Space-time Models and Personal Accessibility to Educational Facilities. Case Study of Space-time Accessibility to Schools in the City of Valencia

Society nowadays makes intensive use of time and extensive use of space. This has implications for spatial planning of facilities and services since it is now essential to look at personal accessibility (in terms of time and choice) and not just physical distance. Over and above spatial accessibility (distance or cost of travel to the facility or service), location models based on space-time accessibility also consider personal accessibility with respect to the time available to access a facility or service. The purpose of this research was to evaluate the practical usefulness of the theoretical approach grounded in the Geography of Time in enhancing personal accessibility to facilities and services which are provided in a specific space and at a specific time and have fixed start and end times, as is the case with schools. To this end, an ad hoc tool was developed to generate a number of scenarios simulating actual and hypothetical conditions for space-time accessibility to schools in the city of Valencia. The results showed how studying space-time accessibility may be extremely useful in drawing up proposals designed to increase personal accessibility to core services such as education and thereby helping to improve work-life balance.


Introduction: School Planning and Personal Accessibility to Educational Services
The main goal of educational spatial planning is to ensure that all pupils have equitable access to schools with respect to educational quality and accessibility by using school facilities efficiently (Price & Blair, 1989).School accessibility is affected by multiple socio-economic and spatial factors such as the geographical criteria for school place allocation (free choice of school or school district system), the income level of families, the school choice preferences or, as we will see in this paper, the spatio-temporal peculiarities of individuals.(Barthon & Monfroy, 2010;Manzo, 2013;Östh, Andersson & Malmberg, 2013;Millington, Butler & Hamnett, 2014;Murillo, Belavi & Pinilla, 2018;Fajardo, Salom & Pitarch, 2022).Ensuring equitable accessibility to educational services is essential to avoid school segregation processes and the adverse effects that result from it.
Two factors stand out in terms of spatio-temporal accessibility to schools: school and personal schedules and the locations of schools, homes and workplaces of parents.In the case of pupils in the second stage of pre-primary education (children from 3 to 6 years old), given their young age, the school journey requires the accompaniment of an adult who is usually one of the child's parents or another direct relative (Fajardo, Salom & Pitarch, 2022).Consequently, the access of a child to a school is shaped by the existence of schools with a timetable which is compatible with the fixed activities of the person accompanying the child, with working hours being the main limiting factor.Therefore, it is essential to know the patterns and timetable peculiarities of those responsible for accompanying children to school in order to establish measures for work-life balance that facilitate the performance of this task.
Furthermore, in addition to timetables, the locations of schools, children's residences and, as will be seen in this study, the work of the people in charge of accompanying children to school are also very important in terms of accessibility to schools.Most town planning studies locate users, in a broad sense, at their place of residence.However, it is often the location of the workplace rather than the home which determines the space-time accessibility of schools, and even other kind of services.This is because the two main activities which circumscribe the area of school accessibility are the school and the workplace, specifically the timetable in both cases.So, to improve accessibility to schools for working people and in addition to putting in place measures which help to enhance timetable compatibility, school network planners should design the layout of the school network taking into consideration the main areas where jobs are concentrated in the city.
For these reasons, the purpose of this study is to analyse how personal accessibility varies in schools that teach the second stage of pre-primary education (nursery schools) in the city of Valencia (Spain) from the point of view of spatial-temporal accessibility according to different factors.Specifically, the aim is to answer these two research questions: 1. What are the working and school schedules that are most conducive to spatiotemporal accessibility to schools? 2. How does the location of the workplace and home influence spatial-temporal accessibility to schools?
To answer these two questions, an ad hoc tool was developed to generate a number of scenarios simulating actual and hypothetical conditions for space-time accessibility to schools in the city of Valencia.Analysing the results derived in these scenarios made it possible to test the usefulness of the space-time approach and set out proposals which help towards improving personal accessibility to essential services such as education.

Approaches to the Study of Accessibility and its Application to School Planning
Accessibility rather than distance is a key explanatory variable for the location of most facilities and services, in particular for everyday services such as education.The concept of accessibility does not have a single meaning, although most of them refer to the ease with which it is possible to reach a destination.Therefore, accessibility may therefore vary between individuals depending on their capacity and aspirations even when the individuals coincide in space and time (Salado, 2004).Aspects such as income level (Neutens et al., 2010), ethnicity (Blázquez et al., 2010) or even gender (Kwan, 1999) may result in different levels of accessibility.
In geography, the study of accessibility is approached through the use of models.Models are simplified representations of reality that represent in a generalised way facets and relationships that occur in reality (Chorley & Haggett, 1967).There are two major schools of thought in the study of accessibility models to facilities or services: locational accessibility models and personal accessibility models (Salado, 2004;Miller, 2007).On the one hand, the former adopts the place-based perspective.In these models, accessibility is examined by measuring the physical separation between the locations where the desired activities take place and a key location in people's daily lives such as their home or workplace (Miller, 2007).Traditionally, these problems measure aspects such as the distance to the nearest opportunity (journey length, financial cost and/or time), the number of opportunities remaining within a particular area or at a given distance from a particular location, and the gravitational effect which increasing distance has on the attractiveness of services (Neutens et al., 2010).Many studies have been carried out from this perspective and applied to the field of educational planning using different models: multi-criteria models (Church & Schoepfle, 1993); dynamic models (Antunes & Peeters, 2001); hierarchical location models (Teixeira & Antunes, 2008); location-allocation models (Buzai & Baxendale, 2008).However, these studies do not take into account the opening hours of facilities or the space-time constraints of individuals (Neutens et al., 2010).
The second approach embraces the standpoint of personal accessibility and argues that, in addition to physical distance, there are also other explanatory factors (working hours, workplace, means of travel available, etc.) which may influence their accessi-bility (Higgs & White, 1997;Kwan, 1999;Salado, 2004).Within this current, studies based on the geography of time stand out.The pioneer in the study of the Geography of Time was Torsten Hägerstrand, who coined the term in his 1970 paper "What about people in Regional Science?" (Hägerstrand, 1970).In the geography of time studies, geographical aspects are ascribed to the actions of subjects across space and time.Accessibility is derived from detailed observations of each individual's space-time constraints, whereby accessibility varies over the course of the day and even from person to person (Kwan, 1999;Miller, 2007;Neutens et al., 2010).These barriers, coined by Haggett (1972) as the tyranny of space and time, constitute one of the main constraints to personal accessibility to urban services and facilities.This research traditionally follow the principles set out by Lenntorp (1978) and examine whether or not individuals' activity logs are compatible with the space-time constraints imposed by urban space and the performance of fixed activities and then classify the options as accessible or non-accessible.Other papers build on Miller (1999) and measure the desirability of using opportunities in terms of travel time, how attractive the facility or service is and the potential length of the activity.Studies of school accessibility carried out under this approach are not as abundant as in the previous case, although it is possible to find some works such as Salado ( 2004) in which the spatio-temporal accessibility of nursery and kindergarten schools in Alcalá de Henares (Madrid) is analysed.However, society is nowadays time-intensive and space-intensive, which is why Miller and Shaw (2001) contended that planning policies should migrate from the traditional spatial approach to a new concept founded on personal possibilities of access and choice.For this reason, it is necessary to deepen the knowledge of the personal accessibility of the population, as this can be used to detect spatio-temporal patterns that allow decision-makers to establish time and work-life balance measures that are adapted to the real needs of the citizens (work, leisure, family time).

Methodology
The study of space-time accessibility to schools addressed in this paper involved integrated analysis of spatial and time variables which consider the locations of homes, schools and workplaces and also factor in the school and work timetables of children and the people taking them to and from school.An ad hoc tool simulating several scenarios for space-time accessibility to schools was developed to perform this analysis.The purpose of these scenarios was to test the impact on personal accessibility to schools of issues such as location and working hours, the type of school and working day and extending school hours by bringing in additional services.
Firstly, a number of scenarios were generated to simulate the actual accessibility of a group of users to the state and privately-run state-assisted schools teaching the second stage of pre-primary education in the city of Valencia.The main goal was to evaluate the influence of special space-time circumstances (working hours, home and workplace location) on personal accessibility to urban services and facilities.Working and school timetables and the locations of homes, schools and workplaces were real in these scenarios.This information was gleaned from the activity logs compiled in the Mobility and School Choice Preferences Survey conducted in 2018 with par-ents of pupils at state schools teaching the second stage of pre-primary education in the city of Valencia (Fajardo, Salom & Pitarch, 2022).
Secondly, other scenarios were generated in which the locations of homes and jobs along with school and work timetables were fictitious.The objective in this case was to evaluate the impact that the timetables of services and/or the location of the workplace had on personal accessibility to school facilities.These scenarios were used to ascertain which timetable conditions foster personal accessibility and space-time accessibility to schools in the city's neighbourhoods depending on the workplace and the means of transport used for journeys.
Finally, the indicator chosen to measure personal accessibility to schools was the number of schools accessible, both on foot and by public transport, at different times of the day coinciding with school start and end timetables.The variables used to generate the scenarios are discussed below together with the operation of the space-time accessibility calculation tool.

The Variables Defining Personal Accessibility to Schools
Studying space-time accessibility involves the three key variables making up locational accessibility problems: the location of supply, the location of demand and the networks which connect supply with demand.Then there is additionally a fourth time-related variable which is the timetables of people and services.
The workplace is the main fixed location constraining space-time accessibility to schools for people taking children to and from them.Accordingly, the location and working hours of demand were determined from two distinct standpoints depending on the kind of scenarios to be depicted.In the scenarios using actual situations, the location of demand was obtained from the addresses of the respondents' homes and workplaces.This information plus information about working hours was culled from the Mobility and School Choice Preferences Survey, which was carried out in 2018 among parents of pupils in public schools that attend the second stage of pre-primary education in the city of Valencia (Fajardo, Salom & Pitarch, 2022).Forty activity logs were available in which the location of the respondent's home, workplace and working hours were precisely specified.Each person was thus assigned an identification code and had two demand points, one associated with the home and the other with the workplace.This generated two vector layers of points.Firstly, a vector layer was created with 20 points representing the locations of the home addresses.Secondly, another layer was created with 20 points showing the locations of the workplaces along with information about actual working schedules.Specifically, clock-in time and clock-out time were recorded.Furthermore, in cases where work was performed in split shifts, break start time and break end time were also included.The location of homes and workplaces in the scenarios portraying fictitious situations was specified on the basis of the centroid of the city's neighbourhoods, while working hours reflected the most common timetables recorded in the survey's activity logs.
Supply consisted of the 169 state and privately-run state-assisted schools in the city of Valencia in 2018.Information provided by the Regional Ministry of Education, Research, Culture and Sport was used to generate a vector layer with 169 point elements depicting the actual location of the schools.In addition, information about classes starts and end times was added to this vector layer.Although there was a wide range of timetable possibilities for schools in Valencia, they can be summarised by the type of school day and whether or not additional fees had to be paid.Firstly, there were two types of school days where all activities were free of charge: the morning and afternoon school day (from 9 am to 12 noon and from 3 pm to 5 pm) and the continuous school day (from 9 am to 2 pm).Secondly, there are schools that offer activities outside school hours, for which families have to pay.In this case, there are many different timetables and they vary from one school to another.However, albeit with some exceptions, all the schools had a canteen service and lunchtime supervisors which meant that children could stay there from 9 am to 5 pm.The start and end times were stated in minutes and represented the start minute in the morning and the end minute in the afternoon.Likewise, the midday end minute and the afternoon start minute were also included for schools where the school day was split.The timetables could be amended depending on the scenario to be generated, and so in some cases the model operated with the current timetables of each school while in other cases fictitious timetables were set for all schools.
Finally, this research examined the space-time accessibility of schools from the twofold standpoint of journeys on foot and by public transport, which meant two different networks were used.Firstly, the street map in the National Centre for Geographic Information's CartoCiudad project (www.cartociudad.es)was used to calculate accessibility on foot.The average pedestrian travel speed was set at 4.5 kph.Secondly, an intermodal network was generated featuring the metro, tram and bus lines in the city of Valencia and the average speeds of each line to calculate accessibility by public transport.This information was gleaned from the Valencia Municipal Transport Company and Valencia Metro websites.This network also included the CartoCiudad street map since connections between different types of transport frequently need a travel on foot.

The Space-time Accessibility Model
A space-time accessibility model was developed to simulate the space-time accessibility scenarios.It calculated how many schools each individual could go to based on the schools' locations and timetables, the location of their home and the timetable and location of their workplace.All these parameters could therefore be amended to generate different scenarios using both actual and fictitious data.
The model operates by running a Python script integrated into ArcGIS through the ArcPy package.A preliminary step before running the script consisted of calculating the travel times in minutes for the following journeys: each person's home and all schools, each person's workplace and all schools, and each person's home and workplace (Fig. 1).This operation was performed using the cost matrix tool (OD Matrix) included in the ArcGis 10.6 software.Once the three cost matrixes had been calculated, the three tables generated were merged into a single table showing the minutes required for each individual to make these three journeys.The journeys were calculated both on foot and by public transport, and so two tables were generated.
On the one hand, the field which represents the journey between school and work and vice versa is generated based on these three journeys.On the other hand, another field was created, which sums the times of the journeys between work and home and between home and schools.This field was created to depict the situation of people who after finishing their working day have to go home to pick up their child and take them to school (for example, night shift workers).
Next, the first issue when running the script was the type of working day of the person or people whose space-time accessibility to schools was to be analysed.The type of working day determines the kind of suitability test to be conducted later on as split working days have more restrictions (two clock-in and two clock-out times) than continuous working days (one clock-in and one clock-out time).After choosing the type of working day, the space-time tool merged the journey cost matrix built in the previous step with the information about school timetables (school start and end minute) and work timetables (clock-in and clock-out minutes).The model then added multiple fields in which school and work start and end times were summed with the corresponding journey times.
Finally, the script added new fields on which it performed a suitability test in order to determine the potential accessibility of each school at the different start and end times.Specifically, six new fields were added.The first four fields referred to each of the start and end times of the schools and were: school morning start suitability, school afternoon end suitability, school midday end suitability, and school afternoon  2 shows the criteria which had to be met for a school to be accessible at morning start time.The last two fields grouped the starts and ends into two types of days.The continuous working day suitability field determines which schools a family can access if they have to attend at morning start time and afternoon end time, while the total suitability field determines which schools a family can access if they have to attend at all start and end times, including at midday.
In short, the tool makes it possible to determine which schools are accessible at certain times of the day depending on the spatial-temporal peculiarities of the people in charge of accompanying the children.Figure 3 shows, as an example, the school accessibility maps that can be built using this tool.In this case, the accessible centres are shown, both on foot and by public transport, for a person with a working timetable from 9:30 am to 3:00 pm and taking into account the actual location of their workplace and home, as well as the actual timetable and location of the school centres.

Personal Accessibility Conditions: Space-Time Accessibility to Schools, Extended Hours and Work-Life Balance
The purpose of this section is to ascertain how the working conditions (working hours and workplace) of people accompanying children impact the space-time accessibility of schools.Here it is crucial that everyone has similar conditions of spatial accessibility to schools.Hence it was decided to work with activity logs whose owners lived  in two specific neighbourhoods of the city.Firstly, the 11 activity logs from the Sant Marcel•lí neighbourhood, which is located in the southwest of the city, characterised by a low socio-economic level, were analysed.Secondly, the nine activity logs from the centrally located Russafa neighbourhood, which has a high socio-economic level, were examined.Both neighbourhoods have four schools teaching the second stage of nursery and primary education.
The parameters entered into the model were the homes and the timeables and places of work recorded in the 20 activity logs belonging to people living in the Sant Marcel•lí and Russafa neighbourhoods together with the location of the 169 state and privately-run state-assisted schools teaching the second stage of pre-primary education in the city of Valencia in 2016 with their actual timetables.Accessibility was also calculated both on foot and by public transport.Finally, scenarios have also been created in which the timetables of the schools have been extended as a result of the incorporation of extracurricular services (canteen, morning nursery, etc…).
Work-life balance measures should therefore make it easier for one and the same person to take their children to and from school.However, the results derived showed that no activity log was compatible with the regular school day (Morning and Afternoon School Day and Continuous School Day) (Figs. 4 and 5).This means that the owners of these logs had to turn to other people to undertake this task or they had to take out additional services, such as the canteen or the morning nursery (this is the morning care service, i.e. before the start of school day, normally from 8 to 9 a.m.), which allowed them to extend their child's stay at the school.
Thus, in the case of the Sant Marcel•lí neighbourhood, 100% of the workers who were able do the school run had to take out the canteen service and 41.67% had to Fig. 4 Percentage of activity logs in the Sant Marcel•lí neighbourhood which were compatible with a school based on the type of school day.Prepared by the authors take out both the morning childcare service and the canteen service.The situation was worse in the Russafa logs as 100% of the individuals who had a working timetable compatible with the school run had to use both extra services: canteen and early morning childcare.
Nevertheless, a small change in timetables can lead to a significant increase in the space-time accessibility of schools.Figures 6 and 7 show the percentage of people in each neighbourhood who were able to access a school which had an extended timetable.This timetable included the school day, the canteen service and the morning childcare service.Furthermore, under this timetable morning childcare starts at 7.45 am and allows children to be picked up at 2.15 pm in schools which have a continuous school day and at 5.15 pm in all schools regardless of the type of school day they have.In short, in this scenario schools stay open from 7.45 am to 5.15 pm.
The results demonstrate how this small timetable change led to a significant increase in space-time accessibility to schools, especially for people in the Sant Marcel•lí neighbourhood.There, there is a more than 30-point increase in accessibility with 75% of individuals being able to take their children to and from school.In the Russafa neighbourhood there is also a significant increase, especially if the journey is made by public transport.
Following analysis of the activity logs and after identifying people whose timetables were compatible with taking children to and from school, it is now time to examine how many schools each person can access based on their working hours and the schools' timetables.This information might be an accessibility indicator for   people who have a timetable which is compatible with some type of school day.This indicator also reflects the ability of people who take their children to and from school to choose the school they wish these children to attend.
There was a significant difference in the number of accessible schools depending on how journeys were made.The means of transport used did not, with a few exceptions, engender any variation in the number of people who could access a school or not.By contrast, the mode of transport used to make the school journey did entail a large variation in the number of schools which could be attended by people with timetable compatibility.Tables 1 and 2 show how the use of public transport led to a considerable increase in the number of schools accessible to individuals compared to those accessible on foot.

The Influence of Workplace Location on Space-time Accessibility to Schools in the City of Valencia
Most urban planning studies locate users at their place of residence.However, it is often the location of the workplace rather than the home that determines the spatialtemporal accessibility of schools.Basically, this is due to the time restriction imposed by the work timetable for entering and leaving work, which is not the case at home.Consequently, and given that not all neighbourhoods have the same socio-economic features or facilities, the number of accessible schools should be examined by the neighbourhood in which the workplace is sited and its socioeconomic index.For this purpose, the space-time accessibility model was used to generate a scenario in which the number of accessible schools from the workplace of 88 individuals who had 15 min to travel to school was calculated.In this scenario, each individual worked in a different neighbourhood of the city.The workplace corresponded to the neighbourhood's centroid and all the people had the same working hours (from 8 am to 3 pm).Furthermore, the actual location of the 169 state and privately-run state-assisted schools teaching the second stage of pre-primary education in 2016 was maintained and all of them were assigned the same school hours (from 7.45 am to 5.15 pm).Setting uniform timetables for all users makes it possible to analyse variations in spacetime accessibility depending on the location of homes and workplaces.Accessibility on foot and by public transport was also calculated.
Firstly, it was found that the neighbourhoods in the city's outlying areas had the worst accessibility on foot to schools and there were some neighbourhoods where individuals were unable to reach any school within a travel time of less than 15 min (Fig. 8).Similarly, there were other neighbourhoods where although there are some schools, there was little choice.These neighbourhoods are separated from the compact built-up area and have an urban morphology based on scattered development, which is why the distance to schools is greater than in the city's central neighbourhoods.Moreover, as the potential demand in these areas was lower than in the compact built-up area, they also had a smaller supply of schools which meant that the number of accessible schools was considerably lower than in the central neighbourhoods of the city.Conversely, the neighbourhoods around the historic centre (in the city centre) have the greatest accessibility to schools.In these neighbourhoods with compact development, the distances separating individuals from services are shorter.Furthermore, they have high population densities and a large number of schools and so the number of accessible schools was greater than in other areas of the city.The dichotomy between central and outlying neighbourhoods was maintained when analysing accessibility by public transport, albeit with some changes which suggest differences in the provision of public transport across the city's neighbourhoods (Fig. 9).Firstly, the areas with the worst accessibility were still the outlying neighbourhoods of the city, notwithstanding the improvement that using public transport brought to some of them in providing access to schools within the stipulated time.Secondly, in other neighbourhoods, especially in the south periphery of the city, the inclusion of public transport did not lead to an increase in the number of accessible schools.As well as being separated from the main urban centre, these neighbourhoods also had a somewhat meagre public transport network limited to urban bus lines.Finally, the neighbourhoods with the greatest number of schools accessible by public transport were in the city centre.In addition to having more schools than the outlying neighbourhoods, these neighbourhoods also have a very dense network of different types of public transport.Consequently, people working in the city centre and with working hours which enabled them to take their children to school can access more schools than those who work in the city's outlying neighbourhoods.
Equally, the number of accessible schools vary depending on the level of the socioeconomic index1 of the neighbourhoods where the workplaces were and the means of transport used to make the school journey.If this journey was made on foot, individuals whose workplace was in neighbourhoods with a medium socioeconomic level had access to the most schools (nine schools), followed by individuals working in neighbourhoods with a high socioeconomic index (seven schools) and finally individuals working in neighbourhoods with a low index (five schools) (Table 3).These differences are mainly explained by the urban and demographic characteristics of the neighbourhoods making up each of the groups.Some of the neighbourhoods in the high and low socioeconomic index groups were detached from the main urban centre and had a low population density.The number of schools in these neighbourhoods was also extremely limited as there was very low potential demand.Consequently, individuals working in these neighbourhoods had very few accessible schools in their respective neighbourhoods and had to travel long distances to access other areas where there is a greater number of schools.
Conversely, the picture changed when the school journey was made by public transport.In this case there was a positive correlation between the socioeconomic index of the neighbourhood where the workplace was and the number of accessible schools, meaning that as the SI of the neighbourhoods increased, so did the number of accessible schools (Fig. 10).Thus, the average number of accessible schools in neighbourhoods with a high SI was 56, while in neighbourhoods with a medium and low SI the average number of accessible schools was 36 and 21 respectively.This  indicates that neighbourhoods with a higher SI have a better public transport network and this increased the number of schools accessible to workers and residents in these areas.

Discussion
Drawing on the Geography of Time perspective to study accessibility to schools has led to significant results for school network planners in general and for those in the city of Valencia in particular.In the first place, work is the main fixed activity shaping personal accessibility to schools.Specifically, the incompatibility between working and school hours is the chief barrier to space-time accessibility to schools.
Secondly, one of the factors which most contributes to the time incompatibility of working people is the differing lengths of the school day (5 h) and the working day (6-8 h).As the length of the working day increases, space-time accessibility to schools decreases.This leads many parents to turn to some of the services offered by Table 3 Average number of accessible schools by the Socioeconomic Index of the neighbourhood where the workplace was schools which enable them to extend the time that children spend at school, since as the number of hours that children stay at school increases, the respondents' opportunities for access also rise.Hence the school day allowing for greatest space-time accessibility is one that includes the morning childcare and canteen service, or in other words the one in which children are at school from 8 am to 5 pm.Therefore, the inclusion of these services in the ordinary school day is crucial to ensure the spacetime accessibility of many workers.Nevertheless, these services are not free and the before school club service is not available in all schools.Accordingly, to improve personal accessibility to schools teaching the second stage of pre-primary education, it is recommended that the public authorities should implement these services in all schools and set up financial aid and public grants for people who cannot afford to pay for them.
Thirdly, this research has also shown how a small change in timetables can have a major impact on the space-time accessibility of schools, since a 15-minute extension in school start and end times means a significant increase in the number of workers who can access a school and in the number of schools which each worker can go to.Hence the time factor is more influential than the distance factor in personal accessibility to neighbourhood services because, as shown by this study, the greatest differences between workers who can access a school and those who cannot lie in working hours and not in the distances travelled between home and work.School and working hours therefore play a crucial role in the accessibility of schools, which means that time compatibility should be a key issue for school network planners and for lawmakers involved in work-life balance.Furthermore, and as stipulated in Royal Decree Law 6/2019, businesses have to introduce measures that allow flexible working hours for people with children under 12 in their care and who need to exercise their right to balance work and family life.
Fourthly, the workplace influences the space-time accessibility of schools to a greater extent than the place of residence.This is highly significant since as a rule, studies of accessibility to public facilities such as schools only assess proximity between the service and the homes of potential demand while disregarding other locations such as the workplace.This research confirmed the influence of the workplace on space-time accessibility to schools.Thus, people who work in the centre of the city and have a working timetable compatible with school timetables have greater space-time accessibility to schools than people who work in the outlying neighbourhoods of the city as the supply of schools is greater and the public transport network provides more travel options.Finally, space-time accessibility to schools is also influenced by the socioeconomic level of the neighbourhood where the workplace is since neighbourhoods with a higher level have a better public transport network, and this makes it possible to increase the number of schools accessible to workers and residents in these areas.Due to all these reasons, when planning the school network and in addition to studying where potential demand lives, it is recommended that the location of the main areas where jobs are concentrated and the layout of the city's public transport network should be examined to the extent possible.
Finally, the space-time accessibility instrument developed in this study is a spatial planning tool which adds to location-allocation models and may help improve timetable accessibility to all types of facilities.This tool allows changes to be made quickly and easily in the timetables of facilities and users, which means it is an extremely useful instrument for studying behaviour in personal accessibility to facilities and services depending on the time constraints of people and these facilities.Consequently, it would be useful in future research to continue developing the spacetime accessibility tool employed in this study.Firstly, it would be constructive to investigate how to include calculating multipurpose paths in the tool's operation.Secondly, it is also relevant to assess the options of creating an app with a userfriendly interface that can be effortlessly employed by public authorities, businesses and facility and service users.This tool would enable facility managers to learn what the best opening hours are to meet their potential demand.Users would also be able to find out which facilities they can go to and how long they can be in them depending on their time restrictions and means of transport used for the journey.

Conclusion
This paper has confirmed the suitability of adopting the space-time approach when studying personal accessibility to urban services in general and to schools in particular.The results derived in the scenarios developed by using this methodological approach demonstrated the enormous impact which aspects such as the working day, services timetables and/or the location of the workplace or facilities have on personal accessibility.Accordingly, it is crucial that spatial planning studies for public and private services address accessibility from the theory of the Geography of Time framework, since taking this approach makes it possible to construct more realistic scenarios than the ones derived from traditional locational accessibility models.
There is a long way to go in this line of research and there are many options for further work.Improving the spatial planning of public facilities involves looking at aspects related to personal characteristics, some of which have already been mentioned, along with other factors which are hard to quantify yet nevertheless are crucial to understanding individual or family decision-making.They include one of the parents choosing not to work, the perception of the quality of the school, family strategies for the future (for example, when the child no longer needs to be taken to school), the interest (or otherwise) in a nearby school to foster socialisation in the neighbourhood, personal preferences in means of transport, the type of job (with greater or lesser genuine opportunities to balance work and family life) and the cost of extra services.In short, building qualitative variables into planning models for public facilities is a necessary condition for further improvement in spatial equity and quality of life in cities.  Innovation 2013Innovation -2016Innovation , call 2016.In addition, this study is integrated within the project "Socioeconomic innovation, trajectories and strategies in the post-pandemic city" (PID2020-112734RB-C31 -AEI/ https:// doi.org/10.13039/501100011033),funded by the Ministry of Science and Innovation (Spain), call 2020.Open Access funding provided thanks to the CRUE-CSIC agreement with Springer Nature.

Fig. 1
Fig. 1 Graphical representation of the journeys calculated for the same individual.A: home-school journey; B: work-school journey; C: home-work journey.Prepared by the authors

Fig. 3
Fig. 3 A: Centres accessible by walking for activity log X. B: Centres accessible by public transport for activity log X. Prepared by the authors

Fig. 2
Fig. 2 Example of a morning school start suitability test.Prepared by the authors

Fig. 5
Fig. 5 Percentage of activity logs in the Russafa neighbourhood which were compatible with a school based on the type of school day.Prepared by the authors

Fig. 7
Fig. 7 Percentage of activity logs in the Russafa neighbourhood which are compatible with a school with extended opening hours (from 7.45 am to 5.15 pm).Prepared by the authors

Fig. 6
Fig. 6 Percentage of activity logs in the Sant Marcel•lí neighbourhood which are compatible with a school with extended opening hours (from 7.45 am to 5.15 pm).Prepared by the authors Number of schools accessible to the activity logs in the Russafa neighbourhood by the means of transport used to make the school journey and the type of school

Fig. 9
Fig. 9 Number of schools accessible by public transport by the neighbourhood where the workplace is located.Prepared by the authors

Fig. 8
Fig. 8 Number of schools accessible on foot by the neighbourhood where the workplace is located.Prepared by the authors

Fig. 10
Fig. 10 Scatter plot and polynomial trend line between the socioeconomic index of the neighbourhood where the workplace was and the number of accessible schools

(
CSO2016-74888-C4-1-R), funded by the Spanish State Research Agency and the European Regional Development Fund within the State Program for Research, Development and Innovation Oriented to the Challenges of Society, within the framework of the State Plan for Scientific and Technical Research and

Table 1
Number of schools accessible to the activity logs in the Sant Marcel.lineighbourhood by the means of transport used to make the school journey and the type of