Traffic Management Through Link Tolls---An Approach Utilizing 
Side Constrained Traffic Equilibrium Models

Torbjörn Larsson and Michael Patriksson
Department of Mathematics
Linköping Institute of Technology
S-581 83 Linköping
Sweden 

ABSTRACT:

We propose a systematic means for achieving a set of overall traffic
management or planning goals with respect to the performance of the traffic
network through the use of link tolls.  The primary goals are defined by a set
of link flow restrictions.  The tolls that achieve these goals are 
obtained by solving a generalization of the classical user equilibrium model
which includes a set of side constraints on the link flows.  
The set of toll prices obtained is not necessarily unique; this fact enables
the traffic planner to choose a toll scheme which satisfies exogenous
constraints and which may optimize a secondary goal, such as with respect to
the toll itself.  The overall model is derived as a special case of a
mathematical program with equilibrium constraints (MPEC) describing a
Stackelberg game involving the traffic manager and the users of the network. 
The model is shown to yield valuable information also in the
case where the management goals and exogenous toll constraints are
inconsistent with each other or with the underlying network.  We give several
examples of possible applications of the model, including the achievement of a
system optimal flow and the derivation of actions for making public transport
more attractive, and propose a conceptual algorithm for solving it.  The paper
is hoped to provoke continued research in both theoretical and applied
directions. 

KEY WORDS: Stackelberg Game, Link Tolls, Mathematical Programs with 
Equilibrium Constraints, Side Constrained Traffic Equilibrium, 
Lagrange Multipliers, Toll Optimization, Network Design,
System Optimum Flows, Subsidies