quetzal_germany includes a highly detailed network model based on OpenStreetMap data for (MIT) and GTFS feeds for (PT). The latter is aggregated to the most relevant services for inter-zonal travel, using agglomerative clustering and filtering methods, in order to increase computational performance for the German-wide model. As a blueprint for regional studies however, the whole network graph can be selected. There are seven different network layers for corresponding transport modes:
1
Long-distance rail transport: ICE, IC and EC rail services
2
Short/medium-distance rail transport: Local and regional rail services
3
Local public transport: Bus, ferry, tram and underground services
4
Coach transport: Connections based on FlixBus’ network coverage
5
Air transport: Connections between 22 major airports
6
Road: Motorways, A and B roads, as well as interconnecting links
7
Non-motorised transport: Straight-line connections between zone centroids with distances up to 40 km
All relevant PT interconnections are realised through footpaths between stops of different layers. Network access/egress links connect each layer to sources and sinks of transport demand in the population centroid of each zone. As measures of LoS, every network link is equipped with two attributes: travel time (Eq. (
1)) and monetary travel cost (Eq. (
5); Table
2).
$$\begin{aligned} TT=T^{\text {iv}}+T^{\text {wait}}+T^{\text {ae}}+T^{\text {walk}} \end{aligned}$$
(1)
In-vehicle time
\(T^{\text {iv}}\) results from the network graphs. Road network average speeds are calculated from OpenStreetMap speed limits and conversion factors from [
48]. PT link duration stems from real GTFS schedule data. Waiting time
\(T^{\text {wait}}\) applies as zero for car transport and as the average waiting time at PT stops based on vehicle headways of the respective route. Entering an airplane costs 45 minutes including security checks, luggage handling, boarding, and longer walking distances within airports. Delay times of any kind are currently neglected. Walking time
\(T^{\text {walk}}\) accrues for PT intermodal transfers (at 5 km/h) or cycling connections between centroids (at 17km/h).
\(T^{\text {ae}}\) is the average access/egress time and represents a measure of accessibility. It is constant five minutes for MIT, depicting access, starting, and parking, while PT accessibility depends on the corresponding zone’s and network’s characteristics. Expression (
2) calculates PT
\(T^{\text {ae}}_{z,j}\) for mode
j and zone
z, inspired by a two-step floating catchment technique presented in [
49]:
$$\begin{aligned} T^{\text {ae}}_{z,j}=\sum _{m \in M} \eta _{m,u_z} \cdot \overline{d_{m,n}} \cdot \alpha _m \quad \forall n \in N_{z,j} \end{aligned}$$
(2)
The mean of weighted distance
\(d_{m,n}\) over all PT stops (i.e. nodes)
n in
\(N_{z,j}\) is again, weighted by share
\(\eta _{m,u_z}\) of PT access/egress mode
m in
\(M=\{\text {walk, bicycle, car}\}\). Values for
\(\eta _{m,u_z}\) depend on the zone’s urbanisation degree
\(u_z\) and can be found together with speed variable
\(\alpha _m\) in Table
1.
$$\begin{aligned} d_{m,n}=\sum _{c \in z} \frac{\sum _{n' \in N_{z,j}} s_{n'} \cdot D_{n',c}}{\sum _{n'' \in N_{z,j}} s_{n''}} w^{P}_{m,n} \end{aligned}$$
(3)
Distance measure
\(d_{m,n}\) is based on the geodesic distance
\(D_{n,c}\) from node
n to population cell
c (at a resolution of
\(100\times 100\) m).
\(d_{m,n}\) is weighted by the number of PT vehicles that depart from this stop between 6 a.m. and 6 p.m. during the week
\(s_n\) and by the population weight measure
\(w^{P}_{m,n}\).
$$\begin{aligned} w^{P}_{m,n}=\frac{\sum _{c} D_{n,c} \cdot P_c \cdot \left( \frac{D_{n,c}}{d_{\text {max},m}}\right) }{\sum _{c} P_c \cdot \left( \frac{D_{n,c}}{d_{\text {max},m}}\right) } \quad \forall c \in D_{n,c} \le d_{\text {max},m} \end{aligned}$$
(4)
Each access/egress mode has a catchment area defined by
\(d_{\text {max},m}\), wherein the cell population
\(P_c\) is counted and linearly weighted by its distance to node
n. This double weighting makes population counts close to a node more relevant than distant ones, or, from the perspective of PT users, closer nodes more attractive. It also reduces the impact of distance thresholds choice for access/egress modes. As a result,
\(\overline{d_{m,n}}\) yields realistic average distances relative to population density and service frequency of stops. Access/egress mode parameters can be varied in scenario settings as an approximation to inner-zonal mobility choices.
Table 1
Values for access/egress link parametrisation
\(\eta\) |
\(u_z=1\) | 0.948 | 0.017 | 0.035 |
\(u_z=2\) | 0.899 | 0.034 | 0.067 |
\(u_z=3\) | 0.883 | 0.026 | 0.091 |
\(\alpha\) in km/h | 5 | 17 | 30 |
\(d_{max}\) in km | 0.4 | 10 | 30 |
$$\begin{aligned} TC=\frac{D \cdot c_{\text {d}} + T^{\text {iv}} \cdot c_{\text {t}} + c_{\text {fix}}}{f} \end{aligned}$$
(5)
Travel cost
TC is composed of distance-specific cost
\(c_{\text {d}}\) in EUR/km, in-vehicle time specific cost
\(c_{\text {t}}\) in EUR/h, fix cost
\(c_{\text {fix}}\) in EUR per trip, and a split factor
f, used for car occupancy rates or average shares of PT subscriptions in the population. Sunk costs, like car ownership cost or PT subscriptions, are not included. Empirical evidence frequently shows, that individuals usually do not account them in daily mode choice [e.g.
5]. Table
2 summarises all cost function parameters for the base year except for local PT. Pricing schemes are very diverse within Germany so that the following assumptions apply: Unimodal bus trips cost 7 EUR. They reduce to 5 EUR, if origin or destination is a city, because cities are centers of price zoning systems and there is a higher share of subscriptions in the population. If bus transport occurs on the first or last leg of a multimodal trip, half these cost accrue, respectively.
Table 2
Monetary cost function components by mode of transport in 2017
Rail short | 0.233 | 0 | 1.47 | 2 | 5 | 50 |
Linear regression of DB price list 2nd class; subscription shares from calibration data set |
Rail long | 0.053 | 7.33 | 15.56 | 1 | 19 | 139 |
Linear regression with 56 OD-specific prices from DB website in Jan. 2021; 30% savings tariff |
Coach | 0.057 | 0 | 0 | 1 | 5 | 60 |
Average coach prices in Germany |
Airplane | 0 | 0 | OD-specific | 1 | 50 | - |
Economy prices from Sept. 2020 where available; 50 EUR elsewhere |
MIT | 0.114 | 0 | 0 | 1.5 | - | - |
Average fuel cost for 2017’s new car models with mileage of 15,000 km/a; average car occupancy in Germany |
Non-motorised | 0 | 0 | 0 | 1 | - | - |
Travellers decide upon their route and mode based on a set of shortest paths between their origin and destination. The Dijkstra algorithm computes shortest paths for car and bicycle transport, and for every PT mode combination available. The main leg’s transport mode represents the path’s main mode, which is the decision variable in the mode choice model.