Our model should analyse large scale impacts of failing critical nodes on the European TEN-T network. This TEN-T network consists of a multi-modal network of relatively high density which provides all European regions (including peripheral and outermost regions) with an accessibility that supports their economic, social and territorial development as well as the mobility of their citizens [7]. European transport models built for analysing the TEN-T network usually have a very low level of spatial detail (e.g. considering highways and neglecting local roads) and temporal detail (e.g. only modelling four time periods: weekday peak, weekday off-peak, holiday, weekend). Therefore, these models are not sufficiently detailed to model all detours in the vicinity of the infrastructure failure, as well as not detailed enough to model the built up and propagation of traffic over time and excluding any changes in departure times. Generally, static traffic assignments are employed, whereas a dynamic assignment would be more suitable for modelling disruptions. In a dynamic assignment, smaller time-periods are modelled, and traffic flows are modelled realistically instead of based on arbitrary functions of experienced travel time given a certain amount of vehicles.

Performing dynamic traffic assignments on a detailed European network is computationally very expensive and currently not feasible. But it should be noted that most effects of disruptions are not noticeable throughout Europe: they are resolved within a small area around the disruption. We therefore assume that disruptions only directly affect traffic in the vicinity of the infrastructure object in terms of choices made. On a European level, only secondary effects are noticed (e.g. congestion). The Disruption Transport Model therefore combines these two types of models: a detailed dynamic model for the region in the vicinity of the infrastructure element, referred to as Local Disruption model (LD) and a static traffic assignment model for the rest of the network of interest, referred to as Global Spill-over model (GS). One can see it as zooming in around the object of interest, while zooming out when looking at a European level, as can be seen in Fig. 2. This simulation approach ensures that disruption effects are modelled accurately, whilst also considering the broader impacts at European scale.

The complete model overview is shown in Fig. 3, with the transport model of the LD model on top, the GS model below. Both transport models are based on the well-known 4-step passenger [15] and 5-step freight transport models [18], combined in a shared traffic assignment step. As stated before, we assume that disruptions only affect choices made in the vicinity of the infrastructure object. As such, trip cancellations, modal shifts and departure time changes are only modelled at the detailed model. The resulting choices and delays are used in the GS model. The number of *iterations* (i.e. steps toward reaching an equilibrium) are used to model the day-to-day variability. We believe that the process of reaching an equilibrium by a transport model reflects the process of travellers adjusting toward a new situation in selection of routes.

### 3.1 Procedure *for running the model*

The general steps for running the Disruption Transport Model as shown in Fig. 3 are as follows:

- 1.
Initially, the area in the region of the infrastructure failure (i.e. detailed study area) is defined. This area is modelled with high level of detail and referred to as the *Local Disruption model (LD)*. The remainder of the network is modelled with a lower level of detail, referred to as the *Global Spill-over model (GS)*.

- 2.
The trip generation, trip distribution and mode choice models for passengers, as well as the alike production/consumption, trade patterns, logistic choice and mode choice models for freight, are performed on the *LD model*. No disruption is assumed at this stage – basic models are run.

- 3.
The mode choice model is performed again on the *LD model* for a percentage of the travellers assuming a disrupted network (i.e. including the broken link). The percentages of travellers per mode and user class (passenger/freight) that can shift modes are given by the parameter “Mode shifts”.

- 4.
The OD-matrices of the *LD model* are adjusted given a certain percentage of trip cancellations.

- 5.
An initial departure time profile is used to split the OD-matrices into time-dependent OD-matrices on the *LD model* (i.e. specifying demand for every 5 min).

- 6.
The dynamic assignment is run on the *LD model*. The number of iterations specifies the adaptability toward route change, typically increasing after multiple days.

- 7.
The output of the dynamic assignment is used as an input for the departure time choice model. The percentage of travellers willing to shift departure time is used as an input.

- 8.
Procedure 6 and 7 are repeated depending on the amount of iterations specified.

- 9.
The final link flows and travel times of the *LD model* provide the input to the *GS model*.

- 10.
A static assignment is performed at the *LD model*.

- 11.
The total user delays associated with the disruption are calculated as the sum of those predicted by the *LD model* and the *GS model.*

Due to the learning effect of travellers resulting in day-to-day variability, the model should be rerun for every time period of interest, each involving a different set of parameters (e.g. the percentage of travellers that want to shift mode or departure time), as well as the number of iterations ran. Typically, every additional day corresponds to one additional iteration, with equal number of iterations specified for every module.

### 3.2 Constructing the LD & GS model

The transport model uses two networks: a detailed one covering the region of the infrastructure failure (local disruption model, LD), and one covering Europe completely (global spill-over model, GS). Both networks differ greatly in the level of detail, spatial and temporal resolution. The LD model should be selected in such a way that all mode, route or departure time changes are made by people travelling (partly) via the LD model area. Of course, it is possible that traffic jams propagate over the boundaries of the LD model. Dependent on the area of interest, the LD model covers 30-50 km around the infrastructure object. Additionally, a large level of detail is required: typically, all roads, rail tracks and waterways should be included. During severe disruptions, even very unattractive roads (e.g. with speed limits of just 30 km/h) might provide viable alternatives to the broken link.

The boundaries of the LD network should correspond with the boundaries of one or more of the zones of the GS model to correctly model demand. A small example is shown in Fig. 4, where zone 2 is replaced by the LD model. The LD model splits the GS-zone(s) of interest into multiple smaller zones. For every ingoing and outgoing link of this detailed model, an external centroid should be added. To ensure correspondence of both models, it is not allowed to have any link crossing the boundary of the LD network that does not exist in the GS model. After addition of the external centroids in the LD model, the original nodes and links in the GS model should be replaced by artificial links, that represent travelling the zone.

Once both networks have been constructed, the (mode-specific) OD-matrices of both LD and GS model should be calibrated. Traffic entering or exiting the LD model should correspond to the GS model: both through-traffic (e.g. from zone 1 to 3) as well as departing (e.g. from zone 2 to 3) and arriving traffic (e.g. from zone 1 to 2). An example OD-matrix of the example networks is shown next to the example networks. For example, 200 veh/h travelling from zone 2 to zone 3 (GS model) correspond to the sum of vehicles travelling from zones a, b, c and d to external zone B (LD model). This calibration process requires to know affected OD-pairs (i.e. OD-pairs (partly) travelling via the zone of interest), which can be obtained by analysing a basic traffic assignment of the GS model. Since multiple routes between a single OD-pair might be used, weight factors (i.e. a percentage of traffic normally travelling through the affected zone) might be necessary.

### 3.3 Local disruption model

The first steps of the LD model consist of computing trip generation, distribution and mode choice for passengers, and production/consumption, trade patterns, logistic services and mode choice for freight. This results in mode-specific OD-matrices. The modules should be based on a non-disrupted situation – we do not assume any changes in residential location or job selection.

Next, the mode choice model is run on the disrupted network. Not all travellers are able to switch to a different mode (e.g. due to non-possession of a car) or are willing to do so. Additionally, the elasticities of switching to a different mode are not equal: switch from train to car is often easier than vice versa. For freight traffic, mode switching might not even provide a viable option due to absence of intermodal terminals. It is likely that these elasticities change gradually over time. The mode choice model can be implemented using a simple logit model based on travel times. At the first day of disruption, no travellers will make a mode shift due to absence of knowledge on the new traffic situation. For the second day, travel times of the first day are used as an input, etc.

Trip cancellations can be modelled by adjusting the trip generation module, or by adjusting the OD-matrices directly. The latter is assumed to represent the behavioural responses by travellers in a better way – it is seen as a temporary reduction in traffic, not a reduction in travel demand due to changes in residential locations or jobs. Trip cancellations also represent flexibility used within the supply chain in terms of cancelled freight trips.

Dynamic assignment is employed for modelling route changes due to a disruption. Two types of dynamic assignment algorithms are commonly used: en-route and equilibrium. The en-route assignment models traffic flows according to how drivers react to information received en route, for example via radio broadcasts or variable message signs. On the other hand, the equilibrium assignment only assumes that drivers have full knowledge on travel times accomplished during previous iterations. By running several iterations, an equilibrium in traffic state is reached. The LD model uses this equilibrium assignment algorithm such that iterations reflect the number of days that have passed by since the disruption started. The achieved traffic flows then show the learning effect of travellers, i.e. acquiring knowledge on the traffic situation as days progress.

The dynamic assignment is combined with a departure time choice model. First,a time-dependent OD-matrix is initially generated using a departure time profile, and in further iterations updated according to the departure time choice model. This model reassigns portions of traffic to other (time-dependent) OD-matrices. Not all travellers are willing to change their departure time: this is reflected by a percentage of travellers being able to switch. Note that the departure time choice model requires input on travel times per timestep and is therefore only applied after the first time of applying dynamic assignment.

### 3.4 Linking the LD & GS model

After running the LD model, we need to link its output to the GS model. Therefore, we first need to compute mode-specific original OD-matrices (i.e. without assuming a disruption) using a basic transport model. Next, these matrices need to be adjusted according to mode choices and trip cancellations modelled by the LD model. For adjusting the GS OD-matrices, the final time-dependent OD-matrices of the LD model should be aggregated to one matrix per time period of the GS model (e.g. peak/off-peak). Next, the OD-matrices of the GS model are adjusted according to these aggregated OD-matrices. This is done in the same way as calibrating the OD-matrices (see Fig. 4): the sum of ingoing, outgoing and through-traffic should be equal. Linking both models in terms of route level (i.e. incorporating route choices and departure time choices) is done by updating travel times for every mode for each of the artificial links in the GS model. Departure time choices are thereby indirectly reflected by resulting delays (e.g. peak spreading results in less delay and thus lower travel times).

### 3.5 Global spill-over model

The only relevant part of the GS model is the static traffic assignment. The process of reaching an equilibrium state is achieved by running multiple iterations. However, the process used with dynamic assignment (i.e. “one iteration = one day”) is not suitable, because traffic further away is presumably not affected by the disruption and keeps its equilibrium state. Therefore, we use the output of an equilibrium assignment (without a disruption) as a starting point for running the traffic assignment. The number of iterations only reflects the changes as a result of introducing the disrupted network and adjusting OD-matrices according to the LD model output.

### 3.6 Running and comparing scenarios

To compute the final output of the model, for example the total travel time, the sum of travel time spent in the LD model and the GS model should be taken. To prevent counting delays in the detailed area double, the “artificial links” in the GS model within the zone of interest should be left out. Additionally, the travel time can be split per user class (passenger/freight, but also commuter, business, leisure and bulk, liquid, containerized) and per time period. This is helpful to consider monetary values – typically, the “Value of Time” of a freight vehicle is much higher than that of a leisure traveller. Also, cancellation of trips should be considered carefully in terms of monetary values.