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Infrastructure resilience

The Dutch road network is vulnerable to all kinds of disruptions such as incidents, road works, bad weather, events, vacation crowds, etc. For example, Snelder and Drolenga (2012) showed that about 25% of the total travel time loss on the main road network is caused by incidents. According to the Knowledge Institute for Mobility Policy, 8% of all travel time loss is extreme (KiM, 2015). The extent to which extreme travel time loss occurs depends, among other things, on the robustness of the road network. It is therefore important to be able to quantify robustness.

Road robustness indicator

Robustness is described in the 'Integral Mobility Analysis' (IMA) 2021 and updated in the IMA 2023 as follows: disruptions, such as incidents, can impede the functioning of the mobility system, thereby temporarily deteriorating accessibility and flow. The more sensitive to disruptions, the longer the resulting extra travel time and the less robust the network is. The existing robustness indicator consistently revealed that areas experiencing the highest congestion are also deemed the most vulnerable. The more congested a location is, the higher the extra travel time experienced by travelers. This can be explained by the fact that locations with high traffic volumes have a higher number of expected disruptions, and the impact of those disruptions is higher as well, because more vehicles are affected, and they experience higher delays due to a lack of spare capacity on the road itself and on alternative roads. Consequently, investment initiatives to enhance the robustness will be prioritized largely based on traffic flows and capacities on specific road sections or routes.

To strategically invest in network components that offer the highest added value within the network structure, an enhanced robustness indicator is introduced that considers delays upstream of a disruption, extra travel time caused by taking alternative routes and delays caused by extra congestion on alternative routes. The robustness scores are determined collectively for all road users. This considers both probability (of local disruptions) and consequence (extreme travel time loss).

\[ Robustness = Chance \cdot Consequence \]

Determine the chance

The expected number of incident in an hour at a specific day part is calculated by multiplying the risk (i.e., probability) of an incident and the vehicle kilometers traveled as specified in Snelder et al. 2012 :

\[ E_{link,p} = Risk* LaneChangeIndicator_p \cdot VTK_p \]
\[ VTK_p = \frac {I_{corr}} {I} \cdot I \cdot Length_{link} \cdot 10^{-6} \]

where:

  • \(E_{link,p}\) - expected chance of an incident at the link on day part p
  • \(Risk\) – chance of single lane closure per Million kilometer
  • \(LaneChangeIndicator_p\) - lane change indicator at day part p, as described by Snelder (2012).
  • \(VTK_p\) - vehicle million kilometers traveled in an hour at day part p

Determine the Consequence

When an incident happens, it may lead to longer travel time and longer travel distance. They are merged by converting the time and distance to generalized cost(Zhou et al., 2023).

\[ Consequence = VLH \cdot FTS \cdot VoT + ExtraKm \cdot CostPerKm \]

where:

  • \(Consequence\) - extra cost due to the incident
  • \(VLH\) - total vehicle loss hours due to the incident
  • \(FTS\) - FileTerugSlag. It indicates the spillback of congestion to upstream roads which gives an indication of the extra delays caused by spillback. For more information, refer to (Snelder et al. 2016)
  • \(VoT\) - value of time (€/h)
  • \(ExtraKm\) - extra travel distance of all vehicles due to the incident
  • \(CostPerKm\) - fuel cost per kilometer

The VoT for passenger cars with different trip purpose and trucks are listed below (RWS 2021):

Travel purpose VoT (€/h)
Work (PA) 10.422
Business (PA) 32.082
Others (PA) 8.488
Heavy trucks (L2 & L3) 50.862
Light-duty trucks (L1 & L2) 32.082

The fuel cost per kilometer per travel purpose (RWS 2021):

Travel purpose average variable cost (fuel) (€/km)
Work (PA) 0.1089
Business (PA) 0.1102
Others (PA) 0.1083
Heavy trucks (L2 & L3) 0.1175
Light-duty trucks (L1 & L2) 0.3982

The average variable cost is calculated based on a weighted average of the kilometers travelled on HWN (hoofdwegennet) and OWN (onderliggend wegennet).

\[ cost = \frac{cost_{HWN} * VTK_{HWN} + cost_{OWN} * VTK_{OWN} } {VTK_{HWN} + VTK_{OWN}} \]

Input data

Computing the indicator for a road network typically requires the following datasets:

  • The LMS geloaded network (shapefile)
  • OD matrices per mode per travel purpose
  • The probability of incidents table (e.g., in Excel)

Output data

After computing the indicator for each link in the network the following values are available:

  • VLH (total vehicle loss hours due to incident)
  • ExtraKm (extra travel distance due to incident)
  • Chance
  • Robustness value

Literature

Snelder, M. and Drolenga, H., 2012. De Robuustheid van het Nederlandse hoofdwegennet, TNO.

KiM, 2015. Mobiliteitsbeeld 2015, Kennisinstituut voor Mobiliteitsbeleid.

RWS, Technische Documentatie Groeimodel 4, 2021.

Zhou, H., Snelder, M., van der Poel, B., Vier, P.J., 2023. R12513 Robustness indicator, TNO.

M. Snelder, E. de Feijter, S. Calvert, J. van Huis, A. Soekroella and H. Zhou, “TNO 2016 R10641,” TNO, 2016.