On Robust Distributed Control of Transportation Networks

With the ever-growing traffic demands, the transportation networks are getting more and more congested. While expanding these networks with more roads is both costly and in many cities not even feasible, the rapid development of new sensing and communication techniques has made it possible to perform control of transportation networks in real-time. With the right usage of such technologies, existing transportation networks' capacities can be utilized better in order to lower the congestion levels. However, the control has to be done robustly, since real-time control and close to maximal utilization also make the networks more fragile and if not, even a small perturbation can have a tremendous impact on the traffic network. In this thesis, a few solutions that lead to better transportation network utilization are presented, designed with said robustness requirements in mind. In the first part of the thesis, a decentralized control strategy for traffic signals is presented. The proposed policy, which we call Generalized Proportional Allocation (GPA), is inspired by the proportional fairness allocation for communication networks. The original proportional fairness controller does not explicitly take the overhead time needed to shift between different activation phases into account. We, therefore, enhance the proportional fairness so that it adapts its cycle length to the current demand. When the demand is higher, one wants longer signal cycles not to waste too much of the time overhead, while for lower demands, the cycle lengths should be shorter, so that the drivers do not have to wait for a long time. Stability for an averaged version of this control strategy is proved together with throughput-optimality of the controller. This means that no other control strategy can handle larger exogenous inflows to the network than the GPA-controller. Since the traffic signal controllers such as the GPA may allocate service to an empty line, due to the fact that several lanes can receive green light simultaneously, a model that handles this issue is proposed. For this model, the well-posedness of the dynamical system is shown when the traffic signal controller is Lipschitz continuous.The GPA controller's performance is also evaluated in a microscopic traffic simulator. In the microsimulations, it is shown how the proposed feedback controller outperforms the standard fixed-time controller for a scenario based on all traffic over the duration of one full day in Luxembourg. The controller's performance is also compared to another decentralized controller for traffic signals, the MaxPressure controller, for an artificial Manhattan-like network. From these simulations, it can be concluded that the GPA performs better than MaxPressure during low demands, but the MaxPressure performs better when the demand is high. The fact that the GPA does not require any information about the network, apart from the current queue lengths, makes it robust to perturbations. In other words, the control strategy does not have to be updated when the demand or topology of the network changes.The second part of the thesis is devoted to routing problems. First, the problem of routing a fleet of vehicles in an optimal way for the whole fleet is considered. The objective is then to achieve a minimum delay in average for the entire fleet. The routing algorithm takes into account the presence of regular drivers that are trying to optimize their own traveling time in the network. Conditions are posted for when such a routing assignment exists, and two algorithms to compute it are shown.At last, a type of dynamic routing policies for multicommodity flows is studied. The routing policies are designed with the objective to avoid congested routes. It has previously been shown that if only one class of vehicles are present, the network is robust to perturbations with these routing policies. A model for multicommodity flows is proposed, and it is shown that the robustness properties for the single-commodity case do not necessarily hold in the multicommodity case

Generalized Proportional Allocation Policies for Robust Control of Dynamical Flow Networks

We study a robust control problem for dynamical flow networks. In the considered dynamical models, traffic flows along the links of a transportation network --modeled as a capacited multigraph-- and queues up at the nodes, whereby control policies determine which incoming queues at a node are to be allocated service simultaneously, within some predetermined scheduling constraints. We first prove a fundamental performance limitation by showing that for a dynamical flow network to be stabilizable by some control policy it is necessary that the exogenous inflows belong to a certain stability region, that is determined by the network topology, link capacities, and scheduling constraints. Then, we introduce a family of distributed controls, referred to as Generalized Proportional Allocation (GPA) policies, and prove that they stabilize a dynamical transportation network whenever the exogenous inflows belong to such stability region. The proposed GPA control policies are decentralized and fully scalable as they rely on local feedback information only. Differently from previously studied maximally stabilizing control strategies, the GPA control policies do not require any global information about the network topology, the exogenous inflows, or the routing, which makes them robust to demand variations and unpredicted changes in the link capacities or the routing decisions. Moreover, the proposed GPA control policies also take into account the overhead time while switching between services. Our theoretical results find one application in the control of urban traffic networks with signalized intersections, where vehicles have to queue up at junctions and the traffic signal controls determine the green light allocation to the different incoming lanes

Macroscopic modelling and robust control of bi-modal multi-region urban road networks

The paper concerns the integration of a bi-modal Macroscopic Fundamental Diagram (MFD) modelling for mixed traffic in a robust control framework for congested single- and multi-region urban networks. The bi-modal MFD relates the accumulation of cars and buses and the outflow (or circulating flow) in homogeneous (both in the spatial distribution of congestion and the spatial mode mixture) bi-modal traffic networks. We introduce the composition of traffic in the network as a parameter that affects the shape of the bi-modal MFD. A linear parameter varying model with uncertain parameter the vehicle composition approximates the original nonlinear system of aggregated dynamics when it is near the equilibrium point for single- and multi-region cities governed by bi-modal MFDs. This model aims at designing a robust perimeter and boundary flow controller for single- and multi-region networks that guarantees robust regulation and stability, and thus smooth and efficient operations, given that vehicle composition is a slow time-varying parameter. The control gain of the robust controller is calculated off-line using convex optimisation. To evaluate the proposed scheme, an extensive simulation-based study for single- and multi-region networks is carried out. To this end, the heterogeneous network of San Francisco where buses and cars share the same infrastructure is partitioned into two homogeneous regions with different modes of composition. The proposed robust control is compared with an optimised pre-timed signal plan and a single-region perimeter control strategy. Results show that the proposed robust control can significantly: (i) reduce the overall congestion in the network; (ii) improve the traffic performance of buses in terms of travel delays and schedule reliability, and; (iii) avoid queues and gridlocks on critical paths of the network