Investigation of the existence of city-scale three-dimensional macroscopic fundamental diagrams for bi-modal traffic

Recent research has demonstrated that the Macroscopic Fundamental Diagram (MFD) is reliable and practical tool for modeling traffic dynamics and network performance in single-mode (cars only) urban road networks. In this paper, we first extend the modeling of the single-mode MFD to a bi-modal (bus and cars) one. Based on simulated data, we develop a three-dimensional MFD (3D-MFD) relating the accumulation of cars and buses, and the total circulating flow in the network. We propose an exponential function to capture the shape of the 3D-MFD, which shows a good fit to the data. We also propose an elegant estimation for passenger car equivalent of buses (PCU), which has a physical meaning and depends on the bi-modal traffic in the network. Moreover, we analyze a 3D-MFD for passenger network flows and derive its analytical function. Finally, we investigate an MFD for networks with dedicated bus lanes and the relationship between the shape of the MFD and the operational characteristics of buses. The output of this paper is an extended 3D-MFD model that can be used to (i) monitor traffic performance and, (ii) develop various traffic management strategies in bi-modal urban road networks, such as redistribution of urban space among different modes, perimeter control, and bus priority strategies

Mitigating Bunching with Bus-Following Models and Bus-to-Bus Cooperation

Bus bunching is an instability problem where buses operating on high-frequency public transport lines arrive at stops in bunches. This work unveils that bus-following models can be used to design bus-to-bus cooperative control strategies and mitigate bunching. The use of bus-following models avoids the explicit modelling of bus-stops, which would render the resulting problem discrete, with events occurring at arbitrary time intervals. In a follow-the-leader two-bus system, bus-to-bus communication allows the driver of the following bus to observe (from a remote distance) the position and speed of the leading bus operating in the same transport line. The information transmitted from the leader is then used to control the speed of the follower to eliminate bunching. A platoon of buses operating in the same transit line can be then controlled as leader-follower dyads. In this context, we propose practical control laws to regulate speeds, which would lead to bunching cure. A combined state estimation and remote control scheme is developed to capture the effect of disturbances and randomness in passenger arrivals. To investigate the performance of the developed schemes the 9-km 1-California line in San Francisco with about 50 arbitrary spaced bus stops is used. Simulations with empirical passenger data are carried out. Results show bunching avoidance and improvements in terms of schedule reliability of bus services and delays. The proposed control is robust, scalable in terms of transit network size, and thus easy to deploy by transit agencies to improve communication and guidance to drivers, and reduce costs. © 2000-2011 IEEE

Interpolating Control with Periodic Invariant Sets

This paper presents a novel low-complexity interpolating control scheme involving periodic invariance or vertex reachability of target sets for the constrained control of LTI systems. Periodic invariance relaxes the strict one-step positively invariant set notion, by allowing the state trajectory to leave the set temporarily but return into the set in a finite number of steps. To reduce the complexity of the representation of the required controllable invariant set, a periodic invariant set is employed. This set should be defined within the controllable stabilising region, which is considered unknown during the design process. Since periodic invariant sets are not traditional invariant sets, a reachability problem can be solved off-line for each vertex of the outer set to provide an admissible control sequence that steers the system state back into the original target set after a finite number of steps. This work develops a periodic interpolating control (pIC) scheme between such periodic invariant sets and a maximal admissible inner set by means of an inexpensive linear programming problem, solved on-line at the beginning of each periodic control sequence. Theorems on recursive feasibility and asymptotic stability of the pIC are given. A numerical example demonstrates that pIC provides similar performance compared to more expensive optimization-based schemes previously proposed in the literature, though it employs a naive representation of the controllable invariant set. © 2020 EUCA

Decentralised interpolating control: A periodic invariance approach

This paper presents a decentralised periodic interpolating control (dpIC) scheme for the constrained control of interconnected systems, which employs periodic invariance and vertex reachability of target sets. Periodic invariance allows the state of the system to leave a candidate set temporarily but return into the set in a finite number of steps. We consider a periodic invariant set with low-complexity (e.g. rectangle, hexagon for planar systems) to replace the expensive controllable invariant outer set. This set is defined within the controllable stabilising region of each subsystem and a reachability problem is solved off-line for each vertex of the outer set to provide an admissible control sequence that steers the system state back into the original target set after a finite number of steps. dpIC is effectuated between such periodic invariant sets for each subsystem and the local maximal admissible inner set by means of an inexpensive linear programming problem, which is solved on-line at the beginning of each periodic control sequence. dpIC is demonstrated on the problem of stabilising a platoon of vehicles. Copyright © 2020 The Authors. This is an open access article under the CC BY-NC-ND licens

Reduced-complexity interpolating control with periodic invariant sets

A low-complexity interpolating control scheme based on the concept of periodic invariance is proposed. Periodic invariance allows the state trajectory to leave the controllable invariant set temporarily but return into the set in a finite number of steps. A periodic set with easy representation is considered to reduce the expensive computation of the controllable invariant set. Since this set is not a traditional invariant set, a vertex reachability problem of target sets is solved off-line for each vertex of the set and provides a contractive control sequence that steers the system state back into the original set. Online, the periodic interpolating control (pIC) scheme allows to transition between such periodic invariant sets and an inner set endorsed with positive invariance properties. Proofs of recursive feasibility and asymptotic stability of the pIC are given. A numerical example demonstrates that pIC provides similar performance compared to more expensive optimisation-based schemes. © 2021 Informa UK Limited, trading as Taylor & Francis Group

Multi-Commodity Traffic Signal Control and Routing With Connected Vehicles

A real-time traffic management policy that integrates traffic signal control and multi-commodity routing of connected vehicles in networks with multiple destinations is developed. The proposed policy is based on a multi-commodity formulation of the store-and-forward model and assumes all vehicles are able to exchange information with the infrastructure. Vehicles share information about their current location and final destination. Based on this information, the strategy determines both optimized signal timings at every intersection and vehicle-specific routing information at every link of the network. The control actions, i.e., signal times and routing information, are updated at every cycle and delivered by a finite horizon optimal control problem cast into a rolling horizon framework. The underlying optimization problem is convex, and thus the method is suitable for real-time operation in large networks. The method is validated via a micro-simulation study in networks with up to twenty intersections and, in all simulations, outperforms a real-time traffic-responsive signal control strategy that is based on a single-commodity store-and-forward model. The scalable computation effort for increasing network sizes and prediction horizon confirms the computational efficiency of the method. © 2000-2011 IEEE

Functional distributional clustering using spatio-temporal data

This paper presents a new method called the functional distributional clustering algorithm (FDCA) that seeks to identify spatially contiguous clusters and incorporate changes in temporal patterns across overcrowded networks. This method is motivated by a graph-based network composed of sensors arranged over space where recorded observations for each sensor represent a multi-modal distribution. The proposed method is fully non-parametric and generates clusters within an agglomerative hierarchical clustering approach based on a measure of distance that defines a cumulative distribution function over temporal changes for different locations in space. Traditional hierarchical clustering algorithms that are spatially adapted do not typically accommodate the temporal characteristics of the underlying data. The effectiveness of the FDCA is illustrated using an application to both empirical and simulated data from about 400 sensors in a 2.5 square miles network area in downtown San Francisco, California. The results demonstrate the superior ability of the the FDCA in identifying true clusters compared to functional only and distributional only algorithms and similar performance to a model-based clustering algorithm. © 2021 Informa UK Limited, trading as Taylor & Francis Group