Dynamic modelling for congestion pricing

Project title:  Dynamic modelling for congestion pricing, and related strategies.

Project duration:  Three years (4/1994 - 7/1997).

Project staff:    Principal Investigator: Professor Malachy Carey

                        Research Assistant:  Michael Bowers

EPSRC grant number: GR/J53171

The following is a one page summary of the 1997 final report to the EPSRC on the above project/ grant.

Objectives of the research

 The main objectives of the research, as set out in the original RG2 application form, were:

(i)                  Develop and extend certain optimization models of time-varying (dynamic) flows on congested networks, so as to model road pricing, and flow controls.

(ii)                Use these to derive analytical relationships between flows, prices and controls, under various proposed pricing structures, and existing and proposed flow control (signal setting) rules.

(iii)               Develop computer programs to implement, test and illustrate these models, algorithms and relationships, and apply to test networks.  Show complementarity of (i)-(ii) to existing methods and research.

We achieved these objectives, and other objectives set out in the original proposal.  We developed several different dynamic optimisation models for road pricing and flow controls.  Each of these focuses on a different aspect of the problem and improves on models currently available.  For example, some of the models focus on congestion in the form of queues at traffic lights, and some on congestion along travel links.  Some are concerned with system optimum and some with user equilibrium.  Some have several variants depending, for example, on the form of localised flow control rules implemented. 

 For each of these models we developed the underlying theory and model formulation; extended static definitions of user equilibrium, externalities, etc., to fit the dynamic context; analysed the properties of the model, including optimality conditions and implied optimal road pricing rules; devised appropriate methods to ensure the first-in-first-out property, etc.  We also encountered and dealt with new problems, for example a `holding-back' problem that appears to be inherent in optimisation models for dynamic traffic assignment. 

 Also, for each of the above models, we devised special purpose algorithms to solve the model; implemented all of these algorithms in computer programmes; used these programmes to test and demonstrate the algorithms by applying to example networks; analysed the resulting numerical solutions; revised the algorithms, and sometimes the models, in the light of problems identified from the computational results. 

 Overall, the research is concerned with modelling for road pricing and flow control for congested networks in the light of the time-varying (dynamic) nature of travel demand and traffic flows (e.g. daily peaks).  Most other approaches to this are based on simulating the effects of toll systems and flow control rules.  However, there are important questions which are difficult, or even impossible, to answer with simulation approaches, and the models and methods developed in this project help us to address these.

Key words: Transport planning. Traffic control. Road pricing. Transport network modelling.