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. In this work, we unveil 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 a lead bus operating in the same transport line. The information transmitted from the lead bus is then used to control the speed of the follower to eliminate bunching. In this context, we first propose practical linear and nonlinear control laws to regulate space headways and speeds, which would lead to bunching cure. Then a combined state estimation and remote control scheme, which is based on the Linear-Quadratic Gaussian theory, is developed to capture the effect of bus stops, traffic disturbances, and randomness in passenger arrivals. To investigate the behaviour and performance of the developed approaches the 9-km 1-California line in San Francisco with about 50 arbitrary spaced bus stops is used. Simulations with real passenger data obtained from the San Francisco Municipal Transportation Agency are carried out. Results show bunching avoidance and significant improvements in terms of schedule reliability of bus services and delays. The proposed control is robust, scalable in terms of public transport network size, and thus easy to implement in real-world settings

A Robust Integrated Multi-Strategy Bus Control System via Deep Reinforcement Learning

An efficient urban bus control system has the potential to significantly reduce travel delays and streamline the allocation of transportation resources, thereby offering enhanced and user-friendly transit services to passengers. However, bus operation efficiency can be impacted by bus bunching. This problem is notably exacerbated when the bus system operates along a signalized corridor with unpredictable travel demand. To mitigate this challenge, we introduce a multi-strategy fusion approach for the longitudinal control of connected and automated buses. The approach is driven by a physics-informed deep reinforcement learning (DRL) algorithm and takes into account a variety of traffic conditions along urban signalized corridors. Taking advantage of connected and autonomous vehicle (CAV) technology, the proposed approach can leverage real-time information regarding bus operating conditions and road traffic environment. By integrating the aforementioned information into the DRL-based bus control framework, our designed physics-informed DRL state fusion approach and reward function efficiently embed prior physics and leverage the merits of equilibrium and consensus concepts from control theory. This integration enables the framework to learn and adapt multiple control strategies to effectively manage complex traffic conditions and fluctuating passenger demands. Three control variables, i.e., dwell time at stops, speed between stations, and signal priority, are formulated to minimize travel duration and ensure bus stability with the aim of avoiding bus bunching. We present simulation results to validate the effectiveness of the proposed approach, underlining its superior performance when subjected to sensitivity analysis, specifically considering factors such as traffic volume, desired speed, and traffic signal conditions

Network-level optimal control for public bus operation

The paper presents modeling, control and analysis of an urban public transport network. First, a centralized system description is given, built up from the dynamics of individual buses and bus stops. Aiming to minimize three conflicting goals (equidistant headways, timetable adherence, and minimizing passenger waiting times), a reference tracking model predictive controller formulated based on the piecewise-affine system model. The closed-loop system is analyzed with three methods. Numerical simulations on a simple experimental network showed that the temporal evolution of headways and passenger numbers could maintain their periodicity with the help of velocity control. With the help of randomized simulation scenarios, sensitivity of the system is analyzed. Finally, infeasible regions for the bus network control was sought using by formulating an explicit model predictive controller

Optimal Control of Electric Bus Lines

Bus lines are inherently unstable systems, where any delay tends to be further amplified by the accrued passenger loads encountered at stops downstream. This self-reinforcing mechanism, when combined with the multiple sources of disturbances of an urban environment, can lead to the problem of bus bunching. To mitigate this, various types of control strategies have been proposed and some are routinely employed by transit agencies around the globe to improve service regularity. They range from simple rule-based ad-hoc solutions, to elaborate real-time prediction-based bus velocity control. However, most of these strategies only focus on service-related objectives, and often disregard the potential energy savings that could be achieved through the control intervention. Velocity-based control, in particular, is very suitable for eco-driving strategies, which can increase the energy efficiency of the transit system by adjusting the planned velocity trajectories of the vehicles based on the road and traffic conditions.This thesis proposes a scalable resolution method for the bus line regularity and eco-driving optimal control problem for electric buses. It is shown how this problem can be recast as a smooth nonlinear program by making some specific modelling choices, thus circumventing the need for integer decision variables to capture bus stop locations and avoiding the infamous complexity of mixed-integer programs. Since this nonlinear program is weakly coupled, a distributed optimization procedure can be used to solve it, through a bi-level decomposition of the optimization problem. As a result, the bulk of the computations needed can be carried out in parallel, possibly aboard each individual bus. The latter option reduces the communication loads as well as the amount of computations that need to be performed centrally, which makes the proposed resolution method scalable in the number of buses. Using the concept of receding horizons to introduce closed-loop control, the optimized control trajectories obtained were applied in a stochastic simulation environment and compared with classical holding and velocity control baselines. We report a faster dissipation of bus bunching by the proposed method as well as energy efficiency improvements of up to 9.3% over the baselines

Bilevel optimization for bunching mitigation and eco-driving of electric bus lines

The problems of bus bunching mitigation and of the energy management of groups of vehicles are traditionally treated separately in the literature, and formulated in two different frameworks. The present work bridges this gap by formulating the optimal control problem of the bus line eco-driving and regularity control as a smooth, multi-objective nonlinear program. Since this nonlinear program only has few coupling variables, it is shown how it can be solved in parallel aboard each bus such that only a marginal amount of computations need to be carried out centrally. This leverages the decentralized structure of a bus line by enabling parallel computations and reducing the communication loads between the buses, which makes the problem resolution scalable in terms of the number of buses. Closed-loop control is then achieved by embedding this procedure in a model predictive control. Stochastic simulations based on real passengers and travel times data are realized for several scenarios with different levels of bunching for a line of electric buses. Our method achieves fast recoveries to regular headways as well as energy savings of up to 9.3% when compared with traditional holding or speed control baselines

Energy-aware predictive control for electrified bus networks

For an urban bus network to operate efficiently, conflicting objectives have to be considered: providing sufficient service quality while keeping energy consumption low. The paper focuses on energy efficient operation of bus lines, where bus stops are densely placed, and buses operate frequentlywith possibility of bunching. The proposed decentralized, bus\ua0 fleet control solution aims to combine four conflicting goals incorporated into a multi-objective, nonlinear cost function. The multi-objective optimization is solved under a receding horizon model predictive framework.The four conflicting objectives are as follows. One is ensuring periodicity of headways by watching leading and following vehicles i.e. eliminating bus bunching. Equal headways are only a necessary condition for keeping a static, predefifined, periodic timetable. The second objective is timetable tracking, and passenger waiting time minimization. In case of high passenger demand, it is desirable to haste the bus in order to prevent bunching. The final objective is energy efficiency. To this end, an energy consumption model is formulated considering battery electric vehicles with recuperation during braking. Alternative weighting strategies are compared and evaluated through realistic scenarios, in a calibrated microscopic traffic simulation environment. Simulation results confirm of 3-8% network level energy saving compared to bus holding control while maintaining punctuality and periodicity of buses

Optimal headway merging for balanced public transport service in urban networks

This paper presents a velocity control/advise algorithm relying on vehicle-to-vehicle communication, to ensure the headway homogeneity of buses on a joint corridor, i.e. when multiple lines merge and travel on the same route. The proposed control method first schedules merging buses prior to entering a common line. Second, based on the position and velocity of the bus ahead of the controlled one, a shrinking horizon model predictive controller (MPC) calculates a proper velocity profile for the merging bus. The model is able to predict short time- space behavior of public transport buses enabling constrained, finite horizon, optimal control solution to reach the merging point with equidistant headways, taking all buses from different lines into account. The controller is tested in a high fidelity traffic simulator with realistic scenarios

Optimally combined headway and timetable reliable public transport system

This paper presents a model-based multiobjective control strategy to reduce bus bunching and hence improve public transport reliability. Our goal is twofold. First, we define a proper model, consisting of multiple static and dynamic components. Bus-following model captures the longitudinal dynamics taking into account the interaction with the surrounding traffic. Furthermore, bus stop operations are modeled to estimate dwell time. Second, a shrinking horizon model predictive controller (MPC) is proposed for solving bus bunching problems. The model is able to predict short time-space behavior of public transport buses enabling constrained, finite horizon, optimal control solution to ensure homogeneity of service both in time and space. In this line, the goal with the selected rolling horizon control scheme is to choose a proper velocity profile for the public transport bus such that it keeps both timetable schedule and a desired headway from the bus in front of it (leading bus). The control strategy predicts the arrival time at a bus stop using a passenger arrival and dwell time model. In this vein, the receding horizon model predictive controller calculates an optimal velocity profile based on its current position and desired arrival time. Four different weighting strategies are proposed to test (i) timetable only, (ii) headway only, (iii) balanced timetable - headway tracking and (iv) adaptive control with varying weights. The controller is tested in a high fidelity traffic simulator with realistic scenarios. The behavior of the system is analyzed by considering extreme disturbances. Finally, the existence of a Pareto front between these two objectives is also demonstrated

MULTILINE HOLDING CONTROL AND INTEGRATION OF COOPERATIVE ITS

Transportation is an important sector of the global economy. The rapid urbanization and urban sprawl comes with continuous demand for additional transportation infrastructure in order to satisfy the increasing and variable demand. Public transportation is a major contributor in alleviating traffic congestion in the modern megacities and provide a sustainable alternative to car for accessibility. Public transport operation is inherently stochastic due to the high variability in travel times and passenger demand. This yields to disruptions and undesired phenomena such as vehicles arriving in platoons at stops. Due to the correlation between the headway between vehicles and passenger demand, bunching leads to long waiting time at stops, overcrowded vehicles, discomfort for the passengers and from the operators side poor management of available resources and overall a low of service of the system. The introduction of intelligent transport systems provided innovative applications in order to monitor the operation, collect data and react dynamically to any disruption of the transit system. Advanced Public Transport Systems extended the range of control strategies and their objectives beyond schedule adherence and reliance on historical data alone. Among strategies, holding is a thoroughly investigated and applicable control strategy. With holding, a vehicle is instructed to remain at a designated stop for an additional amount of time after the completion of dwell time, until a criterion is fulfilled. Depending on the characteristics of the line the criterion aim for schedule adherence or regularity or minimization of passenger costs and its components. So far, holding is used for regulating single line operation. Beyond single line, it has been used for transfer synchronization at transfer hubs and recently has been extended to regulate the operation on consecutive stops that are served by multiple lines. The first part of this dissertation is dedicated to real time holding control of multiple lines. A rule based holding criterion is formulated based on the passenger travel time that accounts for the passengers experiencing the control action. Total holding time is estimated based on the size of all passenger groups that interact. The formulated criterion can be applied on all different parts of trunk and branch network. Additionally, the criterion is coupled with a rule based criterion for synchronization and the decision between the two is taken based on the passenger cost. The criterion has been tested for different trunk and branch networks and compared with different control schemes and its performance has been assessed using regularity indices as well as passenger cost indicators for the network in total but also per passenger group. Finally, an analysis has been conducted in order to define under which network and demand configuration multiline control can be preferred over single line control. Results shown that under specific demand distributions multiline control can outperform single line control in network level. Continuously new technologies are introduced to transit operation. Recently, Cooperative Intelligent Transport Systems utilized in the form of Driver Advisory Systems (DAS) shown that can provide the same level of priority with transit signal priority without changing the time and the phases of a traffic light. However, until now the available DASs focus exclusively on public transport priority neglecting completely the sequence of the vehicles and the effects on the operation. In the second part of the dissertation, two widely used DASs are combined with holding in order to meet both the objective of reducing the number of stops at traffic signals and at the same time maintain regularity. Two hybrid controllers are introduced, a combination of two holding criteria and a combination of holding and speed advisory. Both controllers are tested using simulation in comparison to the independent application of the controllers and different levels of transit signal priority. The hybrid controllers can drastically reduce transit signal priority requests while they manage to achieve both objectives