This paper reviews the methods and technologies for congestion pricing of roads. Congestion tolls can be implemented at scales ranging from individual lanes on single links to national road networks. Tolls can be differentiated by time of day, road type and vehicle characteristics, and even set in real time according to current traffic conditions. Conventional toll booths have largely given way to electronic toll collection technologies. The main technology categories are roadside-only systems employing digital photography, tag & beacon systems that use short-range microwave technology, and in-vehicle-only systems based on either satellite or cellular network communications. The best technology choice depends on the application. The rate at which congestion pricing is implemented, and its ultimate scope, will depend on what technology is used and on what other functions and services it can perform.

Traffic congestion pricing methodologies and technologies

This paper considers a simultaneous route and departure (SRD) time choice equilibrium assignment problem in network with queues The problem is modeled on discrete-time basis and formulated as an equivalent “zero-extreme value” minimization problem, in which the first-in-first-out (FIFO) behavior at intersection is guaranteed by proper formulation of the dynamic link travel times A heuristic solution algorithm is proposed, which simulates a normal day-to-day dynamic system by a route/time-swapping process, thereby reaching to an extreme point of the minimization problem The existence of discrete-time dynamic user-equilibrium (UE) solutions is investigated The iteration-to-iteration stability of the proposed algorithm is discussed, together with numerical results on two example networks

Modeling and solving the dynamic user equilibrium route and departure time choice problem in network with queues

This paper presents a new dynamic model of peak period traffic flows on congested capacity-constrained urban road networks. While respecting the first in, first out (FIFO) discipline of road traffic queues and the exit capacities of road links, the model determines the (time-varying) costs incurred in traversing the various routes when (time-varying) route inflows are specified. It is proved that if this model is used to find route costs then a dynamic user equilibrium exists. The paper also gives four optimisation formulations of the dynamic user equilibrium problem. A descent algorithm is suggested; there is, as yet, no proof that the algorithm converges to an equilibrium. Finally, the paper introduces a family of alternative methods of determining dynamic flows which (almost) satisfy FIFO, and specifies one member of this family in some detail. These alternative methods arise as a consequence of using different ways of specifying the priority of a vehicle or a group of vehicles.

A new dynamic traffic model and the existence and calculation of dynamic user equilibria on congested capacity-constrained road networks

A day-to-day dynamic framework, in which the DYnamic Network Assignment Simulation Model for Advanced Road Telematics (DYNASMART) simulation-assignment model is applied to evaluate the performance of traffic networks, is developed to study network dynamics under real-time information and responsive signal control systems. The focus in this paper is primarily on commuter trips from home to work in a general network. Two levels of tripmaker decision-making processes are incorporated: (1) day-to-day dynamics and (2) real-time dynamics. Day-to-day dynamics consider the choices of departure time and route according to indifference bands of tolerable ‘schedule delay’, defined as the difference between the user's actual and preferred arrival times, and are thus governed by tripmakers' daily learning processes. Real-time dynamics consider en-route switching decisions in response to real-time information on prevailing traffic conditions. The resulting flows could be used in updating the supplied real-time information as well as the traffic control parameters. Two types of traffic control responsiveness are evaluated: (1) daily adjustment of signal timing parameters to reflect the preceding day's traffic patterns; and (2) real-time traffic-responsive signal control driven by prevailing flow patterns. The framework is illustrated through numerical experiments to investigate the day-to-day evolution of network flows under real-time information and responsive signal control, and assess the effectiveness of such information in a proper dynamic perspective.

Day-to-day evolution of network flows under real-time information and reactive signal control

This paper presents a theory of traffic equilibrium which involves responsive signal control policies; in this theory drivers' route choices and the control policy's choice of green times are treated in a symmetrical manner. The central theme of the paper is the iterative optimization assignment algorithm. This algorithm may be considered as a means of calculating equilibria which are consistent with a given responsive control policy. But it may also be regarded as a highly idealized model of the day to day dynamics of drivers' route choices when a responsive signal setting policy is employed; on "day" 1 the signals are held fixed and drivers settle down to an equilibrium flow pattern, on "day 2" the flow pattern is held fixed and the signals are updated according to the control policy for the fixed flow pattern, on "day" 3 the signals are held fixed and drivers settle down to an equilibrium flow pattern'. We state natural but strong conditions on the responsive control policy which guarantee that this algorithm is bound to converge to a convex set of flow, control pairs such that i the flow is a user equilibrium and ii the control parameters satisfy the responsive control policy; and we give a proof of convergence under these conditions-we do not seek to minimize total travel cost. Our conditions involve the delay or cost formula used; with the BPR cost formula, modified in a natural way to allow for green times, the traditional policy of choosing control parameters which minimize delay for the observed traffic pattern does satisfy these conditions in full. However, with Webster's delay formula traditional control policies are a long way from satisfying our conditions; and seeking to satisfy them with this delay formula leads us to two novel control policies. We assume throughout that demand is determined by a fixed OD matrix, giving the steady total flow rates for each OD pair. We also suppose that network characteristics do not change; so that incidents are not considered and saturation flows, for example, are constant.

Traffic Equilibrium with Responsive Traffic Control

We describe a deterministic queueing assignment model which seeks to reduce total travel delays in a road traffic network by routeing drivers according to the total delay caused on each link (the local marginal delay). The model is approximate and is applicable to networks with many origin-destination pairs and many bottlenecks. Optimality of the solution determined by the model is discussed. It is particularly shown that, unlike in the steady state (Dafermos and Sparrow, 1969), reducing total travel times by using the local marginal delay will not generally result in an optimal solution. Results are provided for two networks.

A model for the dynamic system optimum traffic assignment problem

The paper considers traffic assignment, with traffic controls, in an increasingly dynamic way. First, a natural way of introducing the responsive policy, P o , into steady state traffic assignment is presented. Then it is shown that natural stability results follow within a dynamical version of this static equilibrium model (still with a constant demand). We are able to obtain similar stability results when queues are explicitly allowed for, provided demand is constant . Finally we allow demand to vary with time; we consider the dynamic assignment problem with signal-settings now fixed . Here we assume that vehicles are very short and that deterministic queueing theory applies, and show that the time-dependent queueing delay at the bottleneck at the end of a link is a monotone function of the time-dependent input profile to the bottleneck. We have been unable to obtain results when dynamic demand and responsive signal control are combined.

The dynamics of traffic assignment and traffic control: A theoretical study

Current developments in urban road pricing envisage four different systems for charging for road space: (1) point or cordon charging, (2) changing per kms traveled, (3) charging per minute spent traveling, and (4) charging for time spent in congestion. These will have differing impacts on demand and will lead to differing distributions of traffic in the urban road network.

M. Ghali

Papers

A model for the dynamic system optimum traffic assignment problem

The dynamics of traffic assignment and traffic control: A theoretical study

A Comparison of the Performance of Alternative Road Pricing Systems. Volume 3: Transport Policy