Side Constrained Traffic Equilibrium Models---Analysis, Computation and
Applications

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

ABSTRACT:

We consider the introduction of side constraints for refining a descriptive or
prescriptive traffic equilibrium assignment model, and analyze a general such a
model.  Side constraints can be introduced for several diverse reasons; we
consider three basic ones.  First, they can be used to describe the effects of
a traffic control policy.  Second, they can be used to
improve an existing traffic equilibrium model for a given application by
introducing, through them, further information about the traffic flow
situation at hand.  As such, these two strategies complement the refinement
strategy based on the use of non-separable, and typically asymmetric, travel
cost functions.  Third, they can be used to describe flow restrictions that a
central authority wishes to impose upon the users of the network. 

We study a general convexly side constrained traffic equilibrium 
assignment model, and establish several results pertaining to the above
described areas of application.  First, for the case of prescriptive side
constraints that are associated with queueing effects, for example those
describing signal controls, we establish a characterization of the solutions
to the model through a Wardrop user equilibrium principle in terms of
generalized travel costs and an equilibrium queueing 
delay result; in traffic networks with queueing the solutions may therefore be
characterized as Wardrop equilibria in terms of well-defined and natural
travel costs.  Second, we show that the side constrained problem is equivalent
to an equilibrium model with travel cost functions properly
adjusted to take into account the information introduced through the side
constraints.  Third, we show that the introduction of side constraints can be
used as a means to derive the link tolls that should be levied in order to
achieve a set of traffic management goals.  

The introduction of side constraints makes the problem computationally more
demanding, but this drawback can to some extent be overcome through the use of
dualization approaches, which we also briefly discuss.