2.1 Multi-modal transport network model
In this paper we extended the Dutch National Transport Model (NVM) [
22] implemented in the OmniTRANS transport modelling suite to model the mobility and accessibility effects of changes in the (transport) infrastructure. The NVM-model is an aggregate four step transport demand model with simultaneous distribution/mode choice modelling [
23] with detailed national multi-modal transport networks. In trip generation phase, the number of household, inhabitants, number and type of jobs, car ownership, workforce, age of inhabitants and educational places in each zone are the inputs for the calculation of the production from and attraction to each zone. In the trip distribution and mode choice modelling phase, the NVM uses two submodels: a destination/mode choice model and a public transport model. The destination/mode choice model uses three main modes: car, public transport (PT) and bicycle. The public transport model subsequently comprises train, bus, tram, metro and ferry networks. Park and ride facilities are associated with the car network. Each transport service is associated with the infrastructure (train with rail infrastructure, bus with road infrastructure, etc.). For each service the frequency, the stops and the travel time is implemented.
In the simultaneous destination/model choice model the different transport modes are compared with the generalised costs. The generalised costs for zone
i to zone j are calculated by:
$$ G{C}_{ij,m}={\beta}_{ij,m}^d\ast {d}_{ij}+{\beta}_{ij,m}^c\ast {t}_{ij,m} $$
(1)
Where
d
ij
is the trip distance (km),
\( {\beta}_{ijm}^d \) the travel cost parameter by mode
m (euro/km),
t
ij
the travel time (hours) and
\( {\beta}_{ijm}^c \)the value of time (VoT) by mode
m. The travel cost parameter varies by mode (car, bicycle, train, bus/tram/metro) and trip purpose (work, business, shopping, education or other), and are taken from national guidelines. Car travel cost parameters are based on fuel costs (0.1145 euro/km) and passenger occupancy rates, which differ between morning/evening/off peak periods. The VoT values are taken from Dutch appraisal guidelines and vary by mode (car, bike, public transport) and trip purpose. The VoT values range from 5.3 euro/h for a shopping trip by public transport to 30.5 euro/h for a business trip by car.
1 The simulation results in an OD-trip matrix for each mode separately. The matrix for PT can be applied to the PT model, to assign these trips to the PT-network. Passengers travel from the zone to a stop with an access mode, from the stop to their destination with an egress mode. The waiting time for access at the stop is based on the frequency of the public transport service. The formula for the waiting time is:
$$ {w}_{ls}^k=0.3\ast \frac{60}{F_{ls}} $$
(2)
Where
\( {w}_{ls}^k \) is the waiting time at access stop s by the access mode
k,
F
ls
is the frequency of the train line l at station s. The value 0.3 is a penalty to put additional cost on a transit line which is not attributed to travel time or waiting time. The value is calibrated in the NVM model using a linear regression depending on the frequency of train line. The waiting time depends on the transit line and the stop where the transit line is boarded. In many applications the headway is divided by two to calculate the waiting time, but for the first boarding a waiting time of 0.5 x headway is too long for low frequency lines as the passenger typically anticipates for this when leaving home. For any consecutive waits this is no longer true. The same formula is thus used for calculating the waiting time for transfers between public transport services, but the value 0.5 is used [
25].
In the standard NVM-model walking and biking are combined as one access/egress mode with different speeds depending on trip distance. In our study, we extended the NVM model with the following access/egress modes: walk-transit-walk, walk-transit-bicycle, bicycle-transit-walk, bicycle-transit-bicycle and car-transit-walk. With the new settings the public transport model calculates for these five combinations the generalised costs for travelling from each zone to each zone (using Eq.
1). A logit choice model is added to calculate the fractions for each access/egress combination for a zone to zone trip and a trip matrix for every access-egress combination is calculated. The model is specified as follows:
$$ {P}_i=\frac{ex{p}^{-GC\ P{T}_i}}{{\displaystyle \sum } ex{p}^{-GC\ P{T}_j}} $$
(3)
Where i represents the chosen alternative and j represents the choice set, by purpose m. The parameters
α
ij
,
β
ij , m
,
γ
ij , m
and
δ
ij , m
are estimated for distance, travel time, waiting time and penalties, respectively.
d
ij
,
t
ij
,
W
ij
and
p
ij
represent the distance, travel time, waiting time and penalties. Parameters are estimated for each trip between origin i and destination j, by mode
m. In the Generalized Cost function (GC), distance, travel time, waiting time and penalties are added. Table
1 shows the parameter values of the cost function.
$$ GC\ P{T}_{ij,m}={\alpha}_{ijm}\ast {d}_{ij}+{\beta}_{ij,m}\ast {t}_{ij,m}+{\gamma}_{ij,m}\ast {W}_{ij}+{\delta}_{ij,m}\ast {p}_{ij} $$
(4)
Table 1
Parameter values in the generalised cost function of the access/egress mode choice model
Access/egress by car | 0.1 | 18 | 6.86 | 6.86 |
Access/egress by bicycle | 0.05 | 16 | 6.86 | 6.86 |
Access/egress by walk | 0.05 | 6.86 | 6.86 | 6.86 |
Public transport | 0.1 | 6.86 | 6.86 | 6.86 |
The following procedure is followed to calculate fractions of access/egress mode shares. Firstly, the distances and travel times are calculated (Step 1). Distance and travel times depend on origin and (stop) destination. This function is applied for pairs of modes in access and egress combinations (Step 2) to calculate generalized costs. Choice modelling occurs based on generalized costs (Step 3). The results are input for travel time and distance matrix. The same procedure is repeated for different trip purposes (work, leisure, education, etc.).
For the implementation of these access and egress options, a detailed bicycle network obtained from the Dutch Cyclist’s Union [
26] was implemented. The network includes all bicycle trails (on- and off-street trails) in the study area for the year 2013, including link characteristics (i.e. road quality, lighting and nuisance). Here it is assumed that cycle speed is 15 km/h to and from the transit stops and pedestrians use the same infrastructure walking 5 km/h on this network. Furthermore, the influence areas of PT stops is set to 3 km and 5 km for walking and cycling, respectively. In addition, the basic car network is added to the transit network for the Netherlands. This network is connected with the centroids of all zones in the Netherlands and the railway stations in study area. This makes it possible to model park and ride.
2.2 Operationalising accessibility
Accessibility can be defined and operationalised in many different ways. Many different accessibility definitions and operationalisations in accessibility models and instruments have in the past decades been developed and applied by researchers from several academic fields (e.g., urban geography, rural geography, health geography, time geography, spatial economics, transport engineering). An overview of the many different definitions and operationalisations is beyond the scope of this paper. There are extensive reviews on accessibility measures [
27‐
29] in general and public transport accessibility in particular [e.g.,
22]. Accessibility measures can be categorised in several ways. Geurs and Van Wee [
29] distinguish between four groups of accessibility measures. Firstly, infrastructure-based measures analyse the performance or service level of transport infrastructure. These measures vary from simple travel time or congestion level measures to more complex network connectivity/centrality measures based on graph theory. Secondly, location-accessibility measures are a wide range of measures analysing access to spatially distributed activities, with threshold-based measures [e.g.,
30] and Hansen’s gravity-based accessibility measure [
31] as most popular ones. Thirdly, person-based accessibility measures used to analyse accessibility at individual level, taking individual limitations regarding freedom of action in the environment, into account. Fourthly, utility-based accessibility measures, such as logsum accessibility, analysing the welfare benefits that people derive from levels of access to the spatially distributed activities [e.g.,
32,
33]. Recently, a new type of ‘perceived’ accessibility measures was proposed, defining accessibility as the expected number of opportunities “available” for a subject to perform an activity, which contrasts with location-based and utility-based measures which assume that all opportunities are potentially available [
34].
The complexity of the concept of accessibility and of its perception by travellers implies that ideally multiple indexes are to be used in accessibility studies, to provide a better depiction of how individuals respond to the spatial structure of travel opportunities, and configurations and modalities of the transportation networks [
35,
36]. In this paper, however, we are interested in the spatial and network effects of bicycle-train integration policy scenarios at the regional level and not in comparing outcomes of different accessibility specifications. Furthermore, the choice and level of detail of accessibility indicators in this paper is constrained as the indicators are to be estimated using outputs of the NVM-model, which provide a high spatial resolution but does not allow estimations of accessibility for different population segments. A Hansen-based potential accessibility measure is applied here as a simple and effective measure to examine the spatial and network effects of transport infrastructure scenarios. This measure overcomes the well-known problems with the arbitrary selection of time thresholds and extreme sensitiveness of small travel time changes associated with threshold-based accessibility measures [
29]. Person-based accessibility measures are, because of their data need, unfortunately beyond the scope of this research. Logsum accessibility can easily be used to derive accessibility benefits by population segment, but estimating spatial and mode-specific accessibility effects is not straightforward as zones/postcodes and modes are endogenous choice variables in mode/destination logit models [
33]. A potential accessibility measure is used here, measuring the number of opportunities of some type of activity which can be reached over transport networks, weighting opportunities by an impedance function as follows:
$$ {A}_i^{s_k}={\displaystyle {\sum}_{i=1}{D}_j\ast f\left({t}_{ij}\right)} $$
(5)
Where \( {A}_i^{s_k} \) is the accessibility in transport zone i for scenario Sk,
D
j
is the number of destination opportunities (jobs) in a number of zones j reachable from zone i in (a maximum of) 180 min. t
ij
is the travel time by public transport between i and j (modelled with the NVM-model). f(t) is the distance decay function of travel time. A maximum of 180 min is used to exclude the influence of destinations far away from the study area on the accessibility index. The effect of this threshold on the accessibility index is small, however. According to the data from the 2014 Dutch National Travel Survey, less than 2.5 % of public transport trips and less than 0.5 % of car trips made by residents in Randstad South are longer than 180 min.
In this paper we focus on accessibility to jobs, however, job locations are a suitable proxy for many types of activity [
37,
38] since most types of activity participation are associated with the location of some type of corresponding employment (i.e. medical jobs for health care, retail jobs for shopping, etc.)
In the accessibility literature, exponential and power specifications of the distance decay function are often used but also other specifications such as inverse-potential, log-normal, log-logistic, exponential square-root and half-life functions are used [e.g., see for discussions
39‐
41]. From comparative studies is clear that the choice of the distance decay function impacts the outcomes of gravity-based accessibility measures, but generated spatial patterns can be very similar [
35]. We applied and estimated the model fit of the inverse-potential, negative-exponential, gaussian and log-logistic distances decay functions using data from the 2014 Dutch National Travel Survey [
42]. The log-logistic formulation was found to have the best fit with the observed data, using the Akaike information criterion (AIC) indicator to compare models. Other studies also find log-logistic decay functions to provide good model fits to model job accessibility [e.g.,
43,
44], reflecting that for commuters, sensitivity to travel cost (or time or distance) is stronger for intermediate distances than for short and long distances. Thorsen et al. [
44] also provide a theoretical justification for such an S-shaped curve, based on the idea that short distances give random commuting flows, whereas long distances are governed by a minimum cost principle. The log-logistic formulation is as follows:
$$ f\left({t}_{ij}\right)=\frac{1}{1+ \exp \left(a+b \ln {t}_{ij}\right)} $$
(6)
Where
t
ij
is the travel time between
i and
j, and a and b are parameters to be estimated. The parameters for log-logistic distance decay function were estimated for commuting trips of residents of the Randstad South, and shown in Table
2. Table
2 also shows the t-test below for each parameter. All values are statistically significant different from zero, under the 95 % confidence level. T-test is larger than 1.96.
Table 2
Parameter values, standard error and t-test of log-logistic distance decay function
A – PT | -11.467 | 0.086 | -133.337 |
B – PT | -3.007 | 0.022 | -136.682 |
The distance decay functions for the study area are steeper than the national average, with a and b parameters −11.156 and 2.838, respectively. Randstad South is one of the most densely populated areas in the Netherlands and residents make on average shorter trips. For example, in Randstad South, 62 % of public transport trips is shorter than 45 min (including access/egress) compared to 38 % for the Netherlands.
The improvement in accessibility in zone
i (
\( {A}_i^{\Delta} \)) is represented as follows:
$$ {A}_i^{\varDelta }=\frac{A_i^{s_k}-{A}_i^{s_{\mathrm{o}}}}{A_i^{s_{\mathrm{o}}}}\cdot 100 $$
(7)
Where \( {A}_i^{s_k} \) is the accessibility measure in zone i during the scenario S
k
, estimated with the NVM-model, where k is the scenario number, and \( {A}_i^{s_0} \) is the accessibility measure in reference scenario (2012).