Traditionally, traffic assignment models, both for within-day static and dynamic demand, have been formulated following an equilibrium approach in which a state ensuring internal consistency between demand (flows) and costs is sought. However, equilibrium analysis is significant under some assumptions on its “representativeness” (coincidence or closeness with the actual attractor of the system) and analytical properties, such as existence, uniqueness, and stability. Moreover, transients due to modifications of demand and/or supply cannot be simulated through equilibrium models, nor can a statistical description of the state of the system, i.e. means, modes, moments and, more generally, frequency distributions of flows over time be obtained. In this paper, interperiodic (day-to-day) dynamic modeling of transportation networks is addressed following two different approaches, namely deterministic and stochastic processes. In both cases several theoretical results are shown by making use of a formal framework covering most models discussed in the literature as well as some possible extensions. Most of the results reported can be extended to cover within-day dynamic models but these models are not explicitly dealt with. Within the framework of deterministic processes the relevance of day-to-day dynamic models for demand/supply interaction in comparison with the traditional user equilibrium approach is discussed, and conditions for coincidence of fixed-point attractors and equilibrium states are stated. Conditions for existence and uniqueness of fixed-point attractors are proposed, generalizing and extending those presented in the literature for user equilibrium. Conditions for stability of both fixed-points and equilibrium states were formulated by making use of results from non-linear dynamic system theory. Moreover, it is possible to devise a new family of “dynamic” algorithms which simulate the system convergence to a fixed-point in order to obtain an equivalent equilibrium state, as opposed to conventional “optimisation” algorithms. In this case the fixed-point stability analysis can be viewed as a convergence analysis for the algorithms specified this way. Conditions for stochastic process regularity are proposed ensuring, among other things, existence and uniqueness of a stationary probability distribution of system states. These conditions generalize and extend results presented in the literature to a wider class of possible dynamic models. Relationships between a deterministic process, together with corresponding fixed-points or equilibrium states, and stochastic probability distribution are also briefly addressed. Finally, some numerical examples confirming theoretical results are reported for a small test network.

This paper presents a fixed-point formulation of multi-mode multi-user equilibrium assignment with elastic demand. Users of different classes may have different behavioral characteristics as well as sets of available routes and modes. They may also behave according to different deterministic and/or probabilistic choice models with different utility specifications. Demand elasticity is dealt with without using the inverse of demand function; in addition, the mode choice can be explicitly dealt with. Conditions for existence and uniqueness of solutions are stated, which generalize and extend those in the literature. A general framework for solution algorithms is also developed, and a simple new algorithm is proposed to solve asymmetric (stochastic) multi-mode multi-user equilibrium with elastic demand.

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In this paper, urban network design is analysed through a heuristic multi-criteria technique based on genetic algorithms. Both network layout and link capacity (link layout and traffic lights) are optimised. Different optimisation criteria are included for users, non-users and public system managers. Demand is considered elastic with respect to mode choice; both morning and afternoon peak periods are taken into account. In addition, choice of parking location is simulated. The procedure is applied to a test and to a real transportation system. Copyright Springer Science+Business Media B.V. 2006Network Design, Assignment, Multi-objective analysis,

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This paper presents a general modelling approach to day-to-day dynamic assignment to a congested network through discrete-time stochastic and deterministic process models including an explicit modelling of users habit as a part of route choice behaviour, through an exponential smoothing filter, and of their memory of network conditions on past days, through a moving average or an exponentially smoothing filter. An asymptotic analysis of the mean process is carried out to provide a better insight. Results of such analyses are also used for deriving conditions, about values of the system parameters, assuring that the mean process is dissipative and/or converges to some kind of attractor. Numerical small examples are also provided in order to illustrate the theoretical results obtained.