Most Likely Traffic Equilibrium Route Flows --- Analysis and Computation

Torbjörn Larsson, Jan Lundgren, Clas Rydergren
Division of Optimization
Department of Mathematics
Linköping Institute of Technology
S-581 83 Linköping
Sweden

and

Michael Patriksson
Department of Mathematics
Chalmers University of Technology
S-412 96 Gothenburg
Sweden

ABSTRACT:

When analyzing equilibrium traffic flows it is usually the link flows
and link travel demands that are of interest, but in some certain
cases analyses require the knowledge of route flows.  It is well known
that the route flows are non-unique in the static and deterministic
cases of traffic equilibrium.  Furthermore, different assignment
methods can generate different route flow output. We show how this
non-uniqueness can affect the results in applications such as in the
O--D estimation/adjustment problem, in the construction of induced
O--D matrices, exhaust fume emission analyses and in link toll usage
analyses.  We state a model for finding, uniquely, the most likely
route flows given the equilibrium link flows, and propose a solution
algorithm for the problem based on partial dualization. We present
computational results for the proposed algorithm and results from an
application to exhaust fume emissions.

KEY WORDS: Traffic Equilibrium, Route Flows, Entropy Maximization