This paper introduces a polynomial combinatorial optimization algorithm for the dynamic user optimal problem. The approach can efficiently solve single destination networks and can be potentially extended to heuristically solve multidestinational networks. In the model, traffic is propagated according to sound traffic flow theoretical models rather than link exit functions; thereby allowing link queue evolution to be modeled more precisely. The algorithm is designed, proven, implemented and computationally tested.

This paper is concerned with the system optimum-dynamic traffic assignment (SO-DTA) problem when the time-dependent demands are random variables with known probability distributions. The model is a stochastic extension of a deterministic linear programming formulation for SO-DTA introduced by Ziliaskopoulos (Ziliaskopoulos, A.K., 2000. A linear programming model for the single destination system optimum dynamic traffic assignment problem, Transportation Science, 34, 1–12). The proposed formulation is chance-constrained based and we demonstrate that it provides a robust SO solution with a user specified level of reliability. The model provides numerous insights and can be a useful tool in producing robust control and management strategies that account for uncertainty in applications where SO-DTA is relevant (e.g. evacuation modeling, computing alternate routes around freeway incidents and establishing lower bounds on network performance).

This paper presents the functionality of the Visual Interactive System for Transportation Algorithms (VISTA) that utilizes a mesoscopic/microscopic simulation called RouteSim and a Dynamic Traffic Assignment (DTA) routine to emulate the behavior of individual drivers and how they distribute themselves into the transportation network. The principal output of the model is the path chosen by every driver to go from their origin to their destination, and the corresponding departure and arrival time. The paper presents the application of VISTA to evaluate: 1) Intelligent Transportation technologies such as the location of variable message signs, detectors, route diversion plans; 2) Traffic Operations such as signal timing plans, transit signal priority plans, flooding, weather conditions; and 3) Short term and Long term transportation planning such as construction plans, addition/deletion of lanes or roadways, addition or improvement of roadway interchanges. A sample of projects where VISTA has been implemented in the USA is presented.

Dynamic Traffic Assignment (DTA) has evolved substantially since the pioneering work of Merchant and Nemhauser. Numerous formulations and solutions approaches have been introduced ranging from mathematical programming, to variational inequality, optimal control, and simulation-based. The aim of this special issue is to document the main existing DTA approaches for future reference. This opening paper will summarize the current understanding of DTA, review the existing literature, make the connection to the approaches presented in this special issue, and attempt to hypothesize about the future.

In this paper, we are concerned with modeling dynamic networks, when drivers simultaneously optimize their departure time and route choice. We state equilibrium conditions and propose a simulation-based model that can solve large networks accounting for many realities of actual networks. The main components of the model are a time-dependent shortest path algorithm for fixed arrival times and a traffic simulator. The proposed model has the potential to realistically capture user decisions when arrival time based origin–destination tables are easier to obtain than the departure time based ones e.g. in the morning peak and in special events. Two solution methodologies are designed and tested: the first emulates users day-to-day dynamic behavior and does not guarantee convergence; the second is a heuristic approach that adjusts link travel times and always converges to an equilibrium solution, although not at the desired level of schedule delay. Computational experiments on a small street network are presented.