A demand model with departure time choice for within-day dynamic traffic assignment (original) (raw)

Dynamic traffic assignment: model classifications and recent advances in travel choice principles

2011

Dynamic Traffic Assignment (DTA) has been studied for more than four decades and numerous reviews of this research area have been conducted. This review focuses on the travel choice principle and the classification of DTA models, and is supplementary to the existing reviews. The implications of the travel choice principle for the existence and uniqueness of DTA solutions are discussed, and the interrelation between the travel choice principle and the traffic flow component is explained using the nonlinear complementarity problem, the variational inequality problem, the mathematical programming problem, and the fixed point problem formulations. This paper also points out that all of the reviewed travel choice principles are extended from those used in static traffic assignment. There are also many classifications of DTA models, in which each classification addresses one aspect of DTA modeling. Finally, some future research directions are identified.

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.

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.

A system of a within-day dynamic demand and assignment models for scheduled inter-city services

Demand and assignment models adopted to simulate intercity transportation services are usually based on a static representation of the system. This implies that scheduled transport services, such as rail or airplane, are modelled as service "lines", following an approach substantially similar to the one used to represent urban transit services. Consistently, mode and service type choice models include in their utility functions only time averaged attributes of the schedule such as frequencies and average travel times and prices. The static approach, though adequate for the long-term planning of new infrastructures, is not satisfactory to support operational, marketing oriented decisions such as the service schedule and time-varying prices.

Dynamic user optimal traffic assignment model for many to one travel demand

Transportation Research Part B: Methodological, 1995

A freeway or expressway corridor where all vehicles travel to the same destination such as the city centre is considered in this article, similar to the morning commute problem. A continuous time optimal control model that deals with the dynamic user optimal assignment for multiple origins and single destination is proposed. The splitting rates of traffic flows at each network node are defined as the control variables in this model. The optimality conditions are proved to be equivalent to the dynamic user optimal principle or user equilibrium of instantaneous travel cost. In order not to solve the complicated two-point boundary-value problem with substantial computational times for obtaining the optimal control solution, a steady state-costate solution algorithm is developed that generates an approximate solution to the network optimal control problem. This algorithm exploits advantage of the embedded network structure of the problem and would be computationally efficient. A numerical example with two peak period traffic demands which was drawn from the road network problem between Hong Kong and several adjacent cities of inland China is used to demonstrate the performance of the proposed algorithm.

On a link-based day-to-day traffic assignment model

Transportation Research Part B: Methodological, 2012

In this paper, we perform a rigorous analysis on a link-based day-to-day traffic assignment model recently proposed in . Several properties, including the invariance set and the constrained stability, of this dynamical process are established. An extension of the model to the asymmetric case is investigated and the stability result is also established under slightly more restrictive assumptions. Numerical experiments are conducted to demonstrate the findings. j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / t r b