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

Multi-Gated Perimeter Flow Control of Transport Networks

This paper develops a control scheme for the multi-gated perimeter traffic flow control problem of urban road networks. The proposed scheme determines optimally distributed input flows (or feasible entrance link green times) for a number of gates located at the periphery of a protected network area. A macroscopic model is employed to describe the traffic dynamics of the protected network. To describe traffic dynamics outside of the protected area, we augment the basic state-space model with additional state variables to account for the queues at store-and-forward origin links at the periphery. We aim to equalise the relative queues at origin links and maintain the vehicle accumulation in the protected network around a desired point, while the system's throughput is maximised. The perimeter traffic flow control problem is formulated as a convex optimal control problem with constrained control and state variables. For real-time control, the optimal control problem is embedded in a rolling-horizon scheme using the current state of the whole system as the initial state as well as predicted demand flows at entrance links. A meticulous simulation study is carried out for a 2.5 square mile protected network area of San Francisco, CA, including fifteen gates of different geometric characteristics. Results demonstrate the efficiency and equity properties of the proposed approach to better manage excessive queues outside of the protected network area and optimally distribute the input flows

Two-layer adaptive signal control framework for large-scale dynamically-congested networks: Combining efficient Max Pressure with Perimeter Control

Traffic-responsive signal control is a cost-effective and easy-to-implement network management strategy with high potential in improving performance in congested networks with dynamic characteristics. Max Pressure (MP) distributed controller gained significant popularity due to its theoretically proven ability of queue stabilization and throughput maximization under specific assumptions. However, its effectiveness under saturated conditions is questionable, while network-wide application is limited due to high instrumentation cost. Perimeter control (PC) based on the concept of the Macroscopic Fundamental Diagram (MFD) is a state-of-the-art aggregated strategy that regulates exchange flows between regions, in order to maintain maximum regional travel production and prevent over-saturation. Yet, homogeneity assumption is hardly realistic in congested states, thus compromising PC efficiency. In this paper, the effectiveness of network-wide, parallel application of PC and MP embedded in a two-layer control framework is assessed with mesoscopic simulation. Aiming at reducing implementation cost of MP without significant performance loss, we propose a method to identify critical nodes for partial MP deployment. A modified version of Store-and-forward paradigm incorporating finite queue and spill-back consideration is used to test different configurations of the proposed framework, for a real large-scale network, in moderately and highly congested scenarios. Results show that: (i) combined control of MP and PC outperforms separate MP and PC applications in both demand scenarios; (ii) MP control in reduced critical node sets leads to similar or even better performance compared to full-network implementation, thus allowing for significant cost reduction; iii) the proposed control schemes improve system performance even under demand fluctuations of up to 20% of mean.Comment: Submitted to Transportation Research Part C: Emerging Technologie

A three-dimensional macroscopic fundamental diagram for mixed bi-modal urban networks

Recent research has studied the existence and the properties of a macroscopic fundamental diagram (MFD) for large urban networks. The MFD should not be universally expected as high scatter or hysteresis might appear for some type of networks, like heterogeneous networks or freeways. In this paper, we investigate if aggregated relationships can describe the performance of urban bi-modal networks with buses and cars sharing the same road infrastructure and identify how this performance is influenced by the interactions between modes and the effect of bus stops. Based on simulation data, we develop a three-dimensional vehicle MFD (3D-vMFD) relating the accumulation of cars and buses, and the total circulating vehicle flow in the network. This relation experiences low scatter and can be approximated by an exponential-family function. We also propose a parsimonious model to estimate a three-dimensional passenger MFD (3D-pMFD), which provides a different perspective of the flow characteristics in bi-modal networks, by considering that buses carry more passengers. We also show that a constant Bus-Car Unit (BCU) equivalent value cannot describe the influence of buses in the system as congestion develops. We then integrate a partitioning algorithm to cluster the network into a small number of regions with similar mode composition and level of congestion. Our results show that partitioning unveils important traffic properties of flow heterogeneity in the studied network. Interactions between buses and cars are different in the partitioned regions due to higher density of buses. Building on these results, various traffic management strategies in bi-modal multi-region urban networks can then be integrated, such as redistribution of urban space among different modes, perimeter signal control with preferential treatment of buses and bus priority

Perimeter Control with Heterogeneous Cordon Signal Behaviors: A Semi-Model Dependent Reinforcement Learning Approach

Perimeter Control (PC) strategies have been proposed to address urban road network control in oversaturated situations by monitoring transfer flows of the Protected Network (PN). The uniform metering rate for cordon signals in existing studies ignores the variety of local traffic states at the intersection level, which may cause severe local traffic congestion and ruin the network stability. This paper introduces a semi-model dependent Multi-Agent Reinforcement Learning (MARL) framework to conduct PC with heterogeneous cordon signal behaviors. The proposed strategy integrates the MARL-based signal control method with centralized feedback PC policy and is applied to cordon signals of the PN. It operates as a two-stage system, with the feedback PC strategy detecting the overall traffic state within the PN and then distributing local instructions to cordon signals controlled by agents in the MARL framework. Each cordon signal acts independently and differently, creating a slack and distributed PC for the PN. The combination of the model-free and model-based methods is achieved by reconstructing the action-value function of the local agents with PC feedback reward without violating the integrity of the local signal control policy learned from the RL training process. Through numerical tests with different demand patterns in a microscopic traffic environment, the proposed PC strategy (a) is shown robustness, scalability, and transferability, (b) outperforms state-of-the-art model-based PC strategies in increasing network throughput, reducing cordon queue and carbon emission

Real-Time Estimation of Critical Vehicle Accumulation for Maximum Network Throughput

Perimeter traffic flow control has recently been found to be a practical and efficient control scheme in mitigating traffic congestion in urban road networks. This control scheme aims at stabilising the accumulation of vehicles of the socalled network fundamental diagram near critical accumulation to achieve maximum network throughput. Nevertheless, the maximum throughput in urban road networks may be observed over a range of accumulation-values. In this work, an adaptive perimeter flow control strategy is proposed that allows the automatic monitoring of the critical accumulation to help maintain the accumulation near the optimal range of accumulation-values, while network's throughput is maximised. To this end, we design a Kalman filter-based estimation scheme that utilises real-time measurements of circulating flow and accumulation of vehicles to produce estimates of the currently prevailing critical accumulation. We use real data from an urban area with 70 sensors and show that the area exhibits a network fundamental diagram with low scatter. We demonstrate that the fundamental diagram is reproduced under different days but its shape and critical occupancy depend on the applied semi-real-time signal control and the distribution of congestion in the network. Results from the application of the estimation algorithm to the experimental data indicate good estimation accuracy and performance, and rapid tracking behaviour

Heterogeneous perimeter flow distributions and MFD-based traffic simulation

This paper investigates how network and traffic heterogeneities influence the accuracy of a simulation based on the Macroscopic Fundamental Diagram (MFD). To this end, the MFD modeling of a simple grid network is compared to the outputs of a mesoscopic kinematic wave model simulating traffic in the same network. Heterogeneous distributions of demand and supply at the boundaries are set to the local entries and exits of the mesoscopic model to generate heterogeneous network loadings. These boundary conditions challenge the MFD simulation, as significant discrepancies are observed between both modeling approaches in steady state. While the accurate calibration of the MFD and the average trip length can reduce the discrepancies for heterogeneous demand settings, no simple solution exists for heterogeneous supply settings, because they may drive very different internal congestion patterns in the network. We propose a correction method to adjust the MFD model outputs in such a case