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

Traffic models for dynamic system optimal assignment

Most analyses on dynamic system optimal (DSO) assignment are done by using a 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 concluding remarks are given

A rolling-horizon quadratic-programming approach to the signal control problem in large-scale congested urban road networks

The paper investigates the efficiency of a recently developed signal control methodology, which offers a computationally feasible technique for real-time network-wide signal control in large-scale urban traffic networks and is applicable also under congested traffic conditions. In this methodology, the traffic flow process is modeled by use of the store-and-forward modeling paradigm, and the problem of network-wide signal control (including all constraints) is formulated as a quadratic-programming problem that aims at minimizing and balancing the link queues so as to minimize the risk of queue spillback. For the application of the proposed methodology in real time, the corresponding optimization algorithm is embedded in a rolling-horizon (model-predictive) control scheme. The control strategy’s efficiency and real-time feasibility is demonstrated and compared with the Linear-Quadratic approach taken by the signal control strategy TUC (Traffic-responsive Urban Control) as well as with optimized fixed-control settings via their simulation-based application to the road network of the city centre of Chania, Greece, under a number of different demand scenarios. The comparative evaluation is based on various criteria and tools including the recently proposed fundamental diagram for urban network traffic

A platoon based model for urban traffic networks: identification, modeling and distributed control

Urban traffic control poses a challenging problem in terms of coordinating the different traffic lights that can be used in order to influence the traffic flow. The goal of this approach is to identify and to develop hybrid system models of controlled and uncontrolled intersections and links in urban traffic networks based on formation of platoons. The other purpose is to develop a feedback control algorithm that optimizes the signal timing plan based on the strategy of platoons formation estimated via the vehicle re-identification technology

Convexity and Robustness of Dynamic Traffic Assignment and Freeway Network Control

We study the use of the System Optimum (SO) Dynamic Traffic Assignment (DTA) problem to design optimal traffic flow controls for freeway networks as modeled by the Cell Transmission Model, using variable speed limit, ramp metering, and routing. We consider two optimal control problems: the DTA problem, where turning ratios are part of the control inputs, and the Freeway Network Control (FNC), where turning ratios are instead assigned exogenous parameters. It is known that relaxation of the supply and demand constraints in the cell-based formulations of the DTA problem results in a linear program. However, solutions to the relaxed problem can be infeasible with respect to traffic dynamics. Previous work has shown that such solutions can be made feasible by proper choice of ramp metering and variable speed limit control for specific traffic networks. We extend this procedure to arbitrary networks and provide insight into the structure and robustness of the proposed optimal controllers. For a network consisting only of ordinary, merge, and diverge junctions, where the cells have linear demand functions and affine supply functions with identical slopes, and the cost is the total traffic volume, we show, using the maximum principle, that variable speed limits are not needed in order to achieve optimality in the FNC problem, and ramp metering is sufficient. We also prove bounds on perturbation of the controlled system trajectory in terms of perturbations in initial traffic volume and exogenous inflows. These bounds, which leverage monotonicity properties of the controlled trajectory, are shown to be in close agreement with numerical simulation results