# Measuring spatiotemporal accessibility to healthcare with multimodal transport modes in the dynamic traffic environment

• Xinxin Zhou , LinWang Yuan , Changbin Wu , Zhaoyuan Yu and Wang Lei
From the journal Open Geosciences

## Abstract

Research on healthcare accessibility is developing with a focus on multimodal transport modes (MTMs) and multiple time-series variations. A dynamic traffic environment leads travelers to make distinct decisions at different time slots, which impacts spatiotemporal accessibility markedly. Our article proposes a methodological framework to measure spatiotemporal accessibility with multimodal transportation modes and its variation at multiple time series, while accounting for traffic congestion and the probability of residential transport mode choices in a dynamic traffic environment. We selected Nanjing, China, as the study area and pediatric clinic services (PCS) as specific healthcare services to estimate the spatiotemporal accessibility at four representative time slots. The results indicate that the weight estimation of travel time based on MTMs is more propitious than the travel time of single-mode to present real-world travel characteristics and reflects the spatiotemporal distribution and variation of services synthetically. Furthermore, the spatiotemporal accessibility variation of PCS in peripheral suburbs is more pronounced than that in urban centers and rural areas. This work holds pragmatic implications for policymakers in terms of services planning and allocation optimization to improve the equity of resource supply.

## 1 Introduction

As potential opportunities for the spatial interaction of geographical entities, the accessibility of services, including healthcare services [1], social amenities [2], emergency services [3], and so on, is widely used in Geography, Urban Studies, and Transportation Research [4,5]. Spatiotemporal accessibility, as one of the foremost directions of accessibility research, considers spatial location and time indicators to evaluate the effectiveness of services. In spatial interaction measurement, the travel impedance factors, commonly including the travel time, distance, and expense of transport modes, are among the fundamental indicators of accessibility, accompanied by the quality/quantity of opportunities [6].

Traditionally, the travel impedance is based on the measurement of single-mode travel time or distance and is commonly calculated by the network analysis in the Geographic Information Systems platform [7,8,9]. There is an underlying assumption of those acquisition methods that residents travel to services through uniform transport mode, which is unrealistic and inevitably introduces errors in accessibility estimations [10]. Meanwhile, the theoretically limited speed [11] neglects travelers’ multimodal preferences between different supply (destination) locations and the demand (origin) locations, preventing accessibility estimations for service planning from offering practical value.

As transportation systems become more diversified, accessibility research based on residents’ mobility becomes more complicated [1,12,13]. To date, some accessibility studies have paid attention to integrating multimodal transport modes (MTMs) into accessibility measures, and this has proven that MTMs are more beneficial for realistic accessibility estimations than single models [14]. However, empirical studies have not been conducted that simultaneously consider the influence of dynamic traffic conditions on travelers’ multimodal choices at different time slots. Dynamic traffic conditions, including traffic congestion [15], public transportation (PT) timetables, intersection delays, searching for parking spaces, time-limited exclusive bus lanes, multijunction crossroads, pedestrian systems separated from vehicle systems, and the required walk from/to one’s car, are also non-negligible factors for implementing sophisticated spatiotemporal accessibility, which is urgently needed for quantitative identification and analysis [15,16,17,18,19]. Meanwhile, when residents travel, they will choose different modes of transportation according to the time of travel, the distance to the destination, the economic cost, and the traffic congestion. Residents’ transportation mode generally has the characteristics of probability selection, non-uniformity, and fluctuation at different moments. However, the influence of travelers’ multimodal choice preferences based on the dynamic traffic environment was ignored in predecessors’ research. It has been difficult for accessibility research to measure the travel potential opportunity of services with residential MTMs at different time slots in the dynamic traffic environment. This research gap poses a considerable challenge to obtaining a comprehensive understanding of spatiotemporal accessibility.

In light of the above limitation, this article will fill the gap in investigating the effects of travelers’ multimodal choices and improve travel impedance’s rationalization. It is one of the primary methodology contributions in our article that evaluates the probability of choosing transportation mode at different time slots quantitatively, namely, the weight estimation of travel time with MTM (WETT-MTM) model, according to the travel time, the distance, the economic cost, and the traffic congestion coefficient. Furthermore, it reveals the dynamic variation of spatiotemporal accessibility of specific healthcare services when selecting pediatric clinic services (PCS) in Nanjing, China. This article is organized as follows: we provide a study area and data overview in Section 2 and the methodology in Section 3; the results are as shown in Section 4; and we end with a brief conclusion and discussion in Section 5.

### 1.1 Related literature review

#### 1.1.1 Spatiotemporal accessibility of healthcare services

The research progress in the spatiotemporal accessibility of healthcare can be summarized from two perspectives: the business field and the methodology field.

In the accessibility business field, the accessibility of healthcare is a multifaceted field that involves primary healthcare [20], access to healthcare in rural areas [21,22], the cross-border spatial accessibility of healthcare [23], the spatial equity of multilevel healthcare [24], hospital care and emergency medical services [1,3], and mental health in childhood and adolescence [25]. Because primary healthcare is closely related to life, relatively inexpensive, and efficiently delivered, primary care has received extensive attention [26]. The other burgeoning thread of research has shifted the focus to accessibility measures for different age groups, highlighting age-level differences, like those between children and older people [8]. PCS resources face high scarcity due to pediatrics’ particular features, especially in developing countries [27,28]. In 2016, the State Health and Family Planning Commission of China issued guidelines for strengthening the reform and development of children’s medical and healthcare services[1]. PCS spatial accessibility is one of the typical and meaningful issues within research on the accessibility of healthcare services [29,30,31], which prompts us to choose PCS as the research object.

In the accessibility methodology field, we can categorize the accessibility models into two categories: place-based (i.e., residential community) and individual-based (i.e., residential individual) accessibility models classified by the number of residents studied [32]. The place-based accessibility measures mainly include cumulative opportunity models and gravity models [33] and the two-step floating catchment area method (2SFCA) [34] and evaluate the opportunities from demand locations to surrounding supply considering the travel impedance [35]. Luo and Wang [34] first proposed 2SFCA, one of the most popular accessibility estimation methods, to measure healthcare’s spatial accessibility. A new wave of development based on the 2SFCA model was widely developed until Wang unified the various accessibility models into the generalized 2SFCA and five types of the expanded form [36]. Individual-based accessibility measures, relying on the construct of the space–time prism in time geography [5,37], have been proposed to represent an individual’s ability to reach opportunities given their motility constraints [35]. More comprehensive accessibility measures, including integrating time and transport modes from open data[38], multitemporal transport network models [39], and a multimodal relative spatial access assessment approach [12], are becoming a critical development branch of dynamic environment changes in spatiotemporal accessibility.

#### 1.1.2 Residential transport mode choices with MTMs

Traditionally, accessibility studies look towards subjectively choosing specific transportation modes [36], but an increasing number of scholars have begun to improve accessibility models by considering the influence of different transport modes [40]. Travel impedance data can be accessed from open data sources [41,42], including individual trip survey data [10], web mapping services (Google Maps [40], Baidu Maps [43], and Amap Maps [44]), and location-based social media data [14], which enable advancements in revealing the characteristics of human activities [45,46,47]. Open data sources provide fine-scale and dynamic spatiotemporal big data for accessibility research [48]. Web mapping services provide a more accurate approach for obtaining travel impedance data between origin and destination [17]. In addition, web mapping platforms have integrated multiple traffic conditions, including fundamental traffic flow principles and historical traffic data, through large-scale users’ behavior data based on mobile Apps [49] and record realistic multimodal transport information [50]. New accessibility models have been developed, such as multimodal 2SFCA [10], a variable-width floating catchment area model [40], multimodal 2SFCA incorporating the spatial access ratio [12], and multimodal accessibility-based equity assessment [11]. However, the influence of travelers’ multimodal choice preferences based on different traffic conditions is ignored in multimodal accessibility research. For example, people usually prefer to bicycle or walk to a hospital if it is less than 5 km away in the case of heavy traffic congestion during commuting time. Inversely, people are more likely to take PT or drive to the hospital, which is far away. Land use mix, population density, and employment density have been proven to influence the multimodal choices for life trips [51].

A multitude of factors, including travel experience [52], travel purpose [53], real-time traffic information [53,54], departure time urgency [55], travel time, and travel distance [56], would all impact residents’ multimodal choice preferences for different transport modes. It appears that there have been fewer experiments on accessibility that consider the influence of residential transport mode choices. One of the key tasks of our article will focus on calculating the probability distribution and combination value of residential transport mode choices and establishing a probability to obtain WETT.

## 2 Study area and data

### 2.1 Study area

With an area of 6,587 km2 and a population of 8,335,000, Nanjing is one of the most significant cities in China. Nanjing, the capital of Jiangsu Province, and the national gateway city for the Yangtze River Delta’s central and western regions (Figure 1), is a world-famous historical and cultural city. In terms of population, as of 2016, the urbanization rate of Nanjing was 82.29%. In terms of transportation, various transport modes coexist, and they are high in number: there are 8,395 buses and trolleybuses and 14,239 taxis. The total length of the Nanjing metro was 381 km at the end of 2015. In addition, there were 2,540,000 personal vehicles in Nanjing and as many as 650,000 and 3,000,000 shared bicycles and e-bikes, respectively, at the end of 2018.[2] The Nanjing traffic road network’s improvement level is at the forefront for China, with a per capita road area of 21.81 m2, far exceeding the national average of 15.6 m2 [57]. In terms of medical services, Nanjing’s medical and health system is flourishing, comprehensive medical resources are relatively abundant, and the overall health services rank behind only Shanghai and Beijing in China. There are 241 public hospitals in Nanjing, of which 22 are top-tier hospitals (3A-hospitals). However, pediatric medical resources in Nanjing are still scarce (Section 2.2.3). Therefore, Nanjing is selected as a metropolitan research area considering its regional representativeness and prominent contradiction. We used the whole administrative scope of Nanjing to generate basic research grids (the total number being 6,936 and cell size being 1 km × 1 km) to facilitate research.

Figure 1

The study area.

### 2.2 Data

Three types data were collected through an open-source approach, including online route planners’ data, spatial distribution data of the population, and PCS data. According to the 2021Q1 Traffic Analysis report of Major Cities in China[3], we selected four typical time slots in the daytime, including 8:00 (morning rush peak), 13:00 (off-peak in noontime), 18:00 (evening rush peak), and 22:00 (off-peak in nighttime) in Nanjing, which is in UTC+8. These four time slots can effectively manifest the dynamic performance of the traffic environment.

#### 2.2.1 Route planning data for MTMs

The route planning API is feasible for travel impedance calculation [17]. The travel impedance requested from the web mapping platform is a historical average; thus, it offers valuable and credible predictions for research purposes and is more accurate in considering the traffic conditions and congestion time loss for actual location data [41]. We selected Amap Maps (www.amap.com) as a data source, as it is one of the most popular web mapping platforms in mainland China. The API returned results for the prescribed transportation modes are the most recommended route path considering time and distance.

To visualize the travel time variation of multimodal at different time slots, we select Nanjing Children Hospital, Guangzhou Branch, as a destination example to show the variation in travel times from full grids at different time slots in 1 day (Figure 2). The travel time variability of different travel modes has apparent differences. The most variable is driving, followed by PT, while walking and bicycling are not affected by different time slots. The travel time of PT has little effect on the morning and evening peak hours. The travel time at 22:00 is more prolonged. The travel time at night is significantly lower than the travel time during the daytime. The above exploratory analysis of online route planning data to Nanjing Children Hospital, Guangzhou Branch, indicates the diversity of the traffic environment.

Figure 2

The travel duration from different origins to Nanjing Children Hospital, Guangzhou Branch, based on four transport modes at four time slots. (a1) PT 08:00, (a2) walking 08:00, (a3) bicycling 08:00, (a4) driving 08:00, (b1) PT 13:00, (b2) walking 13:00, (b3) bicycling 13:00, (b4) driving 13:00, (c1) PT 18:00, (c2) walking 18:00, (c3) bicycling 18:00, (c4) driving 18:00, (d1) PT 22:00, (d2) walking 22:00, (d3) bicycling 22:00, and (d4) driving 22:00.

#### 2.2.2 Spatial distribution data of the population

The spatial distribution data of the population is one of the essential indicators for realizing spatiotemporal accessibility [44]. Similarly, the spatial distribution data of children is the key to evaluate the spatiotemporal accessibility of PCS. In past studies, each administrative unit’s demographic data was commonly used to represent the population directly. The shortcomings of this approach are high data granularity, discrete spatial distribution, and low accuracy. We obtained population spatial distribution data from Tencent Suitable for Travel Platform (TSTP), based on Tencent apps’ user density data. The Tencent apps’ user density data are one of the most popular population data sources in social media data [58,59,60]. They are provided by Tencent (http://www.qq.com), one of the largest internet companies both in China and globally [61]. Seven million seven hundred sixty-nine thousand population data points were requested from TSTP, slightly lower than the 8,335,000 total population found in the statistical yearbook [62]. Because some older adults and young children do not use smartphones and Tencent apps, this error can be explained and accepted. Therefore, requesting and counting TSTP data can reasonably indicate the regional population distribution. We chose the Sixth National Population Census tabulation in China [63] to obtain the proportion in each district and convert proportionally to obtain the percentage of children in each district in 2017 (Figure 3). The spatial population of children is concentrated in the main urban area, with high values distributed together and uneven spatial distributions. The hotspots are centralized in the regions along with the arterial networks of the main urban area.

Figure 3

The spatial distribution map of children in Nanjing.

#### 2.2.3 Healthcare services data

Twenty-six hospitals in Nanjing have established pediatric services, but these services have significant differences in their treatment ability. To effectively measure the pediatric scale of various hospitals considering the availability of data, we estimate the hospitals’ pediatrics level by the number of pediatricians. The number of pediatricians is taken from the Good Doctor website (https://haoping.haodf.com/keshi/3030000/faculty_jiangsu_nanjing.htm). The statistical results are expressed in the form of spatialized drawings (Figure 1(d)). The results show that the total number of pediatric doctors in Nanjing was 603. Compared with 904,000 children [62], the average number of pediatricians per 1,000 people was approximately 0.67. According to the 2015 China Health Statistics Yearbook, the average is 0.43 pediatricians per 1,000 children in China in the past 5 years. Although the average number of pediatricians per 1,000 people in Nanjing is higher than the average for China, it is still far below that in the principal developed countries, which have a ratio reaching 0.85–1.3 pediatricians per 1,000 children.

For the number of pediatricians in each hospital, the number of pediatricians in Nanjing Children Hospital, which consists of Nanjing Children Hospital, Guangzhou Branch (Figure 1(d) “GZ” annotation), and Nanjing Children Hospital, Hexi Branch (Figure 1(d) “HX” annotation), is the largest, including 392 pediatricians and accounting for 65% of the total number of pediatricians in Nanjing. The maximum number of outpatient visits in Nanjing Children Hospital exceeds 11,000, and even the number of outpatient clinics in the evening is over 1,000. From the spatial distribution, the hospitals containing PCS are mainly concentrated in the Gulou District, which is the core urban area of Nanjing and has many essential departments, educational resources, and commercial centers.

## 3 Methods

The proposed methodological framework for spatiotemporal accessibility is shown in Figure 4.

Figure 4

Step 1: Basic data preprocessing (Figure 4I): Through the spider programs for Amap Maps, TSTP, and the Good Doctor website, we obtain the primary data and use basic data processing methods to obtain spatial grids, population data, and hospital data.

Step 2: Online route planning data requesting (Figure 4II): The input data are each origin–destination flow with four transport modes (PT, driving [including taking a taxi], bicycling, and walking). The online route planning data are obtained from the Amap route planning API program at four time slots (Section 2.2.1).

Step 3: The WETT-MTM model designing (Figure 4III): The WETT-MTM model calculates the WETT based on MTMs and the spatiotemporal variation in the WETT will is analyzed with an empirical destination.

Step 4: Spatial distribution data of population measurement (Figure 4IV): The spatial population distribution data of children are generated from the users’ density data from TSTP (Section 2.2.2).

Step 5: Accessibility model calculation (Figure 4V): We adopt the gravity model to calculate the accessibility values at four time slots.

Step 6: Results in analysis (Figure 4VI): The spatiotemporal accessibility characteristics were analyzed and compared to explore the spatial distribution and temporal variation of accessibility.

### 3.1 WETT-MTM model

As we all know, an individual tends to use specific transportation modes when traveling. However, considering individual and traffic environment differences, resident groups present different travel mode choices at the macro level. When individual differences are superimposed as group characteristics, they are characterized as superposition benefits of polymorphism, which sociological research has widely recognized. So the WETT-MTM model is an innovative estimation method of the probability weight method that considers affecting factors and calculates travel time’s weight estimation in the dynamic traffic environment (Figure 5). The theoretical premise of the WETT-MTM model is that MTMs widely exist in each origin–destination trip, while the difference lies in the probability of selection. The probability of choosing between different transport modes is mainly affected by travel time, distance, and dynamic traffic factors. It is a complex problem to determine the weight of each factor in the multi-factor superimposed benefit, according to the factor differences of each origin–destination trip, such as with the highest utility due to the difference of high urgency, short travel time, road traffic density, and economic cost during travel. The detailed design of the WETT-MTM model explicitly includes four steps. The input data is online route planning data, and the output result is the WETT.

Figure 5

Step 1: Transport utility function definition (equation (1))

The traveler selection behavior is in the constraint space–time of finite conditions, so the utility function can be employed to establish the travel mode selection behavior model based on the space–time constraint. The basic premise that the travel utility function satisfies is that residents will choose the transportation mode with the highest utility due to the difference of high urgency, short travel time, road traffic density, and economic cost during travel. The travel utility function Z r t ( ij ) aims to quantitatively depict the travel utility between time t , transportation mode r , demand location i , and supply location j . The higher the utility value indicates, the greater the value of this mode of transportation between demand location i and supply location j , and the greater the selection probability will be calculated by the input into the Softmax function.

(1) Z r t ( ij ) = ε h r t ( ij ) * γ r t ( ij ) * β r ,

where, ε represents the degree of urgency. We are aware that the degree of urgency varies between different parts or activities of the city. Daytime trips for medical services are normalized outpatient clinics, and nighttime trips for medical treatment are mostly emergencies. Therefore, the degree of urgency for day trips is relatively lower than that of late-night trips. After stability testing, we decided to use two empirical values, ε = { 10,12 } , for daytime and nighttime, respectively. γ r t ( ij ) represents the traffic congestion coefficient of transport mode r at time slot t from demand location i to supply location j ; h r t ( ij ) represents the travel duration of transport mode r at time slot t from demand location i to supply location j ; β r represents the economic cost factor of transport mode r .

Step 1.1: Traffic congestion coefficient ( γ r t ( ij ) ) measurement (equations (2) and (3))

Researchers apply a value to measure the degree of spatiotemporal change to directly reflect the comprehensive spatiotemporal variation in geographical features [64]. The dynamic index is widely used in land use type change, as it can depict the general characteristics of the spatiotemporal variation in land use type over multiple years [65]. Based on this inspiration, we design γ r t ( ij ) (equation (2)), the traffic congestion coefficient of demand location i to supply point j , and γ r t ( i ) (equation (3)), traffic congestion coefficient of demand location i , to estimate the traffic congestion as follows:

(2) γ r t ( ij ) = 1 T · t = 1 T h r t ( ij ) h r t 0 ( ij ) h r t 0 ( ij ) , h r t ( ij ) > h r t 0 ( ij ) 0 , & h r t ( ij ) h r t 0 ( ij ) ,

(3) γ r t ( i ) = i = 1 M γ r t ( ij ) ,

where h r t 0 ( ij ) denotes the benchmark of travel duration of transport mode r at time slot t 0 from demand location i to supply location j . Considering nighttime peak being the lowest traffic congestion, our article selects 22:00 as t 0 . T denotes the sum of time slots, being 4 in this article. M denotes the total number of supply points.

Step 1.2: Economic cost factor conversion

The β r , whose unit is expenditure (dollars per km), indicates the economic cost factor for integrating different transport modes. The economic cost factor refers to the trade-offs between the uses of resources [66,67]. The design of β r has had a major adjustment impact on the calculation of WETT-MTM. We use fixed vehicle costs and variable vehicle costs as the users’ money costs. Therefore, the indicators are: average car $0.15, diesel bus:$0.08, bike: $0.03, and walk:$0.01 [66,67]. We establish β r to be {public transportation = 0.08, walking = 0.01, driving = 0.15, bicycling = 0.03}. β r is a negative indicator, and the larger β r is, the lower the residential transport mode choices probability value.

Step 2: Transport mode selection probability P ir t (equation (4))

The Softmax function, also known as the normalized exponential function, generalizes logic functions in probability theory and machine learning fields. It can contain one with any K dimension vector Z , “compress” to another R dimension vector σ ( Z ) (Figure 6). Therefore, every element has a range in ( 0 , 1 ) , and the sum of all elements is equal to 1. The Softmax function is a gradient log normalization of a finite item discrete probability distribution. Therefore, the Softmax function includes multiple logistic regressions, multiple linear discriminant analyses, and a naïve Bayes classifier with artificial neural networks. It has a wide range of applications in various probability-based multiclassification problem methods.

(4) P r t ( ij ) = P ( Z r t ( ij ) ) = e Z r t ( ij ) r = 1 R e Z r t ( ij ) ,

Figure 6

Softmax schematic diagram.

Among them, r = 1 , , R .

Step 3: Calculate WETT t ( ij ) (equation (5))

We apply the weight P r t ( ij ) multiplied by the travel time h r t ( ij ) , then weightily sum by different transport modes to obtain WETT t ( ij ) .

(5) WETT t ( ij ) = r = 1 R h r t ( ij ) * P r t ( ij ) ,

### 3.2 Accessibility model

Our spatiotemporal accessibility research focuses on place-based spatiotemporal accessibility measurements based on residents’ mobility and time slot variations. Among place-based accessibility measurement models, the gravity model is the most widely used [11]. The gravity model, also known as the potential and potential energy models, is derived from Newton’s law of universal gravitation and was proposed by Hansen in 1959 [68]. Hansen introduced the concept of spatial accessibility when analyzing the population distribution of the urban population and the spatial accessibility indicators of residential land. He offered a calculation model of spatial accessibility that used the potential indicators to evaluate spatial accessibility [69]. As a particular form of generalized 2SFCA models, the gravity model belongs to the same theoretical framework as 2SFCA [34]. Both aim to evaluate the physical accessibility to services based on the spatial interaction between supply and demand locations. However, the gravity model adopts the continuous distance attenuation function, while the 2SFCA model adopts the dichotomy method to address the distance attenuation.

The model expression is as follows:

(6) A i = j = 1 M E j f ( d ij ) V j ,

where A i denotes the spatial accessibility of demand location i ; E j denotes the number of pediatricians indicates the service resource supply capacity of supply point j ; M denotes the total number of provider locations.

The spatial accessibility of urban services is determined by both supply and demand sides, while equation (6) only considers the supply points and does not consider the demand locations, which gives rise to the same traffic impedance d ij . Assuming that the attraction of the two supplies E j is equal, the difference in the population of the two supplies does not affect the size of the spatial accessibility at this time, which is not consistent with the facts. To solve this problem, V j , the impact factor of population size, was introduced and can be extended as follows:

(7) V j = k = 1 N Q k f ( d ij ) ,

In summary, the potential model is written as follows:

(8) A i = j = 1 M E j f ( d ij ) V j = j = 1 M E j f ( d ij ) k = 1 N Q k f ( d ij ) ,

where N is the total number of demand locations; Q k is population number at demand location k (unit: 1,000 people, consistent with the dimensions in the previous data description); d ij is the traffic impedance between demand location i and supply point j ; d kj is the traffic impedance between demand location k and supply location j .

(9) f ( d ij ) = d ij σ , d ij d 0 , d ij > 0 ,

where d 0 is the catchment size (i.e., threshold travel time); considering the WETT implying dynamic traffic conditions and reducing filter degree from catchment size, we define d 0 like 2 h, the median value as shown in Figure 9; σ is the coefficient of travel friction, selected as 1 [70].

## 4 Results

To clearly state the dynamic consequence of the WETT-MTM model, we will divide the results into two parts: Part I – base exploration results and Part II – spatiotemporal accessibility results (Figure 7). Wherein, base exploration includes traffic congestion analysis (Section 4.1) and an empirical example of WETT-MTM (Section 4.2). Spatiotemporal accessibility results organize into reference scenario comparison (Section 4.3) and variation scenario comparison (Section 4.4). The reference scenario compares the impact on accessibility between PT and MTM. Nevertheless, the variation scenario comparison compares the dynamic variation in temporal and spatial accessibility brought about by WETT-MTM at different time slots to reveal the changes brought about by the dynamic urban traffic environment.

Figure 7

The organization of results.

### 4.1 Analysis of traffic congestion

First, we performed the calculation γ r t ( ij ) on each origin–destination trip by equation (2) at different time slots to estimate the essential characteristics of four transport modes (Figure 8). One interesting finding was that the traffic congestion of PT and driving is higher than bicycling and walking obviously, which is consistent with our common sense. So we only consider traffic congestion for driving and PT. But another unfamiliar finding was that while the traffic congestion of driving crowds together, the traffic congestion of PT appears to be partial extremum, which surprises us. To further explain this phenomenon, we adapt equation (3) to calculate the traffic congestion of driving and PT on the grid separately (Figure 9). The distribution area and driving range surpassed PT in traffic congestion. They showed a typical center-periphery pattern since it is possible to access more opportunities from central locations than from peripheral areas.

Figure 8

Traffic congestion coefficient of four transport modes.

Figure 9

Traffic congestion spatial distribution maps of driving mode and PT mode. (a) Traffic congestion coefficient of Driving mode. (b) Traffic congestion coefficient of PT mode.

Conversely, PT congestion presented discrete islands of distribution, and some locations were unusually high, mainly in the peripheral suburbs. The driven reasons are that PT is diversified, including the subway, bus with bus-only lanes, light rail, among them, the dense urban subway, light rail distribution, both of which are not affected by road traffic congestion. However, PT in the peripheral areas mainly relies on the bus. Road congestion, combined with the route, is very long in the morning and evening, so the accumulative effect of traffic congestion causes the formation of extremum congestion areas.

### 4.2 An empirical example of WETT-MTM

We selected all grids as the origins and chose Nanjing Children Hospital, Guangzhou Branch, as a representative pediatrics hospital to visualize the spatiotemporal patterns and changes of WETT directly from all demand locations (Figure 10). The natural interval rules of the legend in Figure 10 are consistent with Figure 2 to facilitate the comparison of the difference between WETT and the travel time of each traffic mode at different time slots. In terms of timing sequence, the WETT at 22:00 is the smallest. The value of the WETT at other different time slots has significant volatility, and the weight of travel time will be higher in the morning and evening peak periods. When calculating the value of WETT for the whole research area, the degree of participation in walking and bicycling is relatively low.

Figure 10

The WETT from different origins to Nanjing Children Hospital, Guangzhou Branch, at four time slots. (a) WETT 08:00, (b) WETT 13:00, (c) WETT 18:00, and (d) WETT 22:00.

In comparison, walking and bicycling mainly calculate the main urban area. The potential reason could be that urban travelers have more alternative transport modes based on the well-developed traffic network [71], longer public transport service schedule time [18], and relative proximity to Nanjing Children Hospital, Guangzhou Branch. However, due to being far from Nanjing Children Hospital, Guangzhou Branch, and the imperfect public transport system, the WETT in suburbs and rural areas is volatile and variable.

### 4.3 Reference scenario comparison

At 22:00 considered, we make a cartographic comparison and accumulation graph between accessibility based on WETT-MTM (Figure 11(a) and 13(c)) and accessibility based on PT (Figure 11(b) and 13(e)) in the reference scenario.

1. The spatial distribution of the spatiotemporal accessibility of PCS values indicates that the main urban districts present a high value, form a continuous piece and spread out to have lower spatiotemporal accessibility of PCS. The peripheral districts are relatively low. The accessibility of PCS presents double kernels (the dual cores are Nanjing Children Hospital, Hexi Branch, and Nanjing Children Hospital, Guangzhou Branch, respectively) and gradually diffuses downward.

2. The spatial obstructing effect of the Yangtze River is noticeable. The spatiotemporal accessibility of PCS in the northern part of the Yangtze River is lower. It is affected by the water space barrier and limited pediatric medical resources. The spatiotemporal accessibility values in the area north of the Yangtze River are distributed along with the arterial networks, indicating that traffic conditions are essential to spatiotemporal accessibility.

3. We find that Figure 11(a) (the maximum and minimum values being 4.427 and 0.0049, respectively) is higher than Figure 11(b) (the maximum and minimum value being 1.676 and 0, respectively) in terms of global. A more interesting phenomenon is that the zero value based on PT at 22:00 is as high as 1,137 grids.

4. From the maps’ distribution, it can be found that the accessibility based on WETT-MTM at 22:00 for medium-value and high-value radiation areas greater than 0.4 increased. In addition, the distribution effect of Figure 11(a) along the main traffic arteries is relatively weakened than Figure 11(b).

Figure 11

Reference scenario maps at 22:00. (a) 22:00 based on WETT and (b) 22:00 based on PT.

These distribution results show that the WETT-MTM model is more comprehensive than a single transportation mode. In urgent travel needs, travelers tend to choose more efficient and convenient transportation, which is limited in the available PT. The WETT-MTM model can schedule and select the optimal travel modes of different demand locations, which is also in line with the actual travel situation. Therefore, the WETT-MTM model is more suitable for estimating accessibility than considering a single transportation mode.

### 4.4 Variation scenario comparison

The explanation for temporal changes in spatiotemporal accessibility resides in the dynamic traffic environment. The maps of variation scenario (Figure 12) show that temporal variation exerted a very disparate effect on different demand locations, such as Y1, Y2, and Y3 areas in Figure 12(a). In the Y1, Y2, and Y3 areas, the accessibility value is the lowest in the morning peak period. With the arrival of the off-peak and evening peak, the accessibility value presents an earlier increase and later decrease trend. The evening peak accessibility is still better than that of the morning peak and primarily consists of return journeys home or trips for shopping and leisure. We can also find that the areas with dense variation mainly focus on the peripheral suburbs, but the main urban and rural areas do not have significant variation. The Y1, Y2, and Y3 areas are adequate proof. The low-value spatiotemporal accessibility and high-value variation are concentrated in the peripheral suburbs. The potential reasons for this are that pediatric clinical services are scarce, and PT is inadequate. Most of these travelers’ daily emergency medical travel by bus or driving. Therefore, the traffic congestion accumulation effect is more prominent and makes travelers more sensitive to spatiotemporal accessibility. Although the main urban areas are the prominent locations of traffic congestion, there are diversified alternative modes of transportation. For example, bicycling is a good and stable way to travel with less disturbance. So the main urban areas present a stable and high-value distribution of accessibility. Due to the importance of the WETT considering residential transport mode choices, this finding is just the opposite of traffic congestion in Figure 9.

Figure 12

Variation scenario maps at three time slots. (a) spatiotemporal accessibility at 8:00, (b) spatiotemporal accessibility at 18:00, and (c) spatiotemporal accessibility at 13:00.

To present the spatiotemporal accessibility of PCS cumulative distribution of each time point, we have drawn a hist graph (800 bins) and divided it into four intervals containing the lowest value interval (0–0.2), the median interval (0.2–0.4), the second-highest value interval (0.4–0.6), and the highest value interval (>0.6) (Figure 13). At different time slots, the variation is also concentrated in the lowest and median areas. The trend of the highest and second-highest value intervals tends to be stable.

Figure 13

The spatiotemporal accessibility histogram graph results from different origins to all pediatric hospitals at four time slots. (a) Spatiotemporal accessibility value at 08:00 with MTM, (b) Spatiotemporal accessibility value at 13:00 with MTM, (c) Spatiotemporal accessibility value at 18:00 with MTM, (d) Spatiotemporal accessibility value at 22:00 with MTM, and (e) Spatiotemporal accessibility value at 22:00 with public transportation mode.

## 5 Discussion and conclusion

In this article, we have designed a methodological framework of spatiotemporal accessibility based on online route planning data, which can effectively estimate the spatiotemporal variation characteristics of PCS at different time slots. The dynamic traffic environment would have an overall disturbance effect on the accessibility of services and spatiotemporal heterogeneity. We found three exciting patterns. (1) The traffic congestion of driving crowds together and showed a typical center-periphery pattern, nevertheless the traffic congestion of PT appeared partial extremum and presented discrete islands distribution. (2) The WETT-MTM model is more comprehensive than a single transportation mode in the reference scenario. (3) The low-value spatiotemporal accessibility and high-value variation are concentrated in the peripheral suburbs. The methodological framework of spatiotemporal accessibility of PCS can offer policymakers and planners implications regarding the dynamic accessibility of healthcare services. Typical application directions include optimizing the spatial relocation of hospitals to reduce urban traffic congestion [72], optimizing healthcare services location–allocation problems [73,74], reducing the spatial inequity of multilevel healthcare services [75], and improving the spatial equity of multilevel healthcare in the metropolis [24], which will facilitate movement to optimize the allocation and equity of healthcare services.

The WETT-MTM model proposed in our article has the characteristics of probability selection, non-uniform, and fluctuation at different moments. This model, which sufficiently considers residential transportation mode choices based on dynamic traffic conditions, is a vital component of spatiotemporal accessibility research. This work has filled the gap in modeling travelers’ choices on MTMs integrated with dynamic traffic conditions and improved the incorporation of travel impedance in the spatiotemporal accessibility model. The WETT-MTM model overcomes the singleness or absoluteness of transport mode selection in traditional accessibility research. The disturbance of the WETT value at different time slots has shown a dynamic change, and the peripheral disturbance is evident further away. The WETT-MTM model transforms the equally weighted transport mode into a probabilistic combination of MTMs, analogous to the development of classical physical space into quantum physical space [76]. This methodological framework, wholly based on the open-source data of the internet, can be applied to other cities and regions to evaluate the spatiotemporal accessibility of services, such as medical facilities, parks, and commercial and science facilities. The framework holds pragmatic implications for policymakers on the spatiotemporal accessibility regarding the plan and allocation optimization of special healthcare services to improve the equity of medical resources supply.

Several aspects of our further qualitative research work can still be improved despite the above implications. First, the analysis scale, the catchment size, and the distance decay function significantly influence the accessibility model [32]. A fine-scale or alterable scale cell size of the grid (e.g., community level and statewide) can be found with increasing research to avoid the impact of the modifiable area unit problem. Second, the proposed research framework suitable for the current situation evaluation will be further applied to location optimization of the new PCS plan with a heuristic algorithm and multi-objective location allocation. Third, all open-source research data caters to the real-time trend of Urban Big Data research based on social media data. We can quantitatively find more different spatiotemporal accessibility for PCS. We will also attempt to calibrate or validate the WETT-MTM model and explore commuter-based spatiotemporal accessibility based on dynamic commuting data and dynamic flow data from individuals simultaneously. In brief, travelers’ choice of MTMs with integrated dynamic traffic conditions should be worth considering to reveal the spatiotemporal accessibility of services.

## Acknowledgments

The authors would like to thank the anonymous referees and editor for their valuable comments, which significantly improved this article.

1. Funding information: This research was supported by the Fundamental science (Natural Science) research Project of higher education institutions in Jiangsu Province, grant number 22KJB420004 and the Open Foundation of Key Lab of Virtual Geographic Environment of Ministry of Education, grant number 2021VGE02.

2. Conflict of interest: The authors declare that they have no competing interest.

3. Ethics approval and consent to participate: All the data that are collected from the internet are open source, ethically free, and privacy-free. Also, the openness of data acquisition brings advantages for our research method to be extended to other cities.

4. Consent for publication: This manuscript does not contain any individual person’s data in any form (including any individual details, images, or videos), consent for publication.

5. Data availability statement: The dataset of spatiotemporal accessibility for pediatric clinical services can be available through https://figshare.com/s/f6e86f1367e44bd123b2.

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