Analysis of dynamic system optimum and externalities with departure time choice

This paper aims to analyse the dynamic system optimal assignment with departure time choice, which is an important, yet underdeveloped area. The main contribution of this paper is the necessary conditions and the sensitivity analysis for dynamic system optimizing flow. Following this, we revisit the issue of dynamic externality in a more plausible way. We showed that how the externality can be derived and interpreted from the control theoretic formulation and the sensitivity analysis of traffic flow. To solve the system optimal assignment, we propose a dynamic programming solution approach. We present numerical calculations and discuss the characteristics of the results. In particular, we contrast the system optimal assignment with its equilibrium counterpart in terms of the amount of travel generated, flow profiles, and travel costs

Modelling dynamic stochastic user equilibrium for urban road networks

In this study a dynamic assignment model is developed which estimates travellers' route and departure time choices and the resulting time varying traffic patterns during the morning peak. The distinctive feature of the model is that it does not restrict the geometry of the network to specific forms. The proposed framework of analysis consists of a travel time model, a demand model and a demand adjustment mechanism. Two travel time models are proposed. The first is based on elementary relationships from traffic flow theory and provides the framework for a macroscopic simulation model which calculates the time varying flow patterns and link travel times given the time dependent departure rate distributions; the second is based on queueing theory and models roads as bottlenecks through which traffic flow is either uncongested or fixed at a capacity independent of traffic density. The demand model is based on the utility maximisation decision rule and defines the time dependent departure rates associated with each reasonable route connecting, the O-D pairs of the network, given the total utility associated with each combination of departure time and route. Travellers' choices are assumed to result from the trade-off between travel time and schedule delay and each individual is assumed to first choose a departure time t, and then select a reasonable route, conditional on the choice of t. The demand model has therefore the form of a nested logit. The demand adjustment mechanism is derived from a Markovian model, and describes the day-to-day evolution of the departure rate distributions. Travellers are assumed to modify their trip choice decisions based on the information they acquire from recent trips. The demand adjustment mechanism is used in order to find the equilibrium state of the system, defined as the state at which travellers believe that they cannot increase their utility of travel by unilaterally changing route or departure time. The model outputs exhibit the characteristics of real world traffic patterns observed during the peak, i. e., time varying flow patterns and travel times which result from time varying departure rates from the origins. It is shown that increasing the work start time flexibility results in a spread of the departure rate distributions over a longer period and therefore reduces the level of congestion in the network. Furthermore, it was shown that increasing the total demand using the road network results in higher levels of congestion and that travellers tend to depart earlier in an attempt to compensate for the increase in travel times. Moreover, experiments using the queueing theory based travel time model have shown that increasing the capacity of a bottleneck may cause congestion to develop downstream, which in turn may result in an increase of the average travel time for certain O-D pairs. The dynamic assignment model is also applied to estimate the effects that different road pricing policies may have on trip choices and the level of congestion; the model is used to demonstrate the development of the shifting peak phenomenon. Furthermore, the effect of information availability on the traffic patterns is investigated through a number of experiments using the developed dynamic assignment model and assuming that guided drivers form a class of users characterised by lower variability of preferences with respect to route choice

Analysis of dynamic system optimal assignment with departure time choice

Most analyses on dynamic system optimal (DSO) assignment are done by using the control theory with an outflow traffic model. On the one hand, this control theoretical formulation provides some attractive mathematical properties for analysis. On the other hand, however, this kind of formulation often ignores the importance of ensuring proper flow propagation. Moreover, the outflow models have also been extensively criticized for their implausible traffic behaviour. This paper aims to provide another framework for analysing a DSO assignment problem based upon sound traffic models. The assignment problem we considered aims to minimize the total system cost in a network by seeking an optimal inflow profile within a fixed planning horizon. This paper first summarizes the requirements on a plausible traffic model and reviews three common traffic models. The necessary conditions for the optimization problem are then derived using a calculus of variations technique. Finally, a simple working example and some concluding remarks are given

Existence of simultaneous route and departure choice dynamic user equilibrium

This paper is concerned with the existence of the simultaneous route-and-departure choice dynamic user equilibrium (SRDC-DUE) in continuous time, first formulated as an infinite-dimensional variational inequality in Friesz et al. (1993). In deriving our existence result, we employ the generalized Vickrey model (GVM) introduced in and to formulate the underlying network loading problem. As we explain, the GVM corresponds to a path delay operator that is provably strongly continuous on the Hilbert space of interest. Finally, we provide the desired SRDC-DUE existence result for general constraints relating path flows to a table of fixed trip volumes without invocation of a priori bounds on the path flows.Comment: 21 page

Analysis of dynamic traffic models and assignments

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

User equilibrium, system optimum, and externalities in time-dependent road networks

This paper develops a comprehensive framework for analysing and calculating user equilibrium, system optimum, and externalities in time-dependent road networks. 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 optimal flow is determined by solving a state-dependent optimal control problem, which assigns traffic such that the total system cost of the network system is minimized. The externalities are derived by using a novel sensitivity analysis. The analyses developed in this paper can work with general travel cost functions. Numerical examples are provided for illustration and discussion. Finally, some concluding remarks are given

Formulation, existence, and computation of boundedly rational dynamic user equilibrium with fixed or endogenous user tolerance

This paper analyzes dynamic user equilibrium (DUE) that incorporates the notion of boundedly rational (BR) user behavior in the selection of departure times and routes. Intrinsically, the boundedly rational dynamic user equilibrium (BR-DUE) model we present assumes that travelers do not always seek the least costly route-and-departure-time choice. Rather, their perception of travel cost is affected by an indifference band describing travelers’ tolerance of the difference between their experienced travel costs and the minimum travel cost. An extension of the BR-DUE problem is the so-called variable tolerance dynamic user equilibrium (VT-BR-DUE) wherein endogenously determined tolerances may depend not only on paths, but also on the established path departure rates. This paper presents a unified approach for modeling both BR-DUE and VT-BR-DUE, which makes significant contributions to the model formulation, analysis of existence, solution characterization, and numerical computation of such problems. The VT-BR-DUE problem, together with the BR-DUE problem as a special case, is formulated as a variational inequality. We provide a very general existence result for VT-BR-DUE and BR-DUE that relies on assumptions weaker than those required for normal DUE models. Moreover, a characterization of the solution set is provided based on rigorous topological analysis. Finally, three computational algorithms with convergence results are proposed based on the VI and DVI formulations. Numerical studies are conducted to assess the proposed algorithms in terms of solution quality, convergence, and computational efficiency