## Large-scale International Road Traffic Assignment ? Challenges and Solutions

### Authors

O Anker Nielsen, Technical University of Denmark, Department of Transport, DK; R Dyhr Frederiksen, Rapidis Ltd, DK

### Description

The paper presents a new European traffic assignment model that considers regional variation in utility functions and car fleet. Due to the size of the problem new algorithmic approaches had to be developed to solve the model.

### Abstract

Traffic assignment models usually assign traffic flows matrix-wise. More advanced models account for overlapping routes, e.g. a C-logit, path size logit or Probit models, and they consider variations of preferences by random coefficients (e.g. Mixed Logit and Mixed Probit). Multi-class assignment models are in addition segmented into trip purposes and/or vehicle types, which may use different utility functions and vehicle characteristics. The choice functions for road traffic assignment is typically embedded into an equilibrium algorithm to account for congestion in the network.

Even though such approaches ? e.g. the present European TRANS-TOOLS model ? are quite advanced, they implicitly assume the same parameters (except the random variation) in the utility function within each user class. It is hereby implicitly assumed that there are no spatial differences in e.g. value of time, willingness to pay and vehicle characteristics.

The above assumptions are however not plausible at a European scale model due to very large differences in income levels and vehicle characteristics. The paper thus present work carried out in the TEN-CONNECT project, where the road traffic assignment was improved in various aspects with regard to large-scale international road traffic assignment.

It is reasonable to assume that the utility functions at a European scale should depend on socio economic characteristics of the zone of origin of the traveller, e.g. on regional GDP or income. This also means that the input to the assignment must be GA-based matrices, where half of the trips according to the zone of origin of the traveller are assigned forward in the network and half going back. This basically doubles the number of cells assigned onto the network.

Another challenge is the very high differences in the car fleet at the European scale due to differences in income and tax systems. Some countries use mainly petrol driven cars. Others diesel powered. And the age of the car fleet also varies significantly across countries. For environmental calculations it was therefore necessary to keep track of the car types along the route.

With these requirements, TEN-CONNECT became a very large model with about 1500 traffic model zones, 4 trip purposes (private, holyday, business and commuting) + trucks, 50,000 links in the network, where trips from the GA-matrices should be assigned out and back. The road traffic assignment model included in addition traffic going to and from airports. These specifications would result in huge calculation times as well as problems with memory. The full matrices would e.g. take up 8 GB of memory, which then would not be possible to run in RAM on a normal PC.

To solve this, a ?matrix thinning? approach was used. This located zone-pairs with very little traffic and reallocated the traffic to neighbour pairs after some criterion. Especially at the European scale, one would expect many zone relations to have very little traffic. 77% of the cells had e.g. less than 0.1 trips, but the sum of these cells accounted only for 0.33% of the total traffic. 93% of the cells had less than 1 trip, accounting for 1.88% of the trips. The needed RAM and calculation time was reduced almost proportionally with the number of cells.

The matrix thinning was combined with a data structure that only stored the selected cell. The path search method could then be stopped when destinations were reached. Since very few car trips are very long, this improved the path search significantly (reduction of calculation times with about 80%.

Finally, the overall model was re-coded to utilise parallel computing. Using a quad core processor and the parallelised algorithm reduced the calculation time with a factor 2.5. This revealed a potential benefit of further parallelisation into parallel PC?s.

The paper present empirical tests of the new model concerning the solution algorithm and convergence. Differences using fixed utility functions and functions depending on income and GDP were also presented.

GA-based assignment with zone-based utility functions may have many other applications than international traffic, e.g. in order to reflect that travelers from rich neighborhoods will have a higher value of time and willingness to pay for road pricing than others.

#### Publisher

Association for European Transport