On a link-based day-to-day traffic assignment model (original) (raw)

Infinite Dimensional Formulations of Some Dynamic Traffic Assignment Models

Advances in Spatial Science, 1998

Traffic assignment models attempt to determine the usage of each route andlor link in a transportation network, given information about the number of trips being taken between various locations, the characteristics of the network, and the characteristics of the vehicles on the network. Though the term "assignment" seems to connote a prescriptive process in which vehicles are assigned to particular routes, there are both descriptive/positive and prescriptive/normative traffic assignment models.

Behaviour of a whole-link travel time model used in dynamic traffic assignment

Transportation Research Part B: Methodological, 2002

Whole-link models of trac¯ows have been widely used in mathematical programming models for dynamic trac assignment (DTA). In this paper, we consider a well-known whole-link model in which the link travel time, for trac entering at time t, is a function of the number of vehicles on the link, and may also be a function of the in¯ow rate or out¯ow rate at time t. Instead of considering this in a network context, we examine its behaviour for a single link, for given in¯ow pro®les, so as to distinguish behaviour within a link from network behaviour.

The long term behaviour of day-to-day traffic assignment models

Transportmetrica A: Transport Science, 2013

The dynamical behaviour of deterministic process, day-today traffic assignment models is sometimes characterized by convergence to a variety of different fixed equilibrium points dependent upon the initial flow pattern, even though individual trajectories are unique for a given start point. This non-uniqueness is seemingly in sharp contrast to the evolution of stochastic process, day-today models; under certain assumptions these converge in law to a unique stationary distribution, irrespective of the start point. In this paper we show how models may be constructed which exhibit characteristics of both deterministic models and stochastic models, and illustrate the ideas by using a simple example network.

Quasi-Continuous Dynamic Traffic Assignment Model

Transportation Research Record, 1995

Several variants of combined dynamic travel models in discrete time with dynamic user equilibrium or system optimality as the assignment objective have been presented recently. This modeling approach is converted into quasi-continuous time, which enables two key model improvements : (a) traffic volumes are spread over time intervals in continuous time, allowing trips to be split among successive time intervals, and (b) the first-in first-out ordering of trips between all zone pairs is more precisely maintained. The means by which capacity losses are approximated on upstream links caused by spillback queueing from oversaturated links and accidents are also described. Trips are assumed to have scheduled departure times and variable arrival times, but notational variations allowing other model forms are briefly mentioned. Application of this model to a Denver-area network with comparison of results to observed speeds and volumes is described elsewhere.

A within-day dynamic traffic assignment model for urban road networks

Transportation Research Part B: Methodological, 2005

In this paper a new formulation of within-day dynamic traffic assignment is presented, where dynamic user equilibrium is expressed as a fixed point problem in terms of arc flow temporal profiles. Specifically, it is shown that, by extending to the dynamic case the concept of Network Loading Map, is no more needed to introduce a Dynamic Network Loading in order to ensure the temporal consistency of the supply model. On this basis it is possible to devise efficient assignment algorithms, whose complexity is equal to the one resulting in the static case multiplied by the number of time intervals in which the period of analysis is divided. With specific reference to a Logit path choice model, an implicit path enumeration network loading procedure is obtained as an extension of Dial's algorithm; then, the fixed point problem is solved through the Bather's method.

Analysis of dynamic traffic models and assignments

In Proceedings of the 39th Annual Conference of Universities Transport Study January 3 5 2007 Harrogate Uk Universities Transport Study Group, 2007

This paper develops a comprehensive framework for analysing and solving traffic models and assignments in dynamic setting. Traffic models capture the time-varying travel times and flows on a road network and traffic assignments represent the corresponding responses of travellers. There are two different kinds of traffic assignments: dynamic user equilibrium and dynamic system optimum. Under dynamic user equilibrium, traffic is assigned such that for each origin-destination pair in the network, the individual travel costs experienced by each traveller, no matter which combination of travel route and departure time he/she chooses, are equal and minimal. The system optimum assigns traffic such that the total system cost of the network system is minimized. The system optimal traffic pattern provides a useful benchmark for evaluating various transport policy measures such as implementing dynamic road tolls. This system optimal assignment is formulated as a state-dependent optimal control problem. The analysis developed in this paper is novel and it can work with general travel cost functions. Numerical examples are provided for illustration and discussion. Finally, some concluding remarks are given. previous research (see for example, Friesz et al., 1993;, we have gained substantial knowledge on the formulations, properties, and solution methods of dynamic user equilibrium assignment. Dynamic system optimal assignment is an important yet relatively underdeveloped area. Dynamic system optimal assignment process suggests that there is a central "system manager" to distribute network traffic over time in a fixed study period. Consequently, the total, rather than individual, travel cost of all travellers through the network is minimised. Although system optimal assignment is not a realistic representation of network traffic, it provides a bound on how we can make the best use of the road system, and as such it is a useful benchmark for evaluating various transport policy measures. This paper presents a comprehensive framework of dynamic traffic models and traffic assignments. The paper is organized as follows. In Section 2, we review some fundamental requirements on traffic models for use in dynamic traffic assignments, Section 3 presents the formulation of dynamic user equilibrium assignment and the associated travel cost functions. In Section 4, we present the formulation and optimality conditions of dynamic system optimal assignment. Dynamic system optimal assignment problem is formulated as a state-dependent optimal control problem. To understand and solve the dynamic system optimality conditions, we also provide a detailed interpretation of various cost components appear at system optimality. We further develop a novel sensitivity analysis to derive and compute the dynamic externality. Section 5 presents the solution algorithms for solving the sensitivity analysis and the dynamic traffic assignments. The solution algorithms are developed using a dynamic programming approach. Following this, we show some

Stochastic and deterministic formulations of dynamic traffic assignment

Dynamic traffic assignment is now widely recognised as an appropriate approach for modelling route choice and congestion in urban areas during peak periods, and for the evaluation of traffic management measures that are intended for them. Various formulations have been developed in the literature: in the present paper we consider the within-day dynamics of departure-time and route choice using costs based upon travel times and arrival times. We show how a general formulation of this joint choice process can accommodate either stochastic or deterministic user equilibrium principles. A model of traffic flow is required to provide travel times which determine the propagation of traffic through the network and also contribute to the cost of travel. By adopting mechanistic models of traffic movement and hence travel time, we show how temporal departure profiles and route assignments can be calculated according to each of the choice principles and develop cost-throughput relationships for them from this. We consider the effects on these profiles and relationships of various mechanistic travel time models, including deterministic queueing and the more detailed wave model. Detailed comparisons are made between the results according to the various choice and travel time models; we show that a good degree of commonality can be identified between them. The results of this are plausible and compare favourably with those in the literature that arise from the use of simple but non-mechanistic travel time models. We conclude that mechanistic travel time models have a fundamental importance for satisfactory dynamic modelling of congestion and of users' response to it, whichever choice model is adopted.

Equilibrium Characterizations of Solutions to Side Constrained Asymmetric Traffic Assignment Models

1994

In order to refine the basic model of traffic assignment to capture supplementary flow relationships, the traditional modelling strategy is to modify the travel cost mapping. This strategy is well suited for capturing relationships such as interactions among vehicles on different road links and turning priorities in junctions, and it usually results in nonseparable and asymmetric travel cost functions. It is, however, not the proper approach for incorporating traffic flow restrictions such as those imposed by joint capacities on two-way streets or in junctions, or the presence of a traffic control policy. We consider the introduction of side constraints to describe those flow relationships that have more natural interpretations as flow restrictions than as additional travel costs. Such a refinement should be easier to construct and calibrate as well as lead to more reliable traffic models than that using the traditional refinement strategy only.

Link Travel Times II: Properties Derived from Traffic-Flow Models

Networks and Spatial Economics, 2000

We investigate the properties of travel times when the latter are derived from traffic-flow models. In particular we consider exit-flow models, which have been used to model time-varying flows on road networks, in dynamic traffic assignment (DTA). But we here define the class more widely to include, for example, models based on finite difference approximations to the LWR (Lighthill, Whitham and Richards) model of traffic flow, and 'large step' versions of these. For the derived travel times we investigate the properties of existence, uniqueness, continuity, first-in-first-out (FIFO), causality and time-flow consistency (or intertemporal consistency). We assume a single traffic type and assume that time may be treated as continuous or as discrete, and for each case we obtain conditions under which the above properties are satisfied, and interrelations among the properties. For example, we find that FIFO is easily satisfied, but not strict causality, and find that if we redefine travel time to ensure strict causality then we lose time-flow consistency, and that neither of these conditions is strictly necessary or sufficient for FIFO. All of the models can be viewed as an approximation to a model that is continuous in time and space (the LWR model), and it seems that any loss of desirable properties is the price we pay for using such approximations. We also extend the exit-flow models and results to allow 'inhomogeneity' over time (link capacity or other parameters changing over time), and show that FIFO is still ensured if the exit-flow function is defined appropriately.

Large Problems of Dynamic Network Assignment and Traffic Equilibrium

Transportation Research Record: Journal of the Transportation Research Board, 2009

The paper reports on the algorithmic treatment and computer implementation of a macroscopic dynamic traffic assignment model called LADTA. The modelling assumptions and the mathematical analysis founding the model are first stated. Detailed descriptions of the main algorithms are given, together with the principles of the computer implementation. It is shown how the design of the software architecture allows for distributed computation of a traffic assignment. The practical ability of this implementation to tackle with large size networks is illustrated by an application to the Paris road network, which comprises around 1,300 zones and 39,000 links.