be significantly associated with the proportion of E-bikes. A higher proportion of E-bikes leads to a larger capacity. This is in line with the general fact that E-bikes have a higher free flow speed and more stable operation, as shown by other studies (Lin et al., 2008). Though the size of the E-bike is larger than that of a regular bicycle, their

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Fig. 6. Relationship between total estimated capacities and cycleway widths.

Table 9 Linear regression and correlation analysis between estimated capacity per meter and cycleway width. Model

Mean

SD

Linear regression

R2

P-value

GS GB UW NL NW PM MN LG Overall

2481 2265 2535 2130 2239 2332 2286 2519 2348

312 176 316 276 294 292 296 282 175

Cb = 39.256w + 2348.2 Cb = 47.732w + 2103.7 Cb = 35.262w + 2654 Cb = 81.754w + 2406 Cb = 103.93w + 2589.1 Cb = 125.05w + 1910.5 Cb = 157.22w + 1755.7 Cb = 139.85w + 2990.6 Cb = 1.06w + 2344.7

0.0096 0.0445 0.0075 0.0529 0.0757 0.1106 0.1703 0.1490 0.0040

0.7752 0.5343 0.8001 0.4959 0.4129 0.3180 0.2075 0.2411 0.9907

higher free flow speed may be the primary reason for the larger capacity when there are more E-bikes relative to regular bicycles. Elderly and female cyclists act more cautiously than young and male ones, as shown by other studies (Bernhoft and Carstensen, 2008), but these characteristics of the cyclists (gender and age) failed to have a significantly influence on capacity. This may be resulted from several reasons. Firstly, although there are differences in character between young and elderly or male and female cyclists, the differences in operation and speed are small under conditions where the cycleway is near to capacity. Secondly, the influence of gender on the speed of regular bicycles (male 14.3 km/h vs. female 13.0 km/h) is greater than that on the speed of E-bikes (male 17.9 km/h vs. female 17.8 km/h), and the same is true of age (regular bicycles: young 14.1 km/h vs. others 13.4 km/h; E-bikes: young 17.6 km/h vs. others 17.5 km/h). Therefore, due to the large proportion of E-bikes at the survey sites, the differences between these groups may be negligible. Thirdly, it is also possible that the lack of a significant capacity difference between different gender and age groups may be related to the relatively small numbers of female and elderly cyclists in the current study. Cyclists carrying something on their bicycles was also examined, and it was found that this behavior lowered the cycleway capacity significantly. It is easy to envisage that carrying something will lead to unstable operation of a bicycle, and have a large influence on lateral bicycles. This will provide the evidence and standard for bicycle traffic management.

5. Estimation of bicycle equivalent unit for the E-bike 5.1. Methodology The definition of the BEU is the number of bicycles that can be displaced by one E-bike running at the same road and traffic conditions. The BEU for the E-bike should be calculated by taking several factors into consideration, such as the E-bike proportion, the cycleway width, and the dynamic characteristics of the moving bicycles. Several techniques are

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Fig. 7. Estimated capacities under different influencing factors.

Table 10 Results of the T-tests for a difference in capacity under different conditions. Factor

Proportiona

Capacity mean (bicycles/h/m)

Capacity SD (bicycles/h/m)

P-value

H

Bicycle type

pe 6 70% pe > 70%

2535 2656

136 135

0.005

1

Gender

pm 6 65% pm > 65%

2413 2389

108 155

0.680

0

Age

py 6 67% py > 67%

2381 2384

103 158

0.957

0

Carrying something

pc 6 11% pc > 11%

2412 2263

129 131

0.014

1

a The proportion values used for dividing the sample data into two categories, as listed in this table, are the averages of each variable over the entire dataset, as calculated in Table 4.

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available in the literature for calculating the PCE values for different types of vehicle in a traffic stream. The typical formula that is applied for BEU or PCE conversion is as follows (Chen et al., 2012; Cao and Sano, 2012),

pBEU ¼

V RB V EB



SEB SRB

ð1Þ

where pBEU is the bicycle equivalent unit for the E-bike, V RB and V EB are the mean speeds of regular bicycles and E-bikes, respectively (km/h), and SRB and SEB are the mean effective space (length  width) taken up by regular bicycles and E-bikes, respectively (m2). The idea behind this method is that BEU conversion for E-bikes is based on the same usage of pavement, and the BEU can be calculated using the ratio of pavement occupancy for different types of bicycles. However, there are some weaknesses in this method. First, the mean effective space taken up by regular bicycles and E-bikes is very difficult to define and calculate. Different researchers have used different definitions. Second, it is difficult to determine the effective space taken up by bicycles accurately through video-processing technology. Third, complicated data processing and calculations would lead to sample numbers less than 100, and even as low as 50 (Chen et al., 2012; Cao and Sano, 2012), which would lead to a drop in estimation precision. Fourth, it is not possible to validate this method. Therefore, in order to overcome these weaknesses, we propose a novel calibration method for calculating the BEU value for E-bikes, and validate the proposed method. The bicycle capacity analysis procedures are calibrated for a specific set of ideal conditions. The most important condition is the assumption that the traffic flow contains only regular bicycles. In reality, regular bicycles and E-bikes run together on the shared cycleway. The adjustment factor for the presence of E-bikes is based on the BEU, which should be estimated under saturated conditions. It is assumed that the shared cycleway capacity in ideal conditions is a constant, which is calculated as the sum of the flow rate of regular bicycles and the converted flow rate of E-bikes using the BEU. Therefore, the BEU can be calculated as follows,

Q RB þ pBEU Q EB ¼ C RB

ð2Þ

Q RB ¼ C B ½1  pe 

ð3Þ

Q EB ¼ C B pe

ð4Þ

where QRB = the flow rate of regular bicycles under saturated conditions (RBs/h/m); QEB = the flow rate of E-bikes under saturated conditions (EBs/h/m); CRB = the cycleway capacity when there is pure regular bicycle traffic flow, which should be a constant for each site; CB = the estimated cycleway capacity with a mixture of E-bikes and regular bicycles; pe = the proportion of E-bikes in the heterogeneous bicycle traffic flow. In Eq. (2), pBEU and CRB are two unknown constants that need to be calibrated by a series of pairs (QRB, QEB) using regression analysis. Meanwhile, the values of each pair (QRB, QEB) can be obtained from Eqs. (3) and (4). In order to calibrate the BEU, different values of QRB and QEB that can be collected for different proportions of E-bikes need to be used in the linear regression model. The core of this approach is to estimate the capacity for different E-bike proportions, and obtain a series of pairs (QB, pe). The calibration and validation of the BEU using the datasets collected in Hangzhou will be described in the next subsection. 5.2. Calibration and validation In order to calibrate Eq. (2) using the linear regression model, field sample data of the bicycle traffic flow in one constant time interval were classified into several categories based on the different E-bike proportions. In this study, three sites, named Hushu Road, Tianmushan Road B, and Moganshan Road, which are with larger samples and wider ranges of E-bike proportions, were used for the calibration and validation: the Hushu Road dataset for calibration and the other two for validation. For more accurate calibration of the BEU, the proportion of E-bikes (ranging from 0 to 1) was divided into twenty equal intervals. According to the values of pe, the bicycle traffic flow data Xi were classified into the corresponding categories. After the classification of the bicycle traffic data, seven categories (refer to the intervals [0, 0.05], [0.05, 0.1], [0.1, 0.15], [0.15, 0.2], [0.85, 0.9], [0.9, 0.95], and [0.95, 1.0]) had less than 150 data points in them, which would lead to a failure for the estimation of capacity. Due to the lack of field sample data containing very low or high proportions of E-bikes, we used the other thirteen categories for the calibration and validation. The values of pe in each interval were calculated using the mean of all the pe values from the sample dataset Xi in this interval. The cycleway capacities (CB) in each interval were estimated using the method described in Section 4.1. Therefore, thirteen pairs (CB, pe) were calculated for each site, and the values of QRB and QEB were then simply obtained using Eqs. (3) and (4).

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(a) Hushu Road

(b) Tianmushan Road B

(c) Moganshan Road Fig. 8. Linear regression between the flow rate of E-bikes and the flow rate of regular bicycles under saturated conditions.

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S. Jin et al. / Transportation Research Part A 77 (2015) 225–248 Table 11 Results of linear regression models and correlation analysis for BEU. Model

Linear regression results

R2

P-value

GS GB UW NL NW PM MN LG Overall

QRB + 0.692QEB = 1885.6 QRB + 0.646QEB = 1799.3 QRB + 0.615QEB = 1765.7 QRB + 0.690QEB = 1773.1 QRB + 0.627QEB = 1711.8 QRB + 0.626QEB = 1759.8 QRB + 0.628QEB = 1761.9 QRB + 0.689QEB = 1893.4 QRB + 0.659QEB = 1802.4

0.9483 0.9801 0.8515 0.9582 0.9270 0.9217 0.9108 0.9384 0.9647

<0.001 <0.001 <0.001 <0.001 <0.001 <0.001 <0.001 <0.001 <0.001

Table 12 Performance indices for the proposed linear predicted model. Site

GS

GB

UW

NL

NW

PM

MN

LG

Overall

Tianmushan Road B

RMSE MAPE

66.7 2.4%

133.1 5.4%

115.9 4.5%

127.3 4.6%

149.9 5.4%

100.4 3.5%

74.9 2.7%

99.1 3.8%

63.4 2.1%

Moganshan Road

RMSE MAPE

205.3 8.7%

198.8 8.3%

111.6 3.8%

127.7 5.5%

126.7 4.7%

89.9 2.9%

110.7 4.0%

85.1 3.0%

78.0 3.1%

Table 13 Estimation results of the BEU for the E-bike. Site

GS

GB

UW

NL

NW

PM

MN

LG

Overall

BUE for E-bikes (pBEU)

Hushu Rd. Tianmushan Rd. B Moganshan Rd. Mean

0.692 0.664 0.645 0.667

0.646 0.695 0.639 0.660

0.615 0.647 0.636 0.633

0.690 0.624 0.665 0.660

0.627 0.672 0.651 0.650

0.626 0.673 0.650 0.650

0.628 0.623 0.692 0.648

0.689 0.634 0.644 0.656

0.659 0.661 0.667 0.662

Capacity with all RBs (CRB)

Hushu Rd. Tianmushan Rd. B Moganshan Rd. Mean

1886 1871 1687 1814

1799 1835 1672 1769

1766 1774 1808 1783

1773 1764 1663 1733

1712 1849 1694 1752

1760 1817 1806 1794

1762 1775 1847 1795

1893 1800 1830 1841

1802 1820 1767 1797

Fig. 8 shows the relationships between the flow rate of E-bikes and the flow rate of regular bicycles under saturated conditions, with Fig. 8(a), (b), and (c) referring to Hushu Road, Tianmushan Road B, and Moganshan Road, respectively. Each color of dots and line denote the relationship between the flow rates of E-bikes and regular bicycles using different speed–density relationships. The results in the figures demonstrate a very strong linear correlation. Table 11 shows the linear regression models, correlation coefficients and P-values for the dataset from Hushu Road. The correlation coefficients are all more than 0.9 except in the case of the UW model, and the P-values of all nine equations are far less than 0.05, which implies that the variables QRB and QEB have very strong linear relationships. In order to validate the proposed model, we use Eq. (5) to calculate the predicted cycleway capacity,

bB ¼ C

b RB C ^BEU Þpe 1  ð1  p

ð5Þ

where b B = the predicted cycleway capacity; C b RB = the estimated values of the bicycle capacity when there are only regular bicycles on the cycleway; C ^BEU = the BEU for E-bikes. p Using the estimated parameters from Table 11 and Eq. (5), the predicted cycleway capacities for the other two datasets, from Tianmushan Road B and Moganshan Road, were calculated. Comparing the predicted capacity with the estimated capacity, the performance of the proposed BEU calibration model could be evaluated. We employed two commonly used performance indices to evaluate the proposed BEU estimation model (e.g. Kuang et al., 2015; Jin et al., 2013). The first is the root mean square error (RMSE), and the second is the mean absolute percentage error (MAPE). These indices are given by the following equations,

RMSE ¼

rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi i2 1 XM h b C B ðjÞ  C B ðjÞ j¼1 M

ð6Þ

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MAPE ¼

   M b 1X  C B ðjÞ  C B ðjÞ   100%   M j¼1  C B ðjÞ

ð7Þ

where b B = the predicted cycleway capacity at the jth interval with the proportion of E-bikes; C C B = the estimated cycleway capacity based on field data at the jth interval with the proportion of E-bikes; M = the number of intervals of the E-bike proportion, which is thirteen in this study. Table 12 shows the RMSEs and MAPEs for the two sites. The average RMSEs of Tianmushan Road B and Moganshan Road for the overall models are 63.4 and 78.0 bicycle/h/m, respectively, and their MAPEs are 2.1% and 3.1%, respectively. The proposed model performs very well in estimating the capacity. Therefore, we can use this model to estimate the BEU. 5.3. Results and discussion According to the same linear regression processes, linear regression models of the three selected sites were calibrated, and the results for the two parameters of the regression models (pBEU and CRB) are shown in Table 13. The BEUs for the E-bike vary from 0.6 to 0.7, with a mean of 0.66. The range of cycleway capacities when there are pure regular bicycles on the cycleway is from 1660 to 1900 bicycles/h/m, with a mean of 1800 bicycles/h/m. Therefore, it is simple to see that the capacity when there are pure E-bikes on the cycleway is 1800/0.66 = 2727 bicycles/h/m, 1.5 times the capacity with pure regular bicycles. The results for the estimated BEUs imply that the operating efficiency of E-bikes is better than that of regular bicycles. With an increase in the proportion of E-bikes, the capacity of the shared cycleway will increase linearly. Compared with previous research (Cao and Sano, 2012; Chen et al., 2012; Ye et al., 2012), the BEU values for the E-bike are found to be lower in this paper, namely, there is a higher capacity on the shared cycleway, which may be due to a number of reasons. One is that the free flow speed of E-bikes is larger than that of regular bicycles (25.5 km/h vs. 18.7 km/h). A higher free flow speed means a larger capacity using the fundamental diagram approach. Another reason is that the higher proportion of SSEBs than BSEBs (53.7% vs. 16.4%) would lead to a larger free flow speed and more stable operation of the bicycles. Lastly, the previous methods only considered the operating efficiency of individual bicycles and ignored the overall characteristics of heterogeneous bicycle traffic flow. 6. Conclusions The estimation of cycleway capacity and the BEU for the E-bike are important topics, especially under heterogeneous traffic flow composed of regular bicycles and E-bikes on a shared cycleway. In this paper, we use field survey datasets from eleven cycleway sections in Hangzhou, China for estimation and calibration. The datasets cover congested and uncongested bicycle traffic conditions, different cycleway widths, and various proportions of E-bikes, male cyclists, young cyclists, and cyclists who carrying something. Eight speed–density relationships were utilized for capacity estimation, and a novel method was proposed for the BEU estimation and validation. There are several important results found in this paper. Firstly, the average proportions of E-bikes, male cyclists, and young cyclists are more than 50% at all survey sites. Also, approximately 11% of cyclists using regular bicycles or E-bikes are carrying something, which is illegal in China. Secondly, the estimation results for the capacities demonstrate the ability of the eight density–speed models to estimate capacity, and great differences in the estimated results and errors are found between different speed–density relationships. With an increase in the time interval, the estimated capacity drops linearly. The T-test results show that the cycleway width to have no influence on the estimated capacity. Thirdly, the proportions of E-bikes and cyclists who carrying something have a great influence on the cycleway capacity, while gender and age had no significant influence. Fourthly, the estimated BEU mean for the E-bike is found to be 0.66, and the estimated cycleway capacities with pure regular bicycles and pure E-bikes are found to be 1800 bicycles/h/m and 2727 bicycles/h/m, respectively. The findings and contributions of this paper are significant and useful for proposing several practical countermeasures to improve the cycleway capacity, plan and design bicycle and motorcycle facilities. This topic has been relevant for the traffic engineering not only in China but also in other countries. Further research will be conducted to develop novel techniques and methodologies for optimizing the statistical time interval of bicycle traffic data and to evaluate the level of service (LOS) for the shared cycleway under different traffic conditions with a mixture of regular bicycles and E-bikes. Acknowledgements This work was supported by the National Natural Science Foundation of China (No. 51338008, 51278454, 51208462, and 61304191), the Fundamental Research Funds for the Central Universities (2014QNA4018), the Projects in the National Science & Technology Pillar Program (2014BAG03B05), and the Key Science and Technology Innovation Team of Zhejiang Province (2013TD09). The authors thank the postgraduates of the institute of transportation engineering at Zhejiang University for their assistance in field bicycle data collection. We also want to express our sincere thanks to the Editor in

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