Dynamic Route Control for Motorway Networks
by Jan H. van Schuppen
Control measures have been installed on motorway networks around the main urban centres of several countries and more are planned, see Figure 1. Car drivers on motorway networks may be aided by information about traffic. Route control helps car drivers to select a route that optimizes travel time through a network. CWI has participated in a EU project for the next generation of route control.
Route control aims to provide information to network users such that each user can optimize travel costs. Provision of routing information or route directives is expected to result in an efficient use of the network capacity under all traffic conditions. Route control is likely to be primarily useful in traffic circumstances with traffic queues or with major incidents. Currently used enroute measures of route information include: variable messages signs (VMSs), messages broadcast on radio channels, and variable direction signs. The information may have the form of lengths of traffic queues at particular locations; travel time estimates or predictions for one or several routes; or variable direction signs that should be considered as recommendations. The road user then may make a route choice.
The display of lengths of traffic queues although partly useful is often not accurate enough for the network users. The road user wants to minimize travel costs over the possible routes. In this article travel costs are identified with travel time. Travel time predictions are useful when based on the anticipated effect of the information provided by the signs. This is not yet the case in most current traffic information systems. In the literature there is much confusion about the interaction of information provision and control.
For the next generation of route control measures variable direction signs or travel time predictions are currently considered. The direction signs are to be considered as recommendations, the network user is free to choose a route. This proposal then leads to the problem as to how to compute the variable route directives. The mathematics used in the investigation is control and system theory, in particular control of dynamic games, predictive control, control theory of nonlinear systems, and Modelling.
The route control problem is formulated as a game problem with many decision makers or agents. It will be assumed that all road users for a particular origin-destination (OD) pair can be considered as an agent in the game. Although in principle the road users make the route choice individually, the choice will be the same for all users travelling on the same OD pair. The restriction to OD traffic flows as agents corresponds to a user equilibrium as used in traffic theory.
Each decision maker, an OD traffic flow, must make a choice as to the route to use in case there are two or more routes available. The route directive thus consists of the route choices of all OD pairs. It is further assumed that the control objective of each OD traffic flow is to minimize the travel time from origin to destination. In dynamic game problems an equilibrium must be selected. A Nash equilibrium is a route directive, for all OD traffic flows, such that if only one OD pair deviates from the route of that equilibrium by taking another route then its cost will increase. The restriction to a Nash equilibrium seems quite reasonable considering the fact that drivers on different OD traffic flows generally do not communicate with each other.
Although there is theory available for its solution, the dynamic game problem in its full generality is neither analytically nor numerically tractable. Therefore a control law has been formulated based on a moving horizon algorithm in a discrete-time setting. At each time step a Nash equilibrium of the route directives is searched for, while the travel times of the traffic flow for any OD pair are estimated by a predictive control algorithm.
After the theoretical part of the investigation had been concluded the national road agency asked CWI to carry out a simulation study of the proposed algorithm. A model for traffic flow has been detailed for the flow in a motorway network near Amsterdam, see Figure 2. Route control is considered only for four OD pairs denoted by the major motorways: (A2,A8), (A4,A8), (A8,A2), and (A8,A4).
A particular simulation concerns the following traffic condition. The model is simulated for 15 minutes until it reached an equilibrium state. Then an incident was simulated to occur in the sections directly south of the Coentunnel, resulting in a reduction in the number of lanes in these sections from two to one. Consequently a traffic queue started to build up on the Western part of the ring A10 through the Coentunnel. From the state of the network model at 15 minutes after the start of the incident, travel time estimates were made under all possible route directives. That route directive is a Nash equilibrium where for almost all OD traffic flows the shortest distance route is recommended except for the OD traffic flow (A8,A2) for which the variable route directive points to the alternate route via the Northern and Eastern part of the ring. Densities of traffic on the outer and the inner ring of the A10 motorway ring with this route directive are displayed in the Figures 3 and 4.
A control law for route control of motorway networks has been described. Further development work is needed before the control law can be tested on the road. Mathematics research is needed for control theory of dynamic games, and on the existence, uniqueness, and search algorithms of Nash equilibria in transportation networks.
Jan H. van Schuppen - CWI
Tel: +31 20 592 4085