Dynamic Accessibility Analysis of Urban Road-To-Freeway Interchanges Based on Navigation Map Paths

sustainability

Article Dynamic Accessibility Analysis of Urban Road-to-Freeway Interchanges Based on Navigation Map Paths

Yadan Yan, Tianzhao Guo and Dongwei Wang *

School of Civil Engineering, Zhengzhou University, Zhengzhou 450001, China; [email protected] (Y.Y.); [email protected] (T.G.) * Correspondence: [email protected]

Abstract: Accessibility is important for road network planning and design, especially the accessibility of freeway entrances and exits, which reflects the convenience of travelers using freeways and the rationality of the connection between urban roads and freeways. Based on the path information of navigation map software, a new comprehensive travel impedance model to dynamically analyze the accessibility of freeway entrances and exits was proposed. The dynamic accessibility of freeway entrances and exits in Zhengzhou was studied using the proposed comprehensive impedance model, and the calculation results were analyzed. The accessibility of freeway entrances and exits is characterized by dynamic changes; the accessibility during the off-peak evening period is the highest, while that during the morning peak period and evening peak period is lower. The results of the comprehensive impedance model are roughly consistent with reality. From a location perspective, regardless of the period of time, the accessibility of freeway entrances and exits in the central and surrounding areas of Zhengzhou is always at a lower level, and during the off-peak afternoon period, the accessibility of the eastern part of the city is notably higher than that of the western part. Additionally, the accessibility of freeway entrances and exits is closely related to the traffic status of the road network and the characteristics of regional land use. The information can provide feedback for planning road networks and provide a reference for road network planning and traffic facility design.

Citation: Yan, Y.; Guo, T.; Wang, D. Keywords: accessibility; urban road-to-freeway interchange; navigation map; travel impedance Dynamic Accessibility Analysis of Urban Road-to-Freeway Interchanges Based on Navigation Map Paths. Sustainability 2021, 13, 372. 1. Introduction https://doi.org/10.3390/su13010372 Freeways are corridors of national importance that provide long-distance travel be- Received: 2 December 2020 tween cities [1]. Accessibility has been recognized as a key concept in the field of transporta- Accepted: 30 December 2020 tion [2,3] and an important indicator of transportation system performance, the foundation Published: 3 January 2021 of urban planning and road network construction [3,4]. Accessibility to an external freeway network from an urban road network is important for long-distance travel. Accessibility Publisher’s Note: MDPI stays neu- is a measure of people’s opportunities or ease of access to freeway resources they wish tral with regard to jurisdictional clai- to utilize. The national “Planning Standard for Urban Comprehensive Transport System ms in published maps and institutio- Planning” in China provides general guidelines for the accessibility of freeways and urban nal affiliations. freeways (GB/T 51328-2018) [5]. Important functional areas and major traffic distribution points in cities with a planned population of 1 million and above and cities with a planned population of 500,000 to 1 million should be able to reach a freeway or freeway network within 15 min (GB/T 51328-2018) [5]. However, specific quantitative analysis methods are Copyright: © 2021 by the authors. Li- censee MDPI, Basel, Switzerland. not given in the standard. Although a large number of studies have explored accessibility This article is an open access article from various perspectives [3], none has presented an accessibility analysis of a freeway distributed under the terms and con- network. Evaluating spatial accessibility is helpful for effectively identifying areas where it ditions of the Creative Commons At- is inconvenient to use the external freeway network and spatial barriers. tribution (CC BY) license (https:// Interchanges are essential components for providing reasonable access and mobil- creativecommons.org/licenses/by/ ity [6]. Hence, accessibility to a freeway network can be reflected by accessibility to urban 4.0/). road-to-freeway interchanges, i.e., freeway entrances and exits. For a person traveling long

Sustainability 2021, 13, 372. https://doi.org/10.3390/su13010372 https://www.mdpi.com/journal/sustainability Sustainability 2021, 13, 372 2 of 17

distances between cities, the whole travel process includes reaching the freeway entrance from an urban road, completing a fast and long drive on the freeway, and exiting the freeway to an urban road. The location of urban freeway interchanges has a considerable effect on the connection between the urban road network and the freeway network. It is critical to quickly concentrate traffic flows from urban areas and distribute them across the highway network; this is a topic for which little research has been published. Our objective is to extend the scope of research on accessibility. In addition, although considerable research has considered measurement models and methods of accessibility [3,7,8], the existing studies still have limitations. For example, actual traffic conditions that affect travel time (e.g., turn restrictions and the number of traffic lights) and people’s perceptions of factors influencing accessibility are often neglected as accessibility indicators. With the development of information technology, big data have raised not only many options for accessibility analyses but also methodological challenges due to the characteristics of these data sources [8,9]. Hence, this paper presents a dynamic accessibility analysis method of urban road-to- freeway interchanges based on navigation map path data to provide a clear understanding of the impact of the location of urban road-to-freeway interchanges. The contributions are as follows: (1) The parameters from the path data, including the travel time, travel distance and number of traffic lights, are used in the travel impedance formulation, which has the characteristics of easy access and diverse information. (2) A comprehensive impedance model is constructed and used to calculate the accessibility indicator of the urban road-to- freeway interchange. The remainder of this paper is structured as follows. Section2 presents a literature review on accessibility in transport networks. Section3 reports factors involved in travel impedance through an online survey, and Section4 proposes the accessibility analysis method. Then, Section5 conducts a case study, and Section6 concludes with a summary of the results and directions for future work.

2. Literature Review Accessibility has been widely adopted in transportation planning [3,10,11]. Several review studies have focused on transport accessibility in recent years. Páez et al. (2012) conducted a review of various commonly used measures of accessibility. A number of indicators of accessibility, defined as the potential to reach spatially dispersed opportunities, have been proposed and used to address various substantive planning and policy questions [7]. Three broad classes of indicators, including cumulative opportunities, gravity-based, and utility-based indicators, have been identified in previous typologies of accessibility measures [7,12,13]. Accessibility measures are usually composed of two components, namely opportunities and travel costs [7,14]. These two components can be deployed in a number of different ways to produce location-based indicators of accessibility, a distinction that depends to a large extent on the degree of detail available concerning the situation of the network, different modes of transportation, and inherent differences in the mobility of individuals [7]. Wee [8] proposed avenues for future research focusing on indicators to express accessibility and evaluation, including the impact of information and communications technology on accessibility; the inclusion of the robustness of the transport system in the indicators; comparing perceptions of accessibility and traditional accessibility indicators; the option value; and indicators of accessibility for goods transport, air transport, and slow transport modes [8]. Shi et al. [3] reviewed two decades of publica- tions (2000–2019) and determined the evolutionary pathway of accessibility-related studies. According to the keyword distribution and the output from a citation network analysis, current accessibility studies can be divided into two main categories: new indicator development and accessibility-based applications [3]. Rong et al. [15] classified indicators into place-based accessibility and individual-based accessibility indicators and categorized the research methods into four main types: ratio method, nearest distance method, methods based on cumulative opportunities, and methods based on spatial interaction. Certain Sustainability 2021, 13, 372 3 of 17

locations are commonly desired destinations, such as shops, schools, parks and green spaces, medical services, workplaces, and transportation facilities, including bus stops and subway stations [8,15,16]. Accessibility focuses on the importance of reaching desired destinations [16], and travel time is one of the most important factors [2,17]. As shown in Table1, most of the impedance functions consider travel time or distance separately. In addition to the travel time, people also often attach great importance to travel distance. Moreover, delays due to the number of trafﬁc lights and turn restrictions are ignored. Besides the increase in travel time, an increase in the number of trafﬁc lights on a path also increases its disutility association with the discomfort and frustration for a driver.

Table 1. Impedance functions in some existing studies.

Existing Studies Impedance Function

[2] Travel time tij n [18] −βxij Exponential distance decay function ∑ Mje j=1 [19] Travel time

[20] Network distance dij [21] Negative exponential distance decay function eα·tij

In recent years, integrating emerging sources of data, such as mobile phone data, GPS data, and navigation map data, with the current models has become a trending research area. Abundant data can easily be obtained for accessibility research. Xia et al. [4] utilized the Google Maps API to acquire travel costs at the grid level for the gravity-radiation model. Rong et al. [15] used the Internet map navigation service and GIS spatial analysis technology platform to study the spatial accessibility and equity of the medical treatment of residential buildings in the main urban area of Zhengzhou. Meire and Derudder [22] discussed some of the major strengths and limitations of a Google Maps (API)-based approach to studying accessibility in transport networks. With the development of big data technology, dynamic accessibility that captures the temporal variations of accessibility has also become an important research focus [19]. García-Albertos et al. [2] conducted a dynamic analysis of urban accessibility considering two main components, namely travel times and the attractiveness of destinations, using the Google Maps API and origin and destination (OD) travel matrices from mobile phone records. Guan et al. [19] presented a dynamic modal accessibility gap index, which used taxi and metro travel data and POI data. The index was a dynamic accessibility indicator based on residents’ real-travel covered areas. Few accessibility analyses of urban road-to-freeway interchanges have been reported. Based on the above literature review and to analyze the spatial accessibility of urban road-to-freeway interchanges in Zhengzhou city, we concentrate on two perspectives: (1) improvement to cumulative measures, in particular, travel impedance and (2) factors associated with the travel impedance obtained from the navigation app Baidu Map.

3. Factors Associated with Travel Impedance An online questionnaire survey about which factors are important for accessibility was conducted in Zhengzhou city. A total of 270 questionnaires were collected. The respondents consisted of 185 males and 85 females. Most of the respondents were enterprise staff, teachers, and doctors. The proportion of respondents who used navigation during travel was 98.15%, as shown in Figure1; 25.56% of the respondents always used navigation during travel, and 47.78% of the respondents used it frequently. Furthermore, 63.76% of travelers responded that they preferred to choose the path recommended by the navigation Sustainability 2021, 13, x FOR PEER REVIEW 4 of 17

factors associated with the travel impedance obtained from the navigation app Baidu Map.

Sustainability 2021, 13, x FOR PEER REVIEW 4 of 17 3. Factors Associated with Travel Impedance An online questionnaire survey about which factors are important for accessibility was conducted in Zhengzhou city. A total of 270 questionnaires were collected. The re- factorsspondents associated consisted with of 185 the males travel and impedance 85 female obtaineds. Most of fromthe respondents the navigation were app enterprise Baidu Sustainability 2021, 13, 372 Map.staff, teachers, and doctors. The proportion of respondents who used navigation during4 of 17 travel was 98.15%, as shown in Figure 1; 25.56% of the respondents always used naviga- 3.tion Factors during Associated travel, and with 47.78% Travel of the Impedance respondents used it frequently. Furthermore, 63.76% of travelersAn online responded questionnaire that they survey preferred about to which choose factors the path are recommendedimportant for accessibilityby the navi- mapwasgation conducted as map the travelas the in travel path.Zhengzhou path. Especially Especially city. whenA total when the of travelers270the travelersquestionnaires were were unfamiliar unfamiliar were collected. with with the theThe trafﬁc traf- re- conditions,spondentsfic conditions, consisted the the proportion proportion of 185 was males was as and high as high85 as female 97.41%. as 97.41%.s. Most of the respondents were enterprise staff, teachers, and doctors. The proportion of respondents who used navigation during travel was 98.15%, as shown in Figure 1; 25.56% of the respondents always used naviga- 1.85% tion during travel, and 47.78% of the respondentsDo not use used it frequently. Furthermore, 63.76% of travelers responded that they preferredAlways to choose use the path recommended by the navi- Occasionally use gation map as the travel path. Especially when the travelers were unfamiliar with the traf- Frequently use fic conditions, the proportion25.56% was as high as 97.41%. 47.78%

1.85% Do not use 24.81% Always use Occasionally use Frequently use 25.56%

47.78% FigureFigure 1.1. NavigationNavigation usage.usage.

AccordingAccording toto traveltravel24.81% time,time, traveltravel byby carcar waswas divided divided into into three three types: types: short-distance short-distance traveltravel (travel(travel time time less less than than 15 15 min), min), medium-distance medium-distance travel travel (travel (travel time time more more than than 15 min 15 andmin lessand than less than 30 min), 30 min), and long-distanceand long-distance travel tr (travelavel (travel time time more more than than 30 min). 30 min).Figures Figures2–4 show2–4 show the factorsthe factors preference preference for for different different age age groups. groups. For For the the three three types types of of travel, travel, inin additionFigureaddition 1. Navigation toto congestion, usage. the the travel travel time, time, travel travel distance, distance, and and the the number number of oflights lights were were the thetop topthree three important important factors. factors. There There was was no su nobstantial substantial difference difference about about the thepreferred preferred fac- factorstors betweenAccording between age to age groups. travel groups. time, The The impacttravel impact byof trafficcar of trafficwas congestion divided congestion into on travel onthree travel types:path path impedance short-distance impedance was wastravelreflected reflected (travel in the intime travel the less travel time. than time. In 15 addition, min), In addition, medium for a forspecific-distance a specific road travel roadsegment, (travel segment, the time estimated themore estimated than travel 15 travelmintime and in time the less innavigation than the navigation30 min), app and was app long-distance related was related to the tr togradeavel the (travel gradeof the oftimeroad the more and road the than and speed 30 the min). speedlimit. Figures Infor- limit. Information2–4mation show about the about factorsthe recommended the preference recommended fortravel different travel path pathinage the groups. in navigation the navigation For the app three consisted app types consisted ofof thetravel, of travel the in traveladditiontime, travel time, to travelcongestion,distance, distance, and the the andtravel number the time, number of travel lights, of distance, lights, as shown as and shown in theFigure innumber Figure 5. of5. lights were the top threeMoreover, important a survey factors. on the There preferences was no su ofbstantial travelers difference with respect about to timethe preferred and distance fac- factorstors between120 was also age conducted. groups. The As impact shown of intraffic Figure congestion6, 71.48% on of travel the respondents path impedance believed was that the time factor was100 most important, 7.04% of the respondents thought the distance reflected100 in the travel time. In addition, for a specific road segment, the estimated travel factor was most important,76 and the rest75 of the respondents thought the two factors were time in80 the navigation app was related to the grade of the road and the speed limit. Infor- equallymation about important.55 the recommended These results travel were path used in to the determine navigation the app weight consisted coefficient of theof travel the 60 49 46 comprehensivetime, travel42 distance, travel and impedance the number model of describedlights, as shown in the followingin Figure section.5. 40 25 23 15 19 20 7 8 9 11 12 8 8 7 120 3 2 1 2 002 2 3 Number Number of respondents 0 100 100 20−35 years old 35−45 years old 45−55 years old Over 55 years old 76 75 80 Age group 55 Travel distance Travel time 60 49 46 42 Whether the road is elevated or not Number of traffic lights 40 25Number of left turns Traffic congestion23 15 19 20 Is there a 7gas station on8 the path 9 11 12 8 8 7 3 2 1 2 002 2 3 Number Number of respondents 0 Figure 2. Factors20−35 for years short-distance old 35−45 travel. years old 45−55 years old Over 55 years old Age group Travel distance Travel time Whether the road is elevated or not Number of traffic lights Number of left turns Traffic congestion Is there a gas station on the path

FigureFigure 2.2. FactorsFactors forfor short-distanceshort-distance travel.travel. Sustainability 2021, 13, x FOR PEER REVIEW 5 of 17

Sustainability 2021, 13, 372 5 of 17 Sustainability 2021, 13, x FOR PEER REVIEW 5 of 17 Sustainability 2021, 13, x FOR PEER REVIEW 5 of 17

100 83 89 10080 70 100 83 89 68 80 5683 57 89 70 68 8060 70 56 4457 68 60 56 57 39 6040 44 44 27 39 40 3920 19 22 16 12 27 13 4020 27 20 19 2210 10 8 7 16 12 5 513 322 334 4 20 16 20 19 10 1 10 8 0 Number Number of respondents 12 5 5 13 3 334 4 7 20 10 1 10 8 7 0 Number Number of respondents 0 5 5 4 4 0 3 331 0 Number Number of respondents 20−35 years old 35−45 years old 45−55 years old Over 55 years old 0 Over 55 years old 20−35 years old 35−45 years oldAge 45−55 group years old 20−35 years old 35−45 years Ageold group 45−55 years old Over 55 years old Travel distance Age group Travel time Travel distance Travel time WhetherTravelWhether distance the the road road is elevated is elevated or not or notNumberTravelNumber time of traffic of traffic lights lights NumberWhetherNumber ofthe ofleft road left turns isturns elevated or not TrafficNumberTraffic congestion of traffic congestion lights IsNumberIs there there a of gasa leftgas station turns station on theon thepath path Traffic congestion Is there a gas station on the path

FigureFigure 3.3. 3. FactorsFactors Factors forfor for medium-distancemedium-distance medium-distance travel.travel. travel. Figure 3. Factors for medium-distance travel. 100100 9090 84 100 90 84 84 73 8080 68 73 80 6666 68 73 66 68 60 60 4745 47 60 4745 47 4745 35 47 40 3535 2728 27 4040 23 27282728 27 2718 19 15 23 23 19 20 1515 8 18 187 19 7 9 7 8 2020 5 6 3 3 3 Number Number of respondents 8 8 1 9 9 8 8 7 5 7 5 7 76 367 33 73 3 3 Number Number of respondents Number Number of respondents 0 1 1 00 20−35 years old 35−45 years old 45−55 years old Over 55 years old 20−3520−35 years years old old 35−45 35−45 years yearsAge old oldgroup 45−55 45−55 years years old oldOver 55Over years 55 old years old Travel distance AgeAge group groupTravel time WhetherTravelTravel distance distancethe road is elevated or not NumberTravelTravel time of traffic time lights NumberWhetherWhether ofthe theleft road roadturns is elevatedis elevated or not or not TrafficNumberNumber congestion of traffic of traffic lights lights IsNumber there a of gas left station turns on the path Traffic congestion IsNumber there a gas of leftstation turns on the path Traffic congestion Is there a gas station on the path Figure 4. Factors for long-distance travel. FigureFigure 4.4. FactorsFactors forfor long-distancelong-distance travel.travel. Figure 4. Factors for long-distance travel.

Figure 5. Recommended travel path and information in the navigation app. Figure 5. Recommended travel path and information in the navigation app.

Moreover, a survey on the preferences of travelers with respect to time and distance Moreover, a survey on the preferences of travelers with respect to time and distance FigurefactorsFigure 5. 5.wasRecommended Recommended also conducted. travel travel As path pathshown and and information in information Figure 6, in 71.48% the in navigation the of navigation the respondents app. app. believed that factors was also conducted. As shown in Figure 6, 71.48% of the respondents believed that the time factor was most important, 7.04% of the respondents thought the distance factor the time factor was most important, 7.04% of the respondents thought the distance factor was mostMoreover, important, a survey and the on rest the of preferences the respondents of travelers thought withthe two respect factors to were time equally and distance was most important, and the rest of the respondents thought the two factors were equally important.factors was These also resultsconducted. were Asused shown to determi in Figurene the 6, weight 71.48% coefficient of the respondents of the comprehen- believed that important. These results were used to determine the weight coefficient of the comprehensivethe timetravel factor impedance was most model important, described 7.04%in the followingof the respondents section. thought the distance factor sivewas travelmost important,impedance modeland the described rest of the in theresp followingondents section.thought the two factors were equally important. These results were used to determine the weight coefficient of the comprehensive travel impedance model described in the following section. Sustainability 2021, 13, 372 6 of 17 Sustainability 2021, 13, x FOR PEER REVIEW 6 of 17

80.00% 71.48% 70.00% 60.00% 50.00% 40.00%

Proportion 30.00% 21.48% 20.00% 7.04% 10.00% 0.00% Time is more Distance is more Both are equally important important important

FigureFigure 6.6.Result Result ofof travelers’travelers’ preferencepreference for for time time and and distance. distance.

4.4. AccessibilityAccessibility AnalysisAnalysis MethodologyMethodology 4.1.4.1. ComprehensiveComprehensive TravelTravel Impedance Impedance Model Model AccessibilityAccessibility to to urban urban road-to-freeway road-to-freeway interchanges interchanges (i.e., (i.e., freeway freeway entrances entrances and and exits) ex- isits) representative is representative to assess to assess the accessibility the accessibil toity a freewayto a freeway network. network. It should It should be noted be noted that this study focused on car travelers. Accessibility, from the perspective of travel impedance, that this study focused on car travelers. Accessibility, from the perspective of travel im- represents the objective ability to reach freeway entrances and exits via the urban road pedance, represents the objective ability to reach freeway entrances and exits via the urban system. Travel time, travel distance, and the number of traffic lights were comprehensively road system. Travel time, travel distance, and the number of traffic lights were compre- considered to measure the comprehensive travel impedance. hensively considered to measure the comprehensive travel impedance. From an overall perspective, the accessibility of freeway entrances and exits represents From an overall perspective, the accessibility of freeway entrances and exits repre- the convenience for travelers to reach a freeway network via the urban traffic system. sents the convenience for travelers to reach a freeway network via the urban traffic system. Therefore, the accessibility of freeway entrances and exits was defined as the overall Therefore, the accessibility of freeway entrances and exits was defined as the overall dif- difficulty of reaching all freeway entrances and exits in the central urban area from a ficulty of reaching all freeway entrances and exits in the central urban area from a travel travel hotspot through the urban traffic system. Then, comprehensive travel impedance, hotspot through the urban traffic system. Then, comprehensive travel impedance, which which consists of travel time impedance and travel distance impedance, was used to consists of travel time impedance and travel distance impedance, was used to measure measure accessibility. accessibility.The navigation map software Baidu Map was utilized to calibrate the OD points and plan theThe path. navigation The set map of travel software hotspots Baidu in Map the city was is utilized denoted to by calibrateO, and the OD set ofpoints freeway and plan the path. The set of travel hotspots in the city is denoted∈ by O, ∈and the set of freeway entrances and exits is represented by D. For each i (i ∈O) and j (j D), the travel path canentrances be provided and exits by theis represented navigation mapby D. software. For each Ifi ( severali O) and path j ( optionsjD∈ ), arethe given,travel path it is assumedcan be provided the first recommendedby the navigation path map is chosen software by travelers,. If several which path is options usually are the given, path with it is theassumed shortest the estimated first recommended travel time. path is chosen by travelers, which is usually the path withNavigation the shortest maps estimated provide travel information time. including travel time, travel distance, and the numberNavigation of traffic maps lights. provide As drivers information need to be including more focused travel whiletime, drivingtravel distance, in stop-and-go and the trafficnumber (e.g., of traffic traffic lights. light), As it results drivers in need an elevated to be more discomfort focused andwhile frustration driving in level stop-and-go among themtraffic [ 23(e.g.,,24]. traffic Drivers light), tend it results to avoid in travellingan elevated on discomfort paths where and stop-and-go frustration level conditions among arethem prevalent [23,24]. [Drivers25]. Hence, tend besidesto avoid the travelling increase on in paths travel where time, anstop-and-go increase in conditions the number are ofprevalent traffic lights [25]. onHence, a path besides also increases the increase its disutility in travel association time, an increase with the in discomfort the number and of frustrationtraffic lights for on a a driver. path also Saxena increases et al. (2019)its disu [25tility] also association found that with the the amount discomfort of stop-and-go and frus- traffictration (along for a withdriver. time Saxena spent inet stop-and-goal. (2019) [25] traffic) also found contributed that the towards amount the of disutility stop-and-go for a giventraffic path. (along Therefore, with time the spent travel in timestop-and-go impedance traffic) was contributed obtained after towards considering the disutility the travel for timea given estimated path. Therefore, by the navigation the travel map time and im thepedance impairment was obtained effect of traffic after lights.considering the

travel time estimated by the navigationT map and the impairment effect of traffic lights. cij = Tij + Gij · ξ (1) T cTG=+⋅x (1) T ij ij ij where cij is the travel time impedance between i and j; Tij denotes the estimated travel time T provided by the navigation map software; Gij represents the number of traffic lights on the where cij is the travel time impedance between i and j; Tij denotes the estimated travel path; and ξ represents the derogation utility of a single traffic light. Equation (1) accounts fortime both provided delay (i.e.,by the additional navigation travel map time)software; and discomfortGij represents (expressed the number as the of traffic number lights of trafficon the lights path; experienced).and ξ represents the derogation utility of a single traffic light. Equation (1) Sustainability 2021, 13, 372 7 of 17

T∗ Then cij can be obtained using the min–max normalization method, shown as follows:

T cij − min cT∗ = (2) ij max − min

T T where min is the minimum value of cij (j = 1, 2, ... , n); max is the maximum value of cij (j = 1, 2, . . . , n); and n is the number of freeway entrances and exits. L Travel distance cij is another factor influencing accessibility between travel hotspot i L and freeway entrance and exit j. Similarly, using the min–max normalization method, cij L∗ can be normalized and cij obtained. According to the above analysis, the following comprehensive travel impedance model can be proposed by comprehensively considering the travel time, travel distance, and number of traffic lights. As shown in Equation (3), the comprehensive travel impedance is expressed as a linear combination of travel time impedance and travel distance impedance after standardization. T∗ L∗ cij = γ1 · cij + γ2 · cij (3) T∗ L∗ where cij is the comprehensive travel impedance; cij and cij represent the standardized travel time impedance and travel distance impedance, respectively; γ1 and γ2 denote the weight coefficients of the two impedances, respectively; and γ1 + γ2 = 1. The average comprehensive travel impedance is a measure of the overall travel impedance from a hotspot i in the city to all available freeway entrances and exits.

n Ci = ∑ cij/n (4) j=1

where Ci denotes the average comprehensive travel impedance from hotspot i as the starting point to all freeway entrances and exits; n is the total number of freeway entrances and exits. Accessibility is a measure of the degree of difficulty of travel, and the degree of difficulty can be quantified by travel impedance. A comprehensive travel impedance model can thus be formulated to measure accessibility:

Ai = 1/Ci (5)

where Ai denotes the accessibility of freeway entrances and exits for hotspot i.

4.2. Dynamic Analysis Method The obtained data based on navigation maps changes over the time, which thus provides the possibility for dynamic accessibility analysis. This study selected four different time periods to conduct a dynamic accessibility analysis of freeway entrances and exits, i.e., morning peak period (MPP), off-peak afternoon period (OPAP), evening peak period (EPP), and off-peak evening period (OPEP). By applying the proposed model to different time periods, the dynamic trends of accessibility could be captured.

5. Case Study Zhengzhou covers an area of 7446 square kilometers. The ring freeway in the central city of Zhengzhou is composed of the Zhengzhou Ring Expressway, Beijing-Hong Kong- Macao Freeway, and Lianhuo Freeway et al. As shown in Figure7, twenty-six freeway entrances and exits are closely distributed on the Zhengzhou ring freeway. A schematic diagram of the freeway entrances and exits is shown in Figure8, and names of the freeway entrances and exits are shown in Table2. Sustainability 2021, 13, x FOR PEER REVIEW 8 of 17 Sustainability 2021, 13, x FOR PEER REVIEW 8 of 17

5. Case Study Zhengzhou covers an area of 7446 square kilometers. The ring freeway in the central city of Zhengzhou is composed of the Zhengzhou Ring Expressway, Beijing-Hong Kong- Macao Freeway, and Lianhuo Freeway et al. As shown in Figure 7, twenty-six freeway Sustainability 2021, 13, 372 entrances and exits are closely distributed on the Zhengzhou ring freeway. A schematic8 of 17 diagram of the freeway entrances and exits is shown in Figure 8, and names of the freeway entrances and exits are shown in Table 2.

Figure 7. Zhengzhou Ring Expressway. FigureFigure 7.7. Zhengzhou ringRing freeway. Expressway.

Figure 8. Illustration of the freeway entrance and exit (East 3rd Ring Road North Station). FigureFigure 8.8. IllustrationIllustration ofof thethe freewayfreeway entranceentrance andand exitexit (East(East 3rd3rd RingRing RoadRoad NorthNorth Station).Station). Table 2. Freeway entrances and exits. TableTable 2.2. FreewayFreeway entrancesentrances andand exits.exits. Freeways that form the Ring Freeway Entrances and Exits on the Freeway FreewaysFreeways that formform the the Ring Ring Freeway Freeway Entrances Entrances andand Exits Exits on on the the Freeway Freeway Lotus Street; Science Avenue; Zhengshang Road; LotusZhongyuan Street; Science West Road; Avenue; Longhai Zhengshang West Road; Road; ZhongyuanZhongyuan West West Road; Road; Longhai Longhai West Road; West Zhengmi Road; Zhengzhou Ring Expressway Zhengzhou Ring Expressway ZhengmiRoad; University Road; University South Road; South Beijing–Guangzhou Road; Beijing– Freeway;Guangzhou Zheng Freeway; Xin Freeway; Zheng East Xin 3rd Freeway; Circle Road East Zheng Shao3rd Freeway–Navigation Circle Road Road Zhengshao Freeway 3rd Circle Road Zheng Shao Freeway–Navigationconnection Line Road connec- Zhengshao Freeway Zhengluan Freeway South section oftion Songshan Line South Road Zhengluan Freeway Zhongzhou South Avenue; section Navigation of Songshan East South Road; Road South 3rd Airport Freeway Zhongzhou Avenue;Circle Navigation Road East Road; Airport Freeway South 3rd CircleSouth Road; Navigation3rd Circle EastRoad Road; Longhai Beijing–Hong Kong–Macao Freeway South 3rd Circle Road South 3rdFreeway; Circle Road; Zhengkai Navigation Avenue East Road; Beijing–Hong Kong–Macao Freeway East 3rdLonghai Circle Freeway; Road North; Zhengkai Zhongzhou Avenue Avenue; East Garden3rd Circle North Road Road; North; Cultural Zhongzhou North Road; Avenue; Lianhuo Freeway East 3rd Circle Road North; Zhongzhou Avenue; Beijing–Guangzhou Freeway; West 3rd Circle Road; Garden North Road; Cultural North Road; Bei- Lianhuo Freeway West 4th Circle Road jing–Guangzhou Freeway; West 3rd Circle Road; West 4th Circle Road According to “Fifth Comprehensive Urban Traffic Survey of Zhengzhou (2018)”, the central urban area of Zhengzhou is divided into eight districts: Huiji, Gaoxin, Jinshui, Zhengdong New, Zhongyuan, Erqi, Guancheng, and Jingkai Districts, as shown in Figure9. Centroid points of these eight districts were selected as travel hotspots. Then two principles were set for selecting other travel hotspots, i.e., main centers and subcenters of cities and traffic distribution centers. Seventeen travel hotspots were finally selected for accessibility analysis of freeway entrances and exits, as shown in Figure9, and information about the hotspots is shown in Table3. Sustainability 2021, 13, x FOR PEER REVIEW 9 of 17

According to “Fifth Comprehensive Urban Traffic Survey of Zhengzhou (2018)”, the central urban area of Zhengzhou is divided into eight districts: Huiji, Gaoxin, Jinshui, Zhengdong New, Zhongyuan, Erqi, Guancheng, and Jingkai Districts, as shown in Figure 9. Centroid points of these eight districts were selected as travel hotspots. Then two principles were set for selecting other travel hotspots, i.e., main centers and subcenters of cities Sustainability 2021, 13, 372 and traffic distribution centers. Seventeen travel hotspots were finally selected for acces-9 of 17 sibility analysis of freeway entrances and exits, as shown in Figure 9, and information about the hotspots is shown in Table 3.

(a) Division of the central urban area of (b) Coordinate axis and distribution of 17 Zhengzhou city travel hotspots

FigureFigure 9.9. StudyStudy areaarea andand traveltravel hotspotshotspots distribution.distribution.

Table 3. Information about travel hotspots. Table 3. Information about travel hotspots. Travel Hotspot Abbreviation Location (km,km) Travel Hotspot Abbreviation Location (km, km) Erqi Square Main Center EQMC (18.5, 12.3) Erqi Square Main Center EQMC (18.5, 12.3) Zhengdong New District Main Center ZDMC (24.5, 13.4) Zhengdong New District Main Center ZDMC (24.5, 13.4) EastEast Station Station Subcenter Subcenter ESSC ESSC (28.7, (28.7, 12.4) 12.4) LonghuLonghu Subcenter Subcenter LHSC LHSC (24.8, (24.8, 18.1) 18.1) FutaFuta Subcenter Subcenter FTSC FTSC (24.4, (24.4, 8.2) 8.2) BishagangBishagang Subcenter Subcenter BSGSC BSGSC (15.4, (15.4, 11.3) 11.3) Huayuan Road Subcenter HYSC (19.9, 15.0) ZhengzhouHuayuan South Road Passenger Subcenter Station SPS HYSC (17.9, (19.9, 5.2) 15.0) ZhengzhouZhengzhou South Railway Passenger Station Station RS SPS (17.6, (17.9, 10.9) 5.2) CentroidZhengzhou point of Railway Huiji District Station CPHJ RS (15.6, (17.6, 26.3) 10.9) CentroidCentroid point point of Gaoxin of Huiji District District CPGX CPHJ (7.0, (15.6, 18.5) 26.3) Centroid point of Jinshui District CPJS (19.2, 20.0) CentroidCentroid point of point Zhengdong of Gaoxin New District District CPZD CPGX (32.7, (7.0, 16.0) 18.5) CentroidCentroid point point of Zhongyuan of Jinshui District District CPZY CPJS (8.2, (19.2, 11.0) 20.0) CentroidCentroid point point of Zhengdong of Erqi District New District CPEQ CPZD (12.0, (32.7, 2.9) 16.0) CentroidCentroid point point of Guanchengof Zhongyuan District District CPGC CPZY (23.7, (8.2, 3.9)11.0) Centroid point of Jingkai District CPJK (33.6, 4.2) Centroid point of Erqi District CPEQ (12.0, 2.9) Centroid point of Guancheng District CPGC (23.7, 3.9) Sustainability 2021, 13, x FOR PEER REVIEW 10 of 17 TheCentroid 26 freeway point entrances of Jingkai and District exits and 17 travel hotspotsCPJK are integrated (33.6, and 4.2) shown in Figure 10. The 26 freeway entrances and exits and 17 travel hotspots are integrated and shown in Figure 10.

FigureFigure 10.10. TheThe distributiondistribution ofof freewayfreeway entrancesentrances andand exitsexits andand traveltravelhotspots. hotspots.

5.1. Data This study focused on 17 travel hotspots and 26 freeway entrances and exits. Using Baidu Map navigation software as a data acquisition tool for a specified time period, the travel path from a certain travel hotspot to any one of the 26 freeway entrances and exits within the study area could be obtained by calibrating the OD points. By means of the path planning data provided by Baidu Map, the source data of the recommended path, estimated travel time, travel distance, and the number of traffic lights on path could be obtained. These information were in real-time and change over the time. It was assumed that travelers always prefer to choose the recommended path as the travel path, i.e., they change the path choice according to the recommended path over the time. A total of 442 sets of basic data were extracted. The two weight coefficients were determined according to the survey on the preferences of travelers with respect to time and distance factors. Results showed that 71.48% of the respondents believed that the time factor was most important, 7.04% of the respondents thought the distance factor was most important, and the rest of the respondents thought the two factors were equally important. Hence, the set was γ =+−− = γ =− = 1 71.48% (1 71.48% 7.04%) / 2 0.8222 and 2 1 0.8222 0.1778 . The two values are acceptable in practical applications, since when choosing a path, the first subjective reaction of travelers is to pay attention to travel time. The impairment effect caused by a traffic light is equivalent to a travel time of 20 s, referring to Fosgerau et al. [26]. Moreover, the estimated travel time changes over the time of day, so the dynamic analysis of comprehensive travel impedance needs to be discussed in different time periods.

5.2. Calculation Results After data acquisition, cleaning and analysis, the average comprehensive travel impedance results of 17 hotspots were calculated in four time periods: MPP (t = 1; between 9:00 and 10:00), OPAP (t = 2; between 13:00 and 14:00), EPP (t = 3; between 17:00 and 18:00), and OPEP (t = 4; between 23:00 and 24:00), as shown in Figure 11. The average comprehensive travel impedance is a measure of the overall impedance from hotspot to all freeway entrances and exits within the city. By analyzing the results for different periods, we can see the impedance change with the traffic condition for different periods of time. Sustainability 2021, 13, 372 10 of 17

5.1. Data This study focused on 17 travel hotspots and 26 freeway entrances and exits. Using Baidu Map navigation software as a data acquisition tool for a specified time period, the travel path from a certain travel hotspot to any one of the 26 freeway entrances and exits within the study area could be obtained by calibrating the OD points. By means of the path planning data provided by Baidu Map, the source data of the recommended path, estimated travel time, travel distance, and the number of traffic lights on path could be obtained. These information were in real-time and change over the time. It was assumed that travelers always prefer to choose the recommended path as the travel path, i.e., they change the path choice according to the recommended path over the time. A total of 442 sets of basic data were extracted. The two weight coefficients were determined according to the survey on the preferences of travelers with respect to time and distance factors. Results showed that 71.48% of the respondents believed that the time factor was most important, 7.04% of the respondents thought the distance factor was most important, and the rest of the respondents thought the two factors were equally important. Hence, the set was γ1 = 71.48% + (1 − 71.48% − 7.04%)/2 = 0.8222 and γ2 = 1 − 0.8222 = 0.1778. The two values are acceptable in practical applications, since when choosing a path, the first subjective reaction of travelers is to pay attention to travel time. The impairment effect caused by a traffic light is equivalent to a travel time of 20 s, referring to Fosgerau et al. [26]. More- over, the estimated travel time changes over the time of day, so the dynamic analysis of comprehensive travel impedance needs to be discussed in different time periods.

5.2. Calculation Results After data acquisition, cleaning and analysis, the average comprehensive travel impedance results of 17 hotspots were calculated in four time periods: MPP (t = 1; between Sustainability 2021, 13, x FOR PEER REVIEW 11 of 17 9:00 and 10:00), OPAP (t = 2; between 13:00 and 14:00), EPP (t = 3; between 17:00 and 18:00), and OPEP (t = 4; between 23:00 and 24:00), as shown in Figure 11.

1.200

1.000

0.800

0.600

0.400 MPP(9:00−10:00) OPAP(13:00−14:00) 0.200 EPP(17:00−18:00) OPEP(23:00−24:00) Average comprehensive Average comprehensive traffic

0.000

Travel hotspot

FigureFigure 11. 11. AverageAverage comprehensive comprehensive travel travel impedance impedance of of each each travel travel hotspot hotspot in in four four periods. periods.

AccordingThe average to comprehensivethe results in Figure travel 11, impedance the average is a comprehensive measure of the overalltravel impedance impedance offrom each hotspot travel hotspot to all freeway was the entrances lowest during and exits OPEP, within when the traffic city. By conditions analyzing were the results the best. for Accordingly,different periods, each wetravel can hotspot see the had impedance the greate changest accessibility with the trafﬁc during condition this period. for different During theperiods EPP, offor time. most of the travel hotspots, the average comprehensive travel impedance was the highest.According Correspondingly, to the results inmost Figure of the 11 ,trav theel average hotspots comprehensive had less freeway travel entrance impedance and exitof each accessibility travel hotspot during was this the period. lowest Therefore, during OPEP, it was when found trafﬁc that conditionsthe travel impedance were the best. of each hotspot was the lowest during the OPEP, the travel impedance of each hotspot was the highest during the EPP, and the travel impedance of the OPAP was between that of the EPP and OPEP periods and less than that of the MPP. From the perspective of a single travel hotspot, a comprehensive view of the four time periods indicated that the average comprehensive travel impedance of the HYSC hotspot was the highest, and the volatility during the four periods was clear. The HYSC hotspot was located in Jinshui District, which is in the middle of the central city. Jinshui District has the largest population among the eight districts of Zhengzhou. Population has a macroscopic impact on travel impedance; the larger the population is, the higher the impedance may be. The clear volatility reflects that the road network around the HYSC hotspot may change greatly with time, resulting in fluctuations in travel impedance. The average comprehensive traffic impedance of CPZD was the lowest, and the volatility over the four periods was minimal. The CPZD is the geographic centroid of Zhengdong New District, and the main land types of Zhengdong New District are commercial land and university campus land. Furthermore, as a new district, Zhengdong New District has a better level of road network construction, which makes travel in this area convenient and lowers the travel impedance. The above analysis shows that the road network capacity of the area around the CPZD hotspot can meet the traffic demand of different periods. Changes in traffic flow have little influence on the road network conditions, which demonstrates that the road network construction of the surrounding area of the CPZD hotspot is of good quality and resilience.

5.3. Dynamic Accessibility Analysis To more intuitively compare and analyze the accessibility of freeway entrances and exits for each travel hotspot in different periods, an accessibility classification was provided in Table 4. Sustainability 2021, 13, 372 11 of 17

Accordingly, each travel hotspot had the greatest accessibility during this period. During the EPP, for most of the travel hotspots, the average comprehensive travel impedance was the highest. Correspondingly, most of the travel hotspots had less freeway entrance and exit accessibility during this period. Therefore, it was found that the travel impedance of each hotspot was the lowest during the OPEP, the travel impedance of each hotspot was the highest during the EPP, and the travel impedance of the OPAP was between that of the EPP and OPEP periods and less than that of the MPP. From the perspective of a single travel hotspot, a comprehensive view of the four time periods indicated that the average comprehensive travel impedance of the HYSC hotspot was the highest, and the volatility during the four periods was clear. The HYSC hotspot was located in Jinshui District, which is in the middle of the central city. Jinshui District has the largest population among the eight districts of Zhengzhou. Population has a macroscopic impact on travel impedance; the larger the population is, the higher the impedance may be. The clear volatility reflects that the road network around the HYSC hotspot may change greatly with time, resulting in fluctuations in travel impedance. The average comprehensive traffic impedance of CPZD was the lowest, and the volatility over the four periods was minimal. The CPZD is the geographic centroid of Zhengdong New District, and the main land types of Zhengdong New District are commercial land and university campus land. Furthermore, as a new district, Zhengdong New District has a better level of road network construction, which makes travel in this area convenient and lowers the travel impedance. The above analysis shows that the road network capacity of the area around the CPZD hotspot can meet the traffic demand of different periods. Changes in traffic flow have little influence on the road network conditions, which demonstrates that the road network construction of the surrounding area of the CPZD hotspot is of good quality and resilience.

Table 4. Accessibility levels.

Level Accessibility Value Very High A ≥ 1.8 High 1.6 ≤ A < 1.8 Medium 1.4 ≤ A < 1.6 Low 1.2 ≤ A < 1.4 Very Low A < 1.2

The distribution of the average comprehensive travel impedance in the central urban area of Zhengzhou in each period is shown in Figure 12. The classiﬁcation level of the freeway entrance and exit accessibility of each travel hotspot is shown in Figure 13. Comprehensive analysis of the visualization results in Figures 12 and 13 yields the following conclusions. (1) During the MPP As shown in Figure 12a, the impedance in the middle of the central urban area is the highest and the accessibility is the lowest. The center of Figure 13a contains hotspots with low accessibility levels and very low accessibility levels. According to Figure 12a, the impedance in the western part of the central urban area is high, and the accessibility is low. Correspondingly, the western part of Figure 13a has hotspots with low levels of accessibility. As shown in Figure 12a, the impedance in the eastern part of the central urban area is low, the accessibility value is high, and the distribution is relatively even. Thus, as seen in Figure 13a, most of the travel hotspots in the eastern part of the central urban have a medium accessibility level. Sustainability 2021, 13, x FOR PEER REVIEW 12 of 17

Table 4. Accessibility levels.

Level Accessibility Value Very High A ≥ 1.8 High 1.6 ≤ A < 1.8 Sustainability 2021, 13, 372 Medium 1.4 ≤ A < 1.6 12 of 17 Low 1.2 ≤ A < 1.4 Very Low A < 1.2 Figure 13a shows that the accessibility of ﬁve travel hotspots is medium, that of eight The distributionhotspots of the is average low, and comprehens that of four hotspotsive travel is impedance very low. During in the thiscentral morning urban peak period, area of Zhengzhouthe in overall each accessibilityperiod is shown of freeway in Figure entrances 12. andThe exits classification in the central level urban of areathe is medium freeway entrance toand very exit low. accessibility of each travel hotspot is shown in Figure 13.

(a) Morning peak period (MPP)

(b) Off-peak afternoon period (OPAP)

Figure 12. Cont. Sustainability 2021, 13, x SustainabilityFOR PEER REVIEW2021, 13, 372 13 of 17 13 of 17

(d) Off-peak evening period (OPEP)

FigureFigure 12. Three-dimensional 12. Three-dimensional distribution distribution of average comprehensiveof average comprehensive travel impedance travel in centralimpedance urban in area central of Zhengzhou. urban area of Zhengzhou. (2) During the OPAP As shown in Figure 12b, the impedance in the northwest of the central urban area is slightly lower than that in the southwest but both are higher than that in the east. The central impedance is at a peak, while the impedance in the east is at a valley, and the average comprehensive travel impedance decreases gradually from southeast to northeast. Correspondingly, Figure 13b shows that travel hotspots with low accessibility are distributed in the west and middle parts of the central urban area, while travel hotspots in the east have medium and high accessibility. Moreover, in the east, the accessibility gradually increases from south to north. Figure 13b shows that the accessibility of one travel hotspots is high, that of ﬁve hotspots is medium, and that of eleven hotspots is low. Compared with the MPP, during this period, the accessibility of partial travel hotspots changes, and all these hotspots have (a) Morning peak period (MPP) (b) Off-peak afternoon period (OPAP) clearly improved accessibility levels. Sustainability 2021, 13, x FOR PEER REVIEW 13 of 17

(d) Off-peak evening period (OPEP) Sustainability 2021, 13, 372 14 of 17 Figure 12. Three-dimensional distribution of average comprehensive travel impedance in central urban area of Zhengzhou.

Sustainability 2021, 13, x FOR PEER REVIEW 14 of 17

(a) Morning peak period (MPP) (b) Off-peak afternoon period (OPAP)

Figure 13.Figure Hierarchical 13. Hierarchical distribution distribution of accessibility of accessibility values of valueseach travel of each hotspot. travel hotspot.

(3)Comprehensive During the EPP analysis of the visualization results in Figures 12 and 13 yields the followingAs shown conclusions. in Figure 12c, during the EPP, the impedance in the middle of the central urban(1) area During is extremely the MPP high, and the accessibility is very low. Correspondingly, the middle of FigureAs shown 13c contains in Figure hotspots 12a, the with impedance low accessibility in the middle levels andof the very central low levels.urban Accordingarea is the tohighest Figure and 12 thec, the accessibility eastern part is the of thelowest. central The urbancenter areaof Figure has the 13a lowest contains impedance hotspots with and highestlow accessibility accessibility. levels Furthermore, and very low the accessibility eastern part levels. of Figure According 13c shows to Figure travel 12a, hotspots the im- withpedance low in accessibility the western levels, part of and the the central accessibility urban area of travel is high, hotspots and the from accessibility the west is to low. the middleCorrespondingly, and east of the the western central urbanpart of area Figure shows 13a a has low/very hotspots low with distribution. low levels of accessibility.Figure As shown 13c indicates in Figure that 12a, the the accessibility impedance ofin onethe eastern travel hotspot part of isthe medium, central urban that of area ten hotspotsis low, the is accessibility low, and that value of six is travel high, hotspotsand the distribution is very low. Inis relatively summary, even. during Thus, this as period, seen mostin Figure of the 13a, travel most hotspots of the travel have hotspots low accessibility, in the eastern and onlypart oneof the hotspot central in urban the east have has a medium accessibility.accessibility level. During the evening travel peak, the overall accessibility of freeway entrancesFigure and 13a exits shows in thethat central the accessibility urban area of is five low. travel hotspots is medium, that of eight hotspots(4) During is low, theand OPEP that of four hotspots is very low. During this morning peak period, the overallAs shown accessibility in Figure of 12 freewayd, the impedance entrances inan thed exits north in ofthe the central central urban urban area area is ismedium higher thanto very that low. in the south, and the impedance in the west is slightly higher than that in the east.(2) The During peak comprehensive the OPAP impedance is in the northeast, and the valley is in the south. FigureAs 13 shownd shows in hotspotsFigure 12b, of mediumthe impedance accessibility in the in northwest the west andof the high central accessibility urban area in the is middleslightly region.lower than that in the southwest but both are higher than that in the east. The Furthermore, Figure 13d indicates that the accessibility of one travel hotspot is very central impedance is at a peak, while the impedance in the east is at a valley, and the high, that of seven travel hotspots is high, and that of nine travel hotspots is medium. The average comprehensive travel impedance decreases gradually from southeast to north- accessibility distribution has a strong regularity from west to east. During this period, it is east. Correspondingly, Figure 13b shows that travel hotspots with low accessibility are dominated by the hotspots of medium and high accessibility. distributed in the west and middle parts of the central urban area, while travel hotspots Furthermore, we conducted relevant statistical analysis according to the above accessi- in the east have medium and high accessibility. Moreover, in the east, the accessibility bility results. A statistical table of accessibility is provided in Figure 14d, in which different gradually increases from south to north. colors represent different levels of accessibility. Figure 13b shows that the accessibility of one travel hotspots is high, that of five hotspots is medium, and that of eleven hotspots is low. Compared with the MPP, during this period, the accessibility of partial travel hotspots changes, and all these hotspots have clearly improved accessibility levels. (3) During the EPP As shown in Figure 12c, during the EPP, the impedance in the middle of the central urban area is extremely high, and the accessibility is very low. Correspondingly, the middle of Figure 13c contains hotspots with low accessibility levels and very low levels. Ac- cording to Figure 12c, the eastern part of the central urban area has the lowest impedance and highest accessibility. Furthermore, the eastern part of Figure 13c shows travel hotspots with low accessibility levels, and the accessibility of travel hotspots from the west to the middle and east of the central urban area shows a low/very low distribution. Figure 13c indicates that the accessibility of one travel hotspot is medium, that of ten hotspots is low, and that of six travel hotspots is very low. In summary, during this period, most of the travel hotspots have low accessibility, and only one hotspot in the east has Sustainability 2021, 13, x FOR PEER REVIEW 15 of 17

medium accessibility. During the evening travel peak, the overall accessibility of freeway entrances and exits in the central urban area is low. (4) During the OPEP As shown in Figure 12d, the impedance in the north of the central urban area is higher than that in the south, and the impedance in the west is slightly higher than that in the east. The peak comprehensive impedance is in the northeast, and the valley is in the south. Figure 13d shows hotspots of medium accessibility in the west and high accessibility in the middle region. Furthermore, Figure 13d indicates that the accessibility of one travel hotspot is very high, that of seven travel hotspots is high, and that of nine travel hotspots is medium. The accessibility distribution has a strong regularity from west to east. During this period, it is dominated by the hotspots of medium and high accessibility. Furthermore, we conducted relevant statistical analysis according to the above acces- Sustainability 2021, 13, 372 15 of 17 sibility results. A statistical table of accessibility is provided in Figure 14d, in which different colors represent different levels of accessibility.

12 100% 90% 10 80% 8 70% 60% 6 50% 40% Frequeny 4 30% 20% 2

Cumulative percentage Cumulative 10% 0 0% MPP OPAP EPP OPEP MPP OPAP EPP OPEP Time slots Time slots Very High High Very Low Low Medium Low Medium High Very Low Very High

(b) Cumulative percentage of accessibility (a) Frequencies of accessibility levels levels

FigureFigure 14. 14.StatisticalStatistical values values of accessibility of accessibility level. level.

AccordingAccording to Figure to Figure 14, 14low, low levels levels of freeway of freeway entrance entrance and and exit exit accessibility accessibility are aremost most commoncommon in the in theMPP, MPP, OPAP, OPAP, and and EPP. EPP. During During the the MPP MPP and and EPP, EPP, we we observed observed a very a very low low levellevel of accessibility of accessibility due due to the to theintensification intensification of internal of internal travel travel in the in the city city during during the the peak peak periods,periods, the theincrease increase in traffic in traffic pressure, pressure, and the and impact the impact on the onoperation the operation of the urban of the road urban network.road network. DuringDuring the thetwo two off-peak off-peak peri periods,ods, OPAP OPAP and and OPEP, OPEP, we weobserved observed high high and and very very high high levelslevels of accessibility, of accessibility, respectively, respectively, due to due the to smooth the smooth operation operation of the road of the network road network duringduring off-peak off-peak periods. periods. The travel The time travel was time greatly was reduced greatly reduced compared compared to that during to that peak during periods,peak periods,thereby therebyaffecting affecting the accessibility the accessibility of freeway of freeway entrances entrances and andexits exits for fortravel travel hotspots.hotspots. FromFrom the theperspective perspective of time, of time, the the overall overall level level of accessibility of accessibility of freeway of freeway entrances entrances andand exits exits is highest is highest during during the theOPEP OPEP and and the thelowest lowest during during the the EPP. EPP. 6. Conclusions 6. Conclusions Accessibility to an external freeway network from an urban road network is important, Accessibility to an external freeway network from an urban road network is im- especially for outbound transportation of the city. However, although a large number of portant, especially for outbound transportation of the city. However, although a large studies has explored accessibility from various perspectives, few accessibility analyses of number of studies has explored accessibility from various perspectives, few accessibility urban road-to-freeway interchanges have been reported. To fill this research gap, this paper analyses of urban road-to-freeway interchanges have been reported. To fill this research presents a dynamic accessibility analysis of urban road-to-freeway interchanges based on navigation map path data, which reflect the accessibility of the freeway network by analyzing the accessibility of urban road-to-freeway interchanges (i.e., freeway entrances and exits). It can help cities measure their dynamic accessibility for people in the city using the freeway resources and support decision making on where to improve accessibility and for which travel hotspots in the city. The methodology proposed in this study uses the data from the navigation map path, which has the characteristics of easy availability. Besides the travel time, travel distance and the number of traffic lights are both considered in the travel impedance model. The central urban area of Zhengzhou city is taken as the case study. Dynamic accessibility of 17 travel hotspots in the city for 26 outer freeway entrances and exits are analyzed. Four different periods are selected: MPP, OPAP, EPP, and OPEP. It is found that accessibility varies over time. Furthermore, the accessibility of Erqi District is always at the lowest level. As the central area of the city, Erqi District has greater travel demand, which influences the traffic condition and further the accessibility of the freeway network. During off-peak periods, the accessibility of the westward area is lower than that of the eastward area, which is because Zhengdong New District is a newly developed area, the urban road networks and traffic facilities of which are better. Sustainability 2021, 13, 372 16 of 17

However, there are still limitations in this study, which motivates future research directions. First, there is a limitation pertaining to the sample size used in this study, which is just large enough to yield reliable results and capture some medium effects. It may be necessary to collect data from a much larger sample in future studies. Second, further studies can be carried out about using AHP (analytic hierarchy process) or other MCDM (multi-criteria decision making) techniques to determine the weight coefﬁcients. Third, building the model for simulation, including for example other freeways, weather, and connecting restrictions connected with collisions and required speed reductions, also can be combined for accessibility analysis. Moreover, there is currently no literature on dynamic accessibility considering travelers’ preferences, which can be important future work for us to do. Finally, based on the methodology framework proposed in this study, it is not difﬁcult to further extend this study by adding relevant factors that consider demand and different travel modes (e.g., public transport users or other mobility sharing services), which is regarded as our important future work.

Author Contributions: Conceptualization, D.W.; methodology, Y.Y.; validation and writing, T.G.; writing and review, Y.Y. All authors have read and agreed to the published version of the manuscript. Funding: There is no external funding. Institutional Review Board Statement: Not applicable. Informed Consent Statement: Not applicable. Data Availability Statement: Data can be provided upon request from the corresponding author. Acknowledgments: This research was supported by the National Natural Science Foundation of China (No. 51678535), the Youth Talent Support Program of High-Level Talents Special Support Plan in Henan Province, and the Foundation for University Young Key Teacher by Henan Province (No. 2018GGJS004). Conﬂicts of Interest: The authors declare no conﬂict of interest.

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