Model complexities and requirements for multimodal transport
1network design: Assessment of classical, state-of-the-practice, and
2state-of-the-research models
34
Gijsbert van Eck, MSc. 5
Department of Transport & Planning 6
Faculty of Civil Engineering and Geosciences 7
Delft University of Technology 8
Stevinweg 1, P.O. Box 5048, 2600 GA Delft, The Netherlands 9 Phone +31 15 2784977 10 E-mail G.vanEck@TUDelft.nl 11 12 Ties Brands, MSc. 13
Centre for Transport Studies and Goudappel Coffeng 14
Faculty of Engineering Technology 15
University of Twente 16
P.O. Box 217, 7500 AE Enschede, The Netherlands 17 Phone +31 53 489 4704 18 E-mail T.Brands@UTwente.nl 19 20 Luc J.J. Wismans, PhD. 21
Centre for Transport Studies and Goudappel Coffeng 22
Faculty of Engineering Technology 23 University of Twente 24 E-mail LWismans@Goudappel.nl 25 26 Adam J. Pel, PhD. 27
Department of Transport & Planning 28
Faculty of Civil Engineering and Geosciences 29
Delft University of Technology 30
E-mail A.J.Pel@TUDelft.nl 31
32
Rob van Nes, PhD. 33
Department of Transport & Planning 34
Faculty of Civil Engineering and Geosciences 35
Delft University of Technology 36 E-mail R.vanNes@TUDelft.nl 37 38 39 Word Count Abstract 240 Main text 6234 Figures (3) 750 Tables (3) 750 Total 7734 40
ABSTRACT 1
In the aim for a more sustainable transport system, governments try to stimulate multimodal trip 2
making by facilitating smooth transfers between modes. The assessment of related multimodal 3
policy measures requires transport models that are capable of handling the complex nature of 4
multimodality. This complexity sets requirements for adequate modeling of multimodal travel 5
behavior and can be categorized into three classes related to the range and combinatorial 6
complexity of the choice set, the mathematical complexity of the choice model, and the 7
complexity in demand-supply interactions. Classical modeling approaches typically fail to meet 8
these requirements while state-of-the-practice approaches only partly fulfill these. Hence, the 9
underlying hypothesis of this study is that application of such models in network design implies 10
an ill decision-making process. These modelling approaches, as well as the promising state-of-11
the-research super-network approach, are therefore conceptually compared to each other. 12
Requirements for multimodality are constructed, and all three models are tested regarding how 13
these requirements can be met. The findings of this comparison are supported by realistic 14
examples in the real-world transport network of the Amsterdam Metropolitan Area. It is shown 15
that theoretical shortcomings of classical and state-of-the-practice approach indeed result in 16
implausible predictions of multimodal travel behavior. The flexibility of the super-network 17
approach, on the other hand, is well capable of describing the expected impact of supply changes 18
on travel behavior in most situations. Hereby, this study illustrates the urgency for applying 19
sound multimodal modeling approaches in network design studies. 20
21 22
1. INTRODUCTION 1
In many highly urbanized regions around the world transport related costs due to travel time 2
delay and unreliability of the transport system are considered as major problems. Furthermore, 3
large traffic volumes induce sustainability problems in terms of usage of scarce space in cities, 4
energy consumption and the emission of greenhouse gases. A shift to more sustainable modes of 5
transport, such as bicycle and transit, is likely to alleviate these problems by reducing inefficient 6
car usage. However, the strength of the transit system, offering high capacity connections 7
between main nodes, is reduced by its limited flexibility. The generalized costs involved with 8
access and egress, parking of private vehicles and transferring between modes is often too high 9
to be competitive with the car. A more integrated multimodal network would offer smooth 10
transfers and synchronization between all types of private and public transport modes. In such a 11
multimodal network travelers can benefit from the strengths of both private (flexibility) and 12
public (high capacity) modes. Improved integration and coordination of transport modes is likely 13
to lead to more trips in which multiple modes are used between which travelers make a transfer. 14
More multimodal trip making implies an increase in transit and bicycle access and egress shares, 15
and thereby to a more sustainable transport system (1). Typical instruments to facilitate 16
multimodal trips are the establishment of park-and-ride or bike-and-ride facilities, 17
synchronization of transit services, providing multimodal travel information, and offering high 18
quality transit services. 19
20
Transport models are key tools in decision-making processes regarding the implementation of 21
such multimodal policy measures. When searching for effective policy measures, the application 22
of transport models can range from the evaluation of few pre-defined scenarios based on expert 23
judgment to solving a multi-objective network design problem. The urgency for models that are 24
capable of handling multimodal trips is twofold. In the first place, multimodal trip making is 25
expected to become more important in the future. Hence, this type of trips has to be taken into 26
account for accurate modeling of travel behavior. Second, the policy objective to stimulate 27
multimodal trip making requires tools to evaluate the impact of specific measures. Correct 28
modeling of multimodal travel behavior, however, is not a straightforward task. Classical 29
modeling approaches mostly fall short of adequately covering and describing the full 30
combinatorial range across all available modes of transport. This deficiency results from a rather 31
strict separation between private and transit modes, little attention for access and egress modes, a 32
split between the mode and route choice, simplified choice models and utility specifications, the 33
lack of detailed transfer modeling, and the assumption of unlimited service capacities. Hence, 34
these models are not capable of capturing the full complexity of the analysis and prediction of 35
multimodal trip making. 36
37
In the literature two main approaches can be found to handle the complexity of multimodal trip 38
making in transport models. The first approach pre-specifies mode chains as additional artificial 39
modes (2)(3). Classical models can easily be adjusted to incorporate these additional mode 40
chains , which forms the main reason for its popularity in practice. This approach will be referred 41
to as the state-of-the-practice model. The second line of research focusses on the integration of 42
all modes by means of the network representation (4)(5)(6). Routes generated through such a 43
network do not only describe the sequence of links, but also the related mode or combination of 44
modes that is used. In combination with a-priori generation of travel alternatives, simultaneous 45
mode and route choice, and mode exceeding demand-supply interaction, this method is referred 46
to as the state-of-the-research or super-network approach hereafter. Based on its multimodal 1
concept and sound theoretical underpinning this approach is expected to be suitable for handling 2
typical multimodal difficulties in transport modelling. 3
4
It is hypothesized in this study that the application of state-of-the-practice transport models in 5
network design may imply counterproductive or sub-optimal decision making by policymaker 6
regarding the implementation of multimodal network measures. The main objective of this paper 7
is to illustrate that using such models indeed lead to implausible prediction of multimodal travel 8
behavior in numerous situations. To this end, a conceptual comparison is made between the 9
classical transport approach, the state-of-the-practice approach, and the so-called super-network 10
approach. All three models are then applied to assess the impact of a series of typical multimodal 11
supply changes in the real-world case study of the Metropolitan Area of Amsterdam. This 12
analysis provides further insight into the theoretical and conceptual shortcomings of currently 13
used approaches. 14
15
This paper starts in Section 2 by introducing the model complexities that emerge in multimodal 16
networks and discusses the emerging requirements for modelling multimodal travel behavior. 17
Next, in Section 3, the modelling approaches that are discussed in this paper are described, i.e., 18
the classical approach, the state-of-the-practice approach, and the super-network approach. The 19
case study is subject of Section 4. After a short description of the case study, an overview of the 20
evaluated multimodal supply measures is given. Thereafter, a conceptual comparison between 21
the models is made and findings are supported by examples from the case study. The paper ends 22
with some final remarks and conclusions in Section 5. 23
24 25
2. MULTIMODAL TRANSPORT MODELING 26
Multimodal networks are characterized by a diversity in infrastructure (road, light rail, heavy 27
rail), transport services (transit lines, bicycle renting), and modes (train, bus, tram, metro, car, 28
bicycle and pedestrian). This multimodality has to be accounted for when assessing the transport 29
systems’ performance, and even more so, when evaluating typical multimodal policy measures. 30
31
2.1 Multimodal trip making 32
The ability of travelers to choose from a range of continuous (private) and discontinuous (public) 33
modes, and to combine them through intermodal transfers, implies a large number of travel 34
alternatives is available. Such multimodal travel alternative might have complex combinatorial 35
structures. Hence, planning such a trip involves multiple decisions related to the various modes, 36
transport services, boarding and alighting locations, transfer options, and parking facilities. As 37
the variation in characteristics (such a time, costs, and distance) among alternatives can be 38
expected to be higher than in the unimodal case, personal preferences, knowledge, perception 39
play an important role in making this decision. Moreover, from the traveler point of view, not all 40
of these alternatives can be seen as distinct travel options, as there will be large similarities in 41
terms of infrastructure usage, modes of transport, and transit services. Finally, transfer 42
movements will be of major influence on the attractiveness of a multimodal trip and they link the 43
several unimodal sub networks into an integrated multimodal network. This nature of 44
multimodality introduces some complexity that is absent in unimodal transport prediction. The 45
requirements set by this additional complexity should be met by transport modeling tools in 46
order to adequately describe multimodal travel behavior. While state-of-the-practice transport 1
models generally meet some of these requirements, other requirements have been discussed in 2
the literature that are not yet fully adopted in practice. This latter category of requirements will 3
be discussed in the section below. 4
5
2.2 Modeling requirements 6
The requirements that are specific to modeling multimodality can be categorized into three 7
classes, each relating to a particular issue of the assignment process: the range and combinatorial 8
complexity of the choice set, the mathematical complexity of the choice model, and the 9
complexity in demand-supply interactions. In this study the total travel demand is assumed to be 10
given and inelastic (i.e., independent of network performance). The requirements described here 11
relate to the assignment of these travelers to the multimodal network, thus modeling travelers’ 12
mode choices and route choices. The requirements discussed in the ensuing of this section are 13
categorically shown in the first two columns of the overview in Figure 1. 14
15
Range and combinatorial complexity of the choice set 16
In a multimodal network multiple modes of transport and transit services, as well as transfer 17
facilities connecting them, are available to the traveler. A multimodal transport model should be 18
able to predict the usage of the full range of modes and mode chains (8). Routes in which several 19
modes or services are combined can be feasible alternatives and as such need to be considered 20
(representativeness of the choice set). However, not every mode chain is feasible (8). Generally, 21
travelers have no motorized private modes available at the station. A trip composition train-car-22
train is therefore rather unlikely. Such unfeasible travel alternatives should be excluded from the 23
set of considered travel alternatives (realism of the choice set). Furthermore, the attractiveness of 24
a trip leg can depend on the trip composition as a whole (9). For example, the costs for using a 25
bicycle as access or egress mode are usually different at the home-side than at the activity-side of 26
a trip. Where a bicycle is usually available for free at the home-side, a bicycle needs to be rented 27
or parked in advance at the activity-side of a trip, implying extra costs (trip dependent leg 28
properties). 29
30
Mathematical complexity of the choice model 31
The structure of multimodal transport networks is generally more complex than their unimodal 32
counterparts. The planning of a trip in a large multimodal network might involve multiple 33
choices related to the various available modes, transport services, and transit boarding and 34
alighting locations. These additional choice dimensions make it much harder to describe the 35
underlying behavioral choice process in a mathematical (tractable) way. The mode and route 36
choices cannot be seen as two distinct choices anymore as they are heavily correlated (10). 37
Travel alternatives describe both the spatial routes that are taken as well as the chains of modes 38
that are being used. From a behavioral point of view the mode and route choices become 39
integrated into a single simultaneous choice process (choice dependencies). In addition, the 40
increased complexity of the network implies bigger differences in travelers’ knowledge and 41
perception of travel alternatives and their attributes as well as more variation in travelers’ 42
preferences. In general, it is more realistic to model the route choice in a stochastic way rather 43
than performing a deterministic assignment. In modeling multimodal trips this issue becomes 44
even more urgent (heterogeneous perception and preferences). Explicitly modeling the choice 45
between travel alternatives, however, introduces another problem. Mode, services or space 46
related unobserved route attributes could have rather complex correlation patterns (11). This 1
overlap has to be accounted for when predicting route shares (correlated alternatives). Travelers 2
have intrinsic preferences for certain modes that are not represented by any observed attributes. 3
Using the metro, for example, is usually valued less onerous than travelling by car. Besides the 4
attributes of a trip leg, these preferences for a leg can also depend on the trip composition as a 5
whole. Using the bicycle as an access or egress mode has a different impact on the attractiveness 6
of the full trip then when the bicycle is used as the main mode. Similarly, the attractiveness of 7
travelling by train is higher when one can board or alight at an intercity station (12). This is 8
independent of the hierarchic level of the train service (stop, regional, or Intercity) being used 9
(trip dependent leg attractiveness). 10
11
12
Figure 1 - The list of requirements and their evaluation within the case study 13
Complexity in demand-supply interactions 14 CL PR SN Intercity status train station Hoofddorp New train station Amsterdam West Parallel bus service Almere – Amsterdam South
Park and ride facility Amstelveen Representativeness of the
choice set
Realism of the choice set Trip dependent leg properties Choice dependencies
Correlated alternatives Trip dependent leg attractiveness
Heterogeneous perception and preferences
Capacity of transfer locations Performance of transfer movements Demand-supply interaction between alternatives N N N N N N2 P N N2 N N1 Y P P P N2 P N N2 P Y Y Y Y Y Y Y Y N Y 2. Mathematical complexity of the choice model 1. Range and combinatorial complexity of the choice set
3. Complexity in demand-supply interactions CL = classical approach PR = state-of-the-art approach SN = super-network approach N = requirement is not met P = requirement is partly met Y = requirement is fully met
1 This requirement can conceptually be met, but only at the
cost of high computation time or memory requirements and is therefore often refrained from.
2 Model setting can be chosen such that this criteria is met
for a specific network, however without being transparent and transferable to other network variants.
When the travel demand is high and peak periods are heavily loaded the usage of both the 1
physical infrastructure and transit services will impact the (experienced) travel times. The 2
consideration of alternatives in which multiple (private and transit) modes are combined 3
introduces correlations in travel times and demand flows between different modes of transport. 4
Higher travel times on the car network might impact the share of park and ride alternatives. As a 5
consequence, the quality of the transit network is influenced by the usage of the car network 6
(demand-supply interaction between alternatives). Another constraint is the available number of 7
parking places at bike and ride and, in particular, park and ride facilities. More travelers using 8
such a facility will raise walking times to and from the parking location at first (13). Eventually, 9
no more vehicles can be parked when the available capacity is met (capacity of transfer 10
locations). The resistance of making a transfer follows from, among others, parking costs, 11
parking time, walking time, and the risk of missing a transit connection. These transfer related 12
costs are a substantial part of the total generalized costs of a full trip (11)(14). To predict the 13
impact of (changes in) transfer attributes they have to be modeled explicitly (performance of 14
transfer movements). 15
16 17
3. MODEL FORMULATIONS AND COMPARISON 18
In the previous section three main modeling approaches were distinguished: the classical 19
approach, the state-of-the-practice approach, and the super-network approach. For the following 20
comparative analyses, the corresponding operational models that follow the classical approach 21
and state-of-the-practice approach are used (regarding methods and model parameters) according 22
to their current implementation for the considered study area. An operational model of the super-23
network approach has been implemented specifically for this study based on methods and 24
parameters reported from earlier studies and, where needed, re-calibrated with aggregated data 25
for the case study area. Each of the models are described in the following subsections and shown 26
in Figure 2. 27
28
3.1 The classical model 29
The classical model is based on a strict separation between private and transit modes and does 30
not meet the requirements for multimodality. Yet, the model is included here in the case study 31
comparison to show the consequences of ignoring multimodal trips. In the ensuing, the classical 32
model is described according to the network definition, modal split, and network assignment, 33
while the main concepts of this model are shown on the upper left-hand side in Figure 2. 34
35
The multimodal transportation network consists of the infrastructure network defined by nodes 36
and links, and the transit service network defined by lines and stops. Links have characteristics 37
such as speed and capacity, while lines have characteristics such as frequency, travel time, and 38
the network link(s) that are traversed. Transportation zones are used to denote origins and 39
destinations, and form a subset of the network nodes. These zones are connected through 40
connector links representing access and egress to the network. Connector links to the road 41
network enable pedestrians, bicycles, and cars, while connector links to the transit stops only 42
allow for walking. Therefore, although private and transit modes can share the same links, they 43
are dealt with as being two separate networks. 44
1
2
Figure 2 – The classical modeling approach (upper left), the state-of-the-practice approach 3
(upper right), and the super-network approach (down) 4
5
The total (inelastic) transport demand is distributed over the two main modes: car and transit. 6
Bicycle traffic is here ignored as a main mode of transport as the considered demand describes 7
interregional trips. The mode shares are computed using a standard multinomial logit model 8
based on random utility maximization (15), where the error terms are assumed to capture effects 9
of taste variation, knowledge limitations and perception differences across the population. In the 10
Multimodal network loads Super-network
Travel demand
A-priori choice set generation
Mode and route choice (Paired combinatorial logit) Car Route 6 Route 7 Train Route 1 Route 2 P+R Route 8 Route 9 Route 10 BTM Route 3 Route 4 Route 5
Car and transit loads Mode choice (multinomial logit)
DUE car
assignment assignment SA transit Travel
demand Unimodal networks
Car Transit Mode choice (nested logit) DUE Car assign-ment SA Transit assign- ment Travel demand Multi-modal network SA Transit assign- ment SA Transit assign- ment
Car Transit chain Chain1 Chain 2 Chain 3
traffic assignment, car trips are assigned according to the assumption of the deterministic user 1
equilibrium, hence assuming that drivers have perfect information in their route choice. Route 2
costs are based on the weighted sum of the travel distance and travel time, where travel times are 3
modeled according to the BPR function. The equilibrium is computationally reached through 4
applying the Frank-Wolfe algorithm, where enumeration of the route choice set is not needed. 5
6
For the assignment of transit trips, the combinatorial constraints due to the line-bound character 7
of transit lines typically allows for enumeration of choice sets. Travelers’ preferences are 8
explicitly taken into account by the principle of optimal strategies (16) in a stochastic 9
assignment. Optimal strategies imply that travelers choose a set of alternatives that can be 10
optimal rather that choosing a single route. This set of alternatives includes all feasible 11
alternatives between a boarding station and the destination and is also referred to as a hyper-path. 12
During their trip they choose which service lines to board, based on actual arrival times of transit 13
vehicles. In the assignment first a set of candidate alighting stops is defined based on maximum 14
walking distances to the trip destination. Thereafter a branch-and-bound building algorithm is 15
applied backwardly construct the hyper-path. Per stop that is reached, the expected travel time is 16
calculated as the sum of the in-vehicle times (of all calling lines) weighted by their boarding 17
probability and the expected weighting times. Boarding probabilities are calculated through a 18
logit model in which travel times are multiplied by line frequency. The waiting time at a stop is 19
calculated as half of the headway of the combined frequency of all lines that can be used. When 20
all candidate boarding-stops are reached a logit model is applied to distribute travelers over these 21
stops based on the generalized costs of the hyper-path serving this stop. The generalized costs are 22
a weighted sum of monetary costs, in-vehicle time, access time, egress time, waiting time and the 23
number of transfers that has to be made. Hence, the average generalized costs used in the mode 24
choice are the sum of the generalized costs per hyper-path weighted by their choice boarding 25
stop probability. Conceptually, the assignment could be repeated several times with updated 26
perceived travel times to reflect vehicle crowding and reach equilibrium. However, this is 27
seldom done in practice since it would dramatically increase the computation time. 28
29
3.2 The state-of-the-practice approach 30
The state-of-the-practice model is basically an extension of the classical model, mainly differing 31
in the fact that a set of mode chains is pre-specified. To this end, transferring between private 32
(bicycle and car) and transit modes is now allowed at transit stops, and corresponding connecting 33
links between road network nodes and transit stops are included in the network representation. 34
The modes that can traverse such a link determine the feasible transfers at the transit stop. In 35
general, transfers from bicycle are assumed to be possible at any stop, while car transfers are 36
only possible at a limited set of pre-defined stops. The construction of the transit hyper-path 37
follows exactly the same procedure, but note that the branch-and-bound algorithm has to be 38
repeated for every egress mode, as the set of candidate stops depends on the maximum egress 39
distance by this mode. In the model used here, the following mode chains are distinguished as 40
separate modes: walk-transit-walk, bicycle-transit-walk, car-transit-walk, walk-transit-bicycle, 41
and walk-transit-car. These pre-specified mode chains consist of two or more modes, but are 42
modeled as an additional artificial mode. Therefore, mode choice is now applied to a wider set of 43
modes. 44
The generalized costs of each mode chain are calculated similar to the functions used in the 1
classical model. However, due to the correlations in the mode chains the multinomial logit model 2
cannot be used to determined mode shares. This correlation between the unobserved attributes of 3
these alternatives will lead to an overestimation of the transit shares. To account for this the 4
modal split is calculated using a nested logit model (17) with two nests m, corresponding to car 5
trips and chained trips using transit. Nest parameters are estimated to capture the correlation 6
within a nest (while assuming that the nests are uncorrelated). This nested procedure is shown on 7
the upper right-hand side in Figure 2. 8
9
3.3 The super-network approach 10
The (generic) term of super-network approach is here used to indicate (the family of) models that 11
include three main modeling components: construction of an integrated multi-modal network 12
representation (the super-network), a-priori generation of the choice set, and simultaneous mode 13
and route choice modeling Error! Reference source not found.. In this section each of this 14
components is concisely discussed. The modeling framework is shown in the bottom half of 15
Figure 2. 16
17
The network representation in the classical model is the starting point of the automatic super-18
network construction. This super-network is for this case study built up in five layers: heavy 19
transit, light transit, pedestrian, bicycle and car. Instead of allowing (infrastructure) links to be 20
used by multiple modes, these network links now appear in multiple layers (corresponding to 21
modes), and in transit layers are duplicated for every transit service traversing this link. The five 22
layers are integrated into a single network by adding artificial transfer links, connecting the 23
pedestrian network to the remaining layers. These transfer links represent transfer possibilities 24
and hence their cost function is based on attributes such as fixed transit costs, parking time, and 25
parking costs. Private transport layers (car and bicycle) are connected to the pedestrian layer at 26
locations where these vehicles can be parked, for example, centroids, parking lots and park-and-27
ride facilities. At stops and stations the pedestrian layer is connected to transit layers. All origin 28
and destination zone centroids are located in the pedestrian layer implying that a transfer 29
between modes always involves the pedestrian network and thus includes walking. To limit the 30
computation time for the choice set generation both transit layers are simplified by the 31
construction direct links between boarding an alighting stops (18). Given that stop properties are 32
represented through transfer links and lines are modeled as a set of (directed) links, the network 33
representation collapses to a set of nodes and links. 34
35
In contrast to the classical and state-of-the-practice model, the super-network model follows a 36
path-based approach. That is, the set of alternatives is constructed before the assignment step. 37
The choice set is generated by first extracting a subset of available routes, usually done through 38
repeated shortest-path searches with randomized attribute values and preference parameters. For 39
reasons of mode variety, mode-specific route sets are generated and then concatenated at transfer 40
locations into full multimodal travel alternatives. Furthermore, to improve the realism as well as 41
the computational efficiency the full set of feasible routes is filtered imposing a set of logical, 42
feasibility and behavioral constraints. Finally, dominated (i.e., non-competitive) routes and 43
routes showing large overlap with more attractive alternatives are excluded from the set. These 44
filtering procedures prevent the model from assigning travelers to illogical or behaviorally 45
doubtful alternatives even in case of severe congestion. In a second step, for each user class (in 46
this study only home-activity or activity-home) specific attributes are assigned to the generated 1 routes. 2 3
In the assignment, attributes of the generated route-mode alternatives are iteratively updated to 4
account for the effect of predicted links flows, transit vehicle occupation, and parking capacity 5
constraints. The attributes contributing to the generalized costs of a route-mode alternative relate 6
to level of service (e.g., travel time and costs), intrinsic preferences for specific modes and 7
stations (i.e., mode and stop specific constants), intrinsic preferences for specific alternative type 8
distinguishing train, bus/tram/metro, car, and park-and-ride (i.e., alternative specific constant). 9
The shares in travel demand for each route-mode alternative are then computed using the paired 10
combinatorial logit model (20) capturing the complex overlap among alternatives. This model 11
allows different correlation between any pair of alternatives, while still retaining the advantages 12
of a closed form expression. Here, correlations are related to trip type (mode chains), spatial 13
structure (physical links), and transport services (modes and stations). 14
15
4. CONCEPTUAL AND QUANTITATIVE MODEL COMPARISON 16
In this section the classical model (CL), the state-of-the-practice model (PR), and the super-17
network model (SN) are discussed as to how they perform in light of the requirements for 18
multimodality. In the introduction it was hypothesized that shortcomings of the classical and 19
state-of-the-practice models are not only theoretical, but may imply wrong decision-making 20
when the impact of multimodal policy measures is assessed. To illustrate this, a series of 21
examples from the real-network of the Amsterdam Metropolitan Area are shown. Each example 22
relates to a specific multimodal policy measure that is assessed by all three models. The results 23
of these assignments are then used to support the findings of the conceptual comparison. 24
Columns three to five in Figure 1 indicate whether a requirement is fully met (Y), partly met (P), 25
or not met (N). It can directly be noted that the classical model fails to meet almost all 26
requirements. This is expected, given that this approach conceptually excludes multimodal trips. 27
When a requirement can principally be met by state-of-the-practice models, but is typically 28
refrained from for computational reasons, this is indicated in the figure. The model requirements 29
and how they are met are discussed below following the same categories introduced earlier. First 30
the case study with the real-world examples is introduced. 31
4.1 Introduction of the case study 32
The case study area covers the Amsterdam Metropolitan Area in The Netherlands (Figure 3). 33
This region is characterized by dense concentrations of housing, employment and facilities, high 34
costs for parking in city centers due to the scarcity of space, and congested road networks. 35
Origins and destinations are aggregated into 102 transportation zones. Important commercial 36
areas are the city centers of Amsterdam and Haarlem, the business district in the southern part of 37
Amsterdam, the harbor area and airport Schiphol. Other areas are mainly residential, but still 38
small or medium scale commercial activities can be found. Travelers are served by an extensive 39
multimodal network with pedestrian, bicycle, car and transit infrastructure. Transit consists of 40
bus, tram, light rail, bus rapid transit, metro, interliner, local train, regional train and intercity 41
train. Bicycles can be parked at most stops and stations, and 36 transit stops facilitate park-and-42
ride transfers. The total share of multimodal trips is about 6 % on network level, but up to 20 % on 43
relations between urban municipalities or between the region and urbanized area. This clearly 44
illustrates the need for a multimodal modelling approach as is illustrated by the survey results shown 45
in Table 1. The variety of mode chain composition is shown by the shares of access and egress 1
modes for three main modes: train, bus, and tram-metro. 2
3
Table 1 – Access and egress mode shares (x) 4
Access mode Main mode1
Train Tram and metro Bus
Walking 31.1 81.1 89.7
Bicycle 32.6 5.0 8.5
Car 4.1 0.9 1.8
Bus 12.6 4.5 0
Tram/metro 16.8 0 0
Bicycle and bus 0.5 0.4 0
Bicycle and tram/metro 0.3 0 0
Other 1.6 1.1 0
1 Based on hierarchical mode order: train, tram-metro, and bus
5 6
Table 2 compares the survey results on shares of car, transit and combined usage of both modes 7
with predicted model modal shares. Both the classical and state-of-the-art model largely under 8
predict the car share at short distance, while over predicting its share at intermediate distances (7.5-9
30 km). It should be noted that the state-of-the-practice model does not seem to be an improvement 10
over the classical model with regard to this aggregated data. The super-network approach, however, 11
outperforms both models by predicting shares that are in line with the survey results. 12
13
Table 2 – Comparison car, transit and park-and-ride shares 14
Distance
class (combination) Main mode Survey results Classical model practice model State-of-the- Super-network approach
< 7.5 km Car 75.9 68.4 59.3 73.0 Transit 24.1 31.6 40.1 26.0 P+R 0.0 0.0 0.6 0.0 7.5-30 km Car 64.9 80.1 72.3 63.4 Transit 32.9 19.9 26.3 35.0 P+R 2.1 0.0 1.3 1.6 > 30 km Car 72.1 74.0 65.3 73.1 Transit 20.0 26.0 33.6 22.2 P+R 5.3 0 1.1 4.2 15
4.2 Selected policy measures 16
Four hypothetical multimodal policy measures are selected, as indicated in Figure 3. The first 17
one concerns the opening of a new train station in Amsterdam-West on the rail track between 18
Amsterdam and Haarlem. This station is located between the residential area of Amsterdam 19
Slotermeer and the Amsterdam harbor. This additional stop comes at the costs of 2 minutes of 20
additional travel time for through going passengers. The second example is the introduction of a 21
direct bus connection between Almere and Amsterdam South. This bus line serves several 22
neighborhoods in Almere with a frequency of 4 busses per hour. Using the motorway, the travel 1
time is nearly twice as long as that of the parallel train service, however, access and egress times 2
are reduced. Measure 3 regards the upgrade of the station of Hoofddorp to an intercity station. 3
This involves an additional stop for the 6 intercity train services that are running every hour (in 4
both directions) between The Hague, Amsterdam and Almere. This additional stop comes at the 5
costs of 3 minutes extra travel time for through going passengers. Finally, a new park and ride 6
facility in Amstelveen is introduced, connected to the metro line to Amsterdam central station. 7
Each multimodal policy measure is evaluated on itself by each of the three models. Table 3 gives 8
an overview of relevant assignment results. 9
10
Table 3 – Case study results 11
Case study
example Assignment results Classical model
State-of- the- practice-model Super-network model New station Amsterdam West
Station Amsterdam West: Boardings and alightings (non-car access/egress) 0 128 102 Boardings and alightings (car access/egress) 0 9 16
Corridor Amsterdam-Haarlem:
Car shift (%) + 2.5 + 4.8 + 4.2
Transit shift (%) - 2.5 - 4.8 - 4.2
- Private access modes (%) 0 61 54
- Private egress modes (%) 0 19 26
- Private modes at both ends (%) 0 0 1
New parallel bus service Amsterdam Zuid-Almere
Corridor Amsterdam Zuid-Almere:
Travelers by train 5054 7714 6533
Travelers by the new bus service 661 394 278
Upgrade station Hoofddorp to intercity status
Station Hoofddorp
Boardings and alightings intercity 1536 2224 2032 - Taken from stop train users (%) 44 57 51 - Taken from other modes (%) 56 43 49 Rise in number of boardings and alightings (%) 32 20 34 Decline in stop train boardings and alightings (%) 25 26 15
New park-and-ride facility in Amstelveen
Park-and-ride facility Amstelveen Park-and-ride users (unlimited capacity) - 525 434 - Taken from car alternatives (%) - 48 61 - Taken from transit alternatives (%) - 52 39 Park-and-ride users (max. capacity = 200) - - 201 Park-and-ride users (parking costs 2 euro/h) - - 76 Park-and-ride users (walking distance 300 meter) - - 167 12
13 14
1
Figure 3 – The Amsterdam Metropolitan Area 2
3
4.2 Range and combinatorial complexity of the choice set 4
In the state-of-the-practice model the full combinatorial range of access and egress mode 5
combinations can be specified. However, the number of additional mode chains is usually 6
limited to reduce computation time and memory usage. In the super-network approach, all 7
constraints on mode composition are dropped. The results for the new station in Amsterdam 8
West show that the new station hardly attracts any travelers in the classical model. This is caused 9
by the relatively remote location of the station, excluding walking as a feasible access and egress 10
alternative. The state-of-the-practice model and super-network approach predict more boarding 11
and alighting movements, but the benefits of this station are questionable. Especially since the 12
new station causes a shift to car on the corridor Haarlem-Amsterdam as a result of the increased 13
transit in-vehicle times. The introduction of a new parallel bus service between Amsterdam-Zuid 14
and Almere also shows the effect of ignoring other access and egress modes within the set of 15
alternatives. The classical model predicts a considerable number of travelers taking the bus. As 16
walking is the only access and egress mode, bus stops will be easier to reach than the station, 17
compensating for the additional in-vehicle time. This effect will be much smaller in reality, as 18
bicycle provides a good alternative to reach the station. The number of predicted bus travelers is 19
indeed much smaller in the state-of-the-practice model and the super-network model. In the park-20
and-ride example the classical model completely ignores the new park-and-ride facility and thus 21
this combination of private and public modes as a feasible alternative (representativeness of the 22
choice set). Dropping all constraints on mode composition in the super-network approach may 23
lead to the inclusion of unfeasible routes. Hence, in case of a shortest-path based algorithm, a 1
filter process is needed afterwards. In the state-of-the-practice model, the branch-and-bound 2
algorithm for transit and shortest-path search within the car network automatically exclude 3
unfeasible mode compositions (realism of the choice set). For pre-specified mode chains in the 4
state-of-the-practice model no trip dependent attributes can be taken into account. A distinction 5
between trip-ends can only be made if it is assumed that all trips start at the home-end (morning 6
peak) or the activity-end (afternoon peak). In that case bicycle could be valued differently in a 7
walk-transit-bicycle chain than in a bicycle-transit-walk chain. The super-network approach is 8
much more flexible as routes are a-priori generated. Leg attributes can be updated any time while 9
taking properties of the full trip into account. Furthermore, a distinction is made between the 10
home and activity side of trip. The attributes of a route can thus easily be adapted to its position 11
with the full trip. For the new station in Amsterdam West, also the shares of private transport 12
modes as access and egress are shown (for the complete corridor Amsterdam-Haarlem). The 13
state-of-the-practice model assumes all trips to be in the home-activity direction. As the 14
availability of private modes is higher at the home-end, the share of private modes as access is 15
much higher than at the egress side. In the super-network models these shares are more balanced 16
because a distinction between home-activity and activity-home trips has been made (trip 17
dependent leg properties). 18
19
4.3 Mathematical complexity of the choice model 20
Mode and route choice are still two separated steps in the state-of-the-practice model. The mode 21
choice is first modeled by a nested logit model, after which the route choice is modeled 22
individually for every chain including transit. In the super-network approach travelers are 23
assigned to the network in a single assignment procedure by a paired combinatorial logit model. 24
Hence, the share per mode chain is not modeled in a separate step, but follows from the 25
cumulative flow of all alternatives yielding this mode chain (choice dependencies). This choice 26
model is part of a stochastic user equilibrium assignment, taking into account differences in 27
preferences, perception and network familiarity. This requires sufficient spatial, multimodal and 28
preferential variation in the choice set, which is realized by the doubly stochastic shortest-path 29
based generation algorithm. The state-of-the-practice approach only explicitly models the route 30
choice within transit mode chains (heterogeneous perception and preferences). In this route 31
choice overlap between alternatives is ignored. An extra stop, for example, will attract too many 32
travelers if a zone is already served by the same transit services at other boarding stops. Only the 33
correlation between unobserved terms related to the inclusion of transit modes is accounted for 34
by the nested logit model. As car travelers are assigned to the network in a deterministic way, 35
overlap among routes is no issue. A-priori choice set generation in the super-network approach 36
allows for easy incorporation of correlation between alternatives. Overlap between mode types, 37
as well as physical and service overlap between every pair of routes is accounted for by the 38
paired combinatorial logit model. This can be seen from the park-and-ride example. In the super-39
network model most of the park-and-ride users are subtracted from the car. This stems from the 40
correlation parameters between trip types. Park-and-ride and car alternatives have a higher 41
mutual correlation then park-and-ride and transit alternatives. In the state-of-the-practice nested 42
logit model, however, this correlation cannot be accounted for (correlated alternatives). 43
44
Another advantage of a-priori choice set generation is that route-based preference parameters can 45
be applied. Mode specific constants can be attached to legs depending on their role within the 46
full trip, while station specific constants can be added to represent the attractiveness of boarding 1
and alighting stops. Within the state-of-the-practice model intrinsic preferences for certain modes 2
are not explicitly modeled. Only a mode specific constant for car or transit chains can be 3
included. Furthermore, the transfer penalties mentioned before can also be used to represent 4
differences in the attractiveness of boarding a certain mode or hierarchical station level. These 5
pragmatic solutions, however, have little explanatory value and cannot be directly transferred to 6
other network settings. An upgrade of station Hoofddorp to intercity status shows the effect of 7
station specific preferences. Part of the travelers that now make use of the intercity used to travel 8
by stop train while another part did not board or alight at station Hoofddorp before. This is 9
predicted by all three models. However, the super-network approach also shows another effect. 10
While the share of travelers switching from stop train to intercity is comparable, the number of 11
stop train travelers does not decline as much as the other models predict. This means that new 12
stop train travelers are attracted as well by the new status of station Hoofddorp (trip dependent 13
leg attractiveness). 14
15
4.4 Complexity in demand-supply interactions 16
The congestion on the road caused by car drivers in unimodal trips impacts the attractiveness of 17
park-and-ride alternatives in the state-of-the-practice model. This interaction, however, only 18
works in one way. After the assignment of travelers to transit chains including car as access or 19
egress, flows and resulting travel times on the road are not updated. In the super-network 20
approach the demand-supply interaction are automatically accounted for due to the fact that the 21
assignment covers all modes and mode combinations. That is, the choice among the full range of 22
alternatives is modeled as a single choice (demand-supply interaction between alternatives). In 23
this model, limited car parking is modeled through a BPR-type function. Parking times increase 24
slowly when the capacity is approximated, while grow rapidly (to infinity) when the capacity is 25
exceeded. Capacity limitations are not directly taken into account in the state-of-the-practice 26
model. A penalty might be assigned to the utility of using car as access or egress. However, this 27
penalty is not influenced by the occupation rate of the parking facility. This is shown by the 28
introduction of a park-and-ride facility in Amstelveen. The state-of-the-practice model shows the 29
potential of such a parking facility, but clearly over-predicts the number of users. The super-30
network model corrects for this and shows that all parking places will be used (capacity of 31
transfer locations). Through the same penalty, other transfer related attributes are accounted for. 32
Walking time, parking costs, parking time, and fixed transit costs are all represented by the same 33
penalty. The impact of a single attribute can thus not be easily assessed. In the super-network 34
these transfer related attributes are represented by artificial transfer links. As all transfers go via 35
the pedestrian network, walking is automatically included as well. For the park-and-ride 36
example, also the impacts of parking costs and longer walking distances have been assessed. 37
Only the super-network allows the specification of these attributes and indeed shows a decline in 38
park-and-ride usage. These results might be reproducible by the state-of-the-practice model but 39
only by defining a new transfer penalty (performance of transfer movements). 40 41 42 5. CONCLUDING REMARKS 43
In this paper the suitability of transport models to assess multimodal transport systems was 44
tested. To this end, the classical model, the state-of-the-practice model and the super-network 45
approach have been compared. This paper makes three contributions. First of all, specific 46
requirements for modeling multimodality were formulated and categorized in three classes: the 1
range and combinatorial complexity of the choice set, the mathematical complexity of the choice 2
model, and the complexity in demand-supply-interactions. Each of the three models was tested 3
against the multimodal requirements to provide insight into their strengths and shortcomings for 4
modeling multimodal trips. The results of this conceptual comparison show that state-of-the-5
practice models still fall short in handling the behavioral complexity of multimodal trip making. 6
Second, the hypothesis that using classical and state-of-the-practice models may imply wrong 7
decisions in the design process was illustrated by several examples in the real-world network of 8
Amsterdam Metropolitan Area. The differences in assignment results confirm this hypothesis. In 9
relatively simple transport models requirements are either ignored or inefficiently dealt with. 10
Third, newly developed state-of-the-research models are shown to be a promising alternative. 11
The presented super-network approach reproduces expected travel behavior in response to 12
network supply changes. Through the flexibility of the network representation, a-priori choice set 13
generation, and advanced choice models this modeling approach meets the multimodal modeling 14
requirements. 15
16
It has been shown that decision makers might base their choices on systematically incorrect 17
demand predictions. Hence, when modeling travelers’ choices multimodal complexity has to be 18
taken into account as well as when considering the interactions between travel demand and 19
network supply. Four potential directions for further research remain that are both related to the 20
impact of such an ill-decision making process on actual design choices. Firstly, computation time 21
can be an important argument when opting for a certain transport model. Computation times of 22
the models discussed in this paper increase with their complexity. Although assignment times are 23
comparable among the state-of-the-practice and the super-network approach, the latter requires 24
a-priori route set generation (including post-filtering) which can be time consuming. However, 25
different policy measures can be evaluated from subsets of the same route choice set, limiting the 26
additional computation time. Nevertheless, it is suggested for future research to make a 27
quantitative comparison of computation times. Secondly, all examples relate to small parts of the 28
case study area. On this local scale, differences in assignment results are substantial. However, 29
more research is needed to indicate whether these effects might be negligible at the full network 30
scale or indeed systematically bias the assignment results leading to wrong decisions being 31
made. Thirdly, a translation from assignment results to design criteria has to be made. Decisions 32
are generally based on derived network characteristics, such as travel time, energy consumption, 33
car usage in urban areas and the emission of greenhouse gases. Wrong prediction of network 34
usage does not necessarily imply a change in such decision criteria. The last recommendation 35
relates to activity-based modelling. The super-network, as it is used in this study, use information 36
on trip ends (home-based or activity-based) but does not take into account positions of trips 37
within a tour. Such a tour-based approach would be a useful extension as it would be possible to 38
track vehicle availability among the whole tour. Hence, consistency could be reached in the 39
usage of private modes over a longer time period. 40
41
ACKNOWLEDGEMENT 42
The authors thank the developers of the VENOM model for sharing the detailed physical and 43
service network data for the Metropolitan Region of Amsterdam used in this study. This study 44
was funded by the Netherlands Organization for Scientific Research (NWO) as a part of the 45
program Sustainable Accessibility of the Randstad and by Delft University of Technology. 46
1
REFERENCES 2
(1) Ministry of Infrastructure and Environment, Stuctuurvisie Infrastructuur en Ruimte 3
(SVIR), Den Haag, The Netherlands, 2012 4
(2) Florian, M. J, and J. Wu and S. He, A multiclass multimode variable demand network 5
equilibrium model with hierarchical logit structures, Proceedings of the PTRC Conference, 6
pp. 211-224, 2000 7
(3) Zhou X., H. S. Mahmassani, and K. Zhang, Dynamic micro-assignment modeling 8
approach for integrated multimodal urban corridor management, Transportation Research 9
Part C: Emerging Technologies, Vol. 16, No. 2, pp. 167-186, 2008 10
(4) Sheffi, Y. and W. B. Powell, An algorithm for the equilibrium assignment problem with 11
random link times, Networks, Vol. 12, No. 2, pp. 191-207, 1982 12
(5) Abdelghany, K. F. S., and H.S. Mahmassani, Dynamic trip assignment simulation model 13
for intermodal transportation networks, Transportation Research Record: Journal of the 14
Transportation Research Board, Vol. 1771, pp. 52-60, 2000 15
(6) Liao, F., T. Arentze, and H. Timmermans, Super-network approach for multimodal and 16
multi-activity travel planning, Transportation Research Record: Journal of the 17
Transportation Research Board, Vol. 2175, pp. 38-46, 2010 18
(7) Carlier, K., S. Fiorenzo-Catalano, C. Lindveld, and P. H. L. Bovy, A super-network 19
approach towards multimodal travel modelling, Proceedings of the 82th Transportation 20
Research Board Annual Meeting, Transportation Research Board, Washington D. C., 2003 21
(8) Fiorenzo-Catalano, S., Choice set generation in multimodal transport networks, PhD thesis, 22
Delft University of Technology, TRAIL Thesis Series T2007/6, 2007 23
(9) Fiorenzo-Catalano, S. Hoogendoorn-Lanser, and R. van Nes, Choice set composition 24
modelling in multimodal travelling, Proceedings of the 10th International Conference on 25
Travel Behaviour Research, Lucerne, 2003 26
(10) Arentze, T. A., E. J. E. Molin, Traveller’s preferences in multimodal networks: Design and 27
results of a comprehensive series of choice experiments, Transportation Research Part A, 28
Vol. 58, pp. 15-28, 2013 29
(11) Hoogendoorn-Lanser, S., R. van Nes, and S. P. Hoogendoorn, Modelling transfers in 30
multimodal trips: Explaining correlations, Transportation Research Record: Journal of the 31
Transportation Research Board, Vol. 1985, pp. 144-153, 2006 32
(12) Bovy, P. H. L., and S. Hoogendoorn-Lanser, Modeling route choice in multimodal 33
networks, Proceedings of the 10th International Conference on Travel Behavior Research, 34
Lucerne, 2003 35
(13) Hensher, D., and J. King, Parking demand and responsiveness to supply, pricing and 36
location in the Sidney central business district, Transportation Research Part A, Vol. 35, 37
pp. 177-196, 2001 38
(14) Bos, I. D. M., R. E. C. M. van der Heijden, E. J. E. Molin, and H. J. P. Timmermans, The 39
choice of park-and-ride facilities: an analysis using a context-dependent hierarchical choice 40
experiment, Environment and Planning Part A, Vol. 36, pp. 1673-1686, 2004 41
(15) McFadden, D., Conditional logit analysis of qualitative choice behavior, In: Zaremmbka, 42
P. (ed), Frontiers in Econometrics, Academic Press, New York, 1973 43
(16) Spiess H, and M. Florian, Optimal strategies: A new assignment model for transit 44
networks, Transportation Research Part B: Methodological, Vol. 23, No. 2, 1989 45
(17) Ben-Akiva, M., and M. Bierlaire, Discrete choice methods and their application to short 1
term travel decisions, In: Hall R (ed), Handbook of Transportation Science, Kluwer, pp. 5-2
34, 1999 3
(18) De Cea, J., and J. E. Fernandéz, Transit assignment for congested public transport systems: 4
an equilibrium model, Transportation Science, Vol. 27, No. 2, pp. 19-34, 1993 5
(19) Hoogendoorn-Lanser, S., Modeling travel behavior for multimodal transport network, Delft 6
University of Technology, TRAIL Thesis Series T2005/4, 2005 7
(20) Koppelman, F. S., and C. H. Wen, The paired combinatorial logit model: properties, 8
estimation and application, Transportation Research Record Part B, Vol. 34, pp. 75-89, 9
2000 10
