A robust optimization approach for dynamic traffic signal control with emission considerations

We consider an analytical signal control problem on a signalized network whose traffic flow dynamic is described by the Lighthill–Whitham–Richards (LWR) model (Lighthill and Whitham, 1955; Richards, 1956). This problem explicitly addresses traffic-derived emissions as constraints or objectives. We seek to tackle this problem using a mixed integer mathematical programming approach. Such class of problems, which we call LWR-Emission (LWR-E), has been analyzed before to certain extent. Since mixed integer programs are practically efficient to solve in many cases (Bertsimas et al., 2011b), the mere fact of having integer variables is not the most significant challenge to solving LWR-E problems; rather, it is the presence of the potentially nonlinear and nonconvex emission-related constraints/objectives that render the program computationally expensive.To address this computational challenge, we proposed a novel reformulation of the LWR-E problem as a mixed integer linear program (MILP). This approach relies on the existence of a statistically valid macroscopic relationship between the aggregate emission rate and the vehicle occupancy on the same link. This relationship is approximated with certain functional forms and the associated uncertainties are handled explicitly using robust optimization (RO) techniques. The RO allows emissions-related constraints and/or objectives to be reformulated as linear forms under mild conditions. To further reduce the computational cost, we employ a link-based LWR model to describe traffic dynamics with the benefit of fewer (integer) variables and less potential traffic holding. The proposed MILP explicitly captures vehicle spillback, avoids traffic holding, and simultaneously minimizes travel delay and addresses emission-related concerns.     

Dynamic traffic routing in a network with adaptive signal control

In real traffic networks, travellers’ route choice is affected by traffic control strategies. In this research, we capture the interaction between travellers’ route choice and traffic signal control in a coherent framework. For travellers’ route choice, a VANET (Vehicular Ad hoc NETwork) is considered, where travellers have access to the real-time traffic information through V2V/V2I (Vehicle to Vehicle/Vehicle to Infrastructure) infrastructures and make route choice decisions at each intersection using hyper-path trees. We test our algorithm and control strategy by simulation in OmNet++ (A network communication simulator) and SUMO (Simulation of Urban MObility) under several scenarios. The simulation results show that with the proposed dynamic routing, the overall travel cost significantly decreases. It is also shown that the proposed adaptive signal control reduces the average delay effectively, as well as reduces the fluctuation of the average speed within the whole network.     

Multi-commodity traffic assignment by continuum approximation of network flow with variable demand

Consider a city with several highly compact central business districts (CBD), and the commuters’ destinations from each of them are dispersed over the whole city. Since at a particular location inside the city the traffic movements from different CBDs share the same space and do not cancel out each other as in conventional fluid flow problems albeit travelling in different directions, the traffic flows from a CBD to the destinations over the city are considered as one commodity. The interaction of the traffic flows among different commodities is governed by a cost–flow relationship. The case of variable demand is considered. The primal formulation of the continuum equilibrium model is given and proved to satisfy the user optimal conditions, and the dual formulation of the problem and its complementary conditions are also discussed. A finite element method is then employed to solve the continuum problem. A numerical example is given to illustrate the effectiveness of the proposed method.     

A dynamic traffic assignment model for a continuum transportation system

A predictive continuum dynamic user-optimal (PDUO-C) model is formulated in this study to investigate the dynamic characteristics of traffic flow and the corresponding route-choice behavior of travelers within a region with a dense urban road network. The modeled region is arbitrary in shape with a single central business district (CBD) and travelers continuously distributed over the region. Within this region, the road network is represented as a continuum and travelers patronize a two-dimensional continuum transportation system to travel to the CBD. The PDUO-C model is solved by a promising solution algorithm that includes elements of the finite volume method (FVM), the finite element method (FEM), and the explicit total variation diminishing Runge-Kutta (TVD-RK) time-stepping method. A numerical example is given to demonstrate the utility of the proposed model and the effectiveness of the solution algorithm in solving this PDUO-C problem.     

A dynamic behavioural traffic assignment model with strategic agents

Foresee traffic conditions and demand is a major issue nowadays that is very often approached using simulation tools. The aim of this work is to propose an innovative strategy to tackle such problem, relying on the presentation and analysis of a behavioural dynamic traffic assignment.The proposal relies on the assumption that travellers take routing policies rather than paths, leading us to introduce the possibility for each simulated agent to apply, in real time, a strategy allowing him to possibly re-route his path depending on the perceived local traffic conditions, jam and/or time already spent in his journey.The re-routing process allows the agents to directly react to any change in the road network. For the sake of simplicity, the agents’ strategy is modelled with a simple neural network whose parameters are determined during a preliminary training stage. The inputs of such neural network read the local information about the route network and the output gives the action to undertake: stay on the same path or modify it. As the agents use only local information, the overall network topology does not really matter, thus the strategy is able to cope with large and not previously explored networks.Numerical experiments are performed on various scenarios containing different proportions of trained strategic agents, agents with random strategies and non strategic agents, to test the robustness and adaptability to new environments and varying network conditions. The methodology is also compared against existing approaches and real world data. The outcome of the experiments suggest that this work-in-progress already produces encouraging results in terms of accuracy and computational efficiency. This indicates that the proposed approach has the potential to provide better tools to investigate and forecast drivers’ choice behaviours. Eventually these tools can improve the delivery and efficiency of traffic information to the drivers.     

Multi-modal traffic signal control with priority,signal actuation and coordination

Both coordinated-actuated signal control systems and signal priority control systems have been widely deployed for the last few decades. However, these two control systems are often conflicting with each due to different control objectives. This paper aims to address the conflicting issues between actuated-coordination and multi-modal priority control. Enabled by vehicle-to-infrastructure (v2i) communication in Connected Vehicle Systems, priority eligible vehicles, such as emergency vehicles, transit buses, commercial trucks, and pedestrians are able to send request for priority messages to a traffic signal controller when approaching a signalized intersection. It is likely that multiple vehicles and pedestrians will send requests such that there may be multiple active requests at the same time. A request-based mixed-integer linear program (MILP) is formulated that explicitly accommodate multiple priority requests from different modes of vehicles and pedestrians while simultaneously considering coordination and vehicle actuation. Signal coordination is achieved by integrating virtual coordination requests for priority in the formulation. A penalty is added to the objective function when the signal coordination is not fulfilled. This “soft” signal coordination allows the signal plan to adjust itself to serve multiple priority requests that may be from different modes. The priority-optimal signal timing is responsive to real-time actuations of non-priority demand by allowing phases to extend and gap out using traditional vehicle actuation logic. The proposed control method is compared with state-of-practice transit signal priority (TSP) both under the optimized signal timing plans using microscopic traffic simulation. The simulation experiments show that the proposed control model is able to reduce average bus delay, average pedestrian delay, and average passenger car delay, especially for highly congested condition with a high frequency of transit vehicle priority requests.     

A real-time adaptive signal control in a connected vehicle environment

The state of the practice traffic signal control strategies mainly rely on infrastructure based vehicle detector data as the input for the control logic. The infrastructure based detectors are generally point detectors which cannot directly provide measurement of vehicle location and speed. With the advances in wireless communication technology, vehicles are able to communicate with each other and with the infrastructure in the emerging connected vehicle system. Data collected from connected vehicles provides a much more complete picture of the traffic states near an intersection and can be utilized for signal control. This paper presents a real-time adaptive signal phase allocation algorithm using connected vehicle data. The proposed algorithm optimizes the phase sequence and duration by solving a two-level optimization problem. Two objective functions are considered: minimization of total vehicle delay and minimization of queue length. Due to the low penetration rate of the connected vehicles, an algorithm that estimates the states of unequipped vehicle based on connected vehicle data is developed to construct a complete arrival table for the phase allocation algorithm. A real-world intersection is modeled in VISSIM to validate the algorithms. Results with a variety of connected vehicle market penetration rates and demand levels are compared to well-tuned fully actuated control. In general, the proposed control algorithm outperforms actuated control by reducing total delay by as much as 16.33% in a high penetration rate case and similar delay in a low penetration rate case. Different objective functions result in different behaviors of signal timing. The minimization of total vehicle delay usually generates lower total vehicle delay, while minimization of queue length serves all phases in a more balanced way.     

Stochastic cell transmission model (SCTM): A stochastic dynamic traffic model for traffic state surveillance and assignment

The paper proposes a first-order macroscopic stochastic dynamic traffic model, namely the stochastic cell transmission model (SCTM), to model traffic flow density on freeway segments with stochastic demand and supply. The SCTM consists of five operational modes corresponding to different congestion levels of the freeway segment. Each mode is formulated as a discrete time bilinear stochastic system. A set of probabilistic conditions is proposed to characterize the probability of occurrence of each mode. The overall effect of the five modes is estimated by the joint traffic density which is derived from the theory of finite mixture distribution. The SCTM captures not only the mean and standard deviation (SD) of density of the traffic flow, but also the propagation of SD over time and space. The SCTM is tested with a hypothetical freeway corridor simulation and an empirical study. The simulation results are compared against the means and SDs of traffic densities obtained from the Monte Carlo Simulation (MCS) of the modified cell transmission model (MCTM). An approximately two-miles freeway segment of Interstate 210 West (I-210W) in Los Ageles, Southern California, is chosen for the empirical study. Traffic data is obtained from the Performance Measurement System (PeMS). The stochastic parameters of the SCTM are calibrated against the flow-density empirical data of I-210W. Both the SCTM and the MCS of the MCTM are tested. A discussion of the computational efficiency and the accuracy issues of the two methods is provided based on the empirical results. Both the numerical simulation results and the empirical results confirm that the SCTM is capable of accurately estimating the means and SDs of the freeway densities as compared to the MCS.     

Field implementation feasibility study of cumulative travel‐time responsive (CTR) traffic signal control algorithm

The cumulative travel‐time responsive (CTR) algorithm determines optimal green split for the next time interval by identifying the maximum cumulative travel time (CTT) estimated under the connected vehicle environment. This paper enhanced the CTR algorithm and evaluated its performance to verify a feasibility of field implementation in a near future. Standard Kalman filter (SKF) and adaptive Kalman filter (AKF) were applied to estimate CTT for each phase in the CTR algorithm. In addition, traffic demand, market penetration rate (MPR), and data availability were considered to evaluate the CTR algorithm's performance. An intersection in the Northern Virginia connected vehicle test bed is selected for a case study and evaluated within vissim and hardware in the loop simulations. As expected, the CTR algorithm's performance depends on MPR because the information collected from connected vehicle is a key enabling factor of the CTR algorithm. However, this paper found that the MPR requirement of the CTR algorithm could be addressed (i) when the data are collected from both connected vehicle and the infrastructure sensors and (ii) when the AKF is adopted. The minimum required MPRs to outperform the actuated traffic signal control were empirically found for each prediction technique (i.e., 30% for the SKF and 20% for the AKF) and data availability. Even without the infrastructure sensors, the CTR algorithm could be implemented at an intersection with high traffic demand and 50–60% MPR. The findings of this study are expected to contribute to the field implementation of the CTR algorithm to improve the traffic network performance. Copyright © 2017 John Wiley & Sons, Ltd.     

A connected-vehicle-based dynamic control model for managing the bus bunching problem with capacity constraints

This paper describes a connected-vehicle-based system architecture which can provide more precise and comprehensive information on bus movements and passenger status. Then a dynamic control method is proposed using connected vehicle data. Traditionally, the bus bunching problem has been formulated into one of two types of optimization problem. The first uses total passenger time cost as the objective function and capacity, safe headway, and other factors as constraints. Due to the large number of scenarios considered, this type of framework is inefficient for real-time implementation. The other type uses headway adherence as the objective and applies a feedback control framework to minimize headway variations. Due to the simplicity in the formulation and solution algorithms, the headway-based models are more suitable for real-time transit operations. However, the headway-based feedback control framework proposed in the literature still assumes homogeneous conditions at all bus stations, and does not consider restricting passenger loads within the capacity constraints. In this paper, a dynamic control framework is proposed to improve not only headway adherence but also maintain the stability of passenger load within bus capacity in both homogenous and heterogeneous situations at bus stations. The study provides the stability conditions for optimal control with heterogeneous bus conditions and derives optimal control strategies to minimize passenger transit cost while maintaining vehicle loading within capacity constraints. The proposed model is validated with a numerical analysis and case study based on field data collected in Chengdu, China. The results show that the proposed model performs well on high-demand bus routes.     

Quasi-dynamic traffic assignment with residual point queues incorporating a first order node model

Static traffic assignment models are still widely applied for strategic transport planning purposes in spite of the fact that such models produce implausible traffic flows that exceed link capacities and predict incorrect congestion locations. There have been numerous attempts to constrain link flows to capacity. Capacity constrained models with residual queues are often referred to as quasi-dynamic traffic assignment models. After reviewing the literature, we come to the conclusion that an important piece of the puzzle has been missing so far, namely the inclusion of a first order node model. In this paper we propose a novel path-based static traffic assignment model for finding a stochastic user equilibrium in general transportation networks. This model includes a first order (steady-state) node model that yields more realistic turn capacities, which are then used to determine consistent capacity constrained traffic flows, residual point (vertical) queues (upstream bottleneck links), and path travel times consistent with queuing theory. The route choice part of the model is specified as a variational inequality problem, while the network loading part is formulated as a fixed point problem. Both problems are solved using existing techniques to find a solution. We illustrate the model using hypothetical examples, and also demonstrate feasibility on large-scale networks.     

A cell-based Merchant-Nemhauser model for the system optimum dynamic traffic assignment problem

A cell-based variant of the Merchant-Nemhauser (M-N) model is proposed for the system optimum (SO) dynamic traffic assignment (DTA) problem. Once linearized and augmented with additional constraints to capture cross-cell interactions, the model becomes a linear program that embeds a relaxed cell transmission model (CTM) to propagate traffic. As a result, we show that CTM-type traffic dynamics can be derived from the original M-N model, when the exit-flow function is properly selected and discretized. The proposed cell-based M-N model has a simple constraint structure and cell network representation because all intersections and cells are treated uniformly. Path marginal costs are defined using a recursive formula that involves a subset of multipliers from the linear program. This definition is then employed to interpret the necessary condition, which is a dynamic extension of the Wardrop’s second principle. An algorithm is presented to solve the flow holding back problem that is known to exist in many discrete SO-DTA models. A numerical experiment is conducted to verify the proposed model and algorithm.     

A link-node complementarity model and solution algorithm for dynamic user equilibria with exact flow propagations

In this paper, we propose a link-node complementarity model for the basic deterministic dynamic user equilibrium (DUE) problem with single-user-class and fixed demands. The model complements link-path formulations that have been widely studied for dynamic user equilibria. Under various dynamic network constraints, especially the exact flow propagation constraints, we show that the continuous-time dynamic user equilibrium problem can be formulated as an infinite dimensional mixed complementarity model. The continuous-time model can be further discretized as a finite dimensional non-linear complementarity problem (NCP). The proposed discrete-time model captures the exact flow propagation constraints that were usually approximated in previous studies. By associating link inflow at the beginning of a time interval to travel times at the end of the interval, the resulting discrete-time model is predictive rather than reactive. The solution existence and compactness condition for the proposed model is established under mild assumptions. The model is solved by an iterative algorithm with a relaxed NCP solved at each iteration. Numerical examples are provided to illustrate the proposed model and solution approach. We particularly show why predictive DUE is preferable to reactive DUE from an algorithmic perspective.     

A splitting rate model of traffic re-routeing and traffic control

The paper presents an idealised dynamical model of day-to-day or within-day re-routeing using splitting rates at nodes, or node-exit flows, rather than route-flows. It is shown that under certain conditions the dynamical model gives rise to a sequence of link flow vectors which converges to a set of approximate Wardrop equilibria. A special dynamical signal green-time re-allocation model is added; the combination is also shown (in outline) to converge to the set of approximate consistent equilibria under certain conditions. Finally the paper uses model network results to illustrate a method of designing fixed time signal timings to meet different scenarios.     

A network‐based dynamic air traffic flow model for short‐term en route traffic prediction

This paper presents a dynamic network‐based approach for short‐term air traffic flow prediction in en route airspace. A dynamic network characterizing both the topological structure of airspace and the dynamics of air traffic flow is developed, based on which the continuity equation in fluid mechanics is adopted to describe the continuous behaviour of the en route traffic. Building on the network‐based continuity equation, the space division concept in cell transmission model is introduced to discretize the proposed model both in space and time. The model parameters are sequentially updated based on the statistical properties of the recent radar data and the new predicting results. The proposed method is applied to a real data set from Shanghai Area Control Center for the short‐term air traffic flow prediction both at flight path and en route sector level. The analysis of the case study shows that the developed method can characterize well the dynamics of the en route traffic flow, thereby providing satisfactory prediction results with appropriate uncertainty limits. The mean relative prediction errors are less than 0.10 and 0.14, and the absolute errors fall in the range of 0 to 1 and 0 to 3 in more than 95% time intervals respectively, for the flight path and en route sector level. Copyright © 2017 John Wiley & Sons, Ltd.     

Integration of signal timing estimation model and dynamic traffic assignment in feedback loops: system design and case study

This paper presents an integrated framework for effective coupling of a signal timing estimation model and dynamic traffic assignment (DTA) in feedback loops. There are many challenges in effectively integrating signal timing tools with DTA software systems, such as data availability, exchange format, and system coupling. In this research, a tight coupling between a DTA model with various queue‐based simulation models and a quick estimation method Excel‐based signal control tool is achieved and tested. The presented framework design offers an automated solution for providing realistic signal timing parameters and intersection movement capacity allocation, especially for future year scenarios. The framework was used to design an open‐source data hub for multi‐resolution modeling in analysis, modeling and simulation applications, in which a typical regional planning model can be quickly converted to microscopic traffic simulation and signal optimization models. The coupling design and feedback loops are first demonstrated on a simple network, and we examine the theoretically important questions on the number of iterations required for reaching stable solutions in feedback loops. As shown in our experiment, the current coupled application becomes stable after about 30 iterations, when the capacity and signal timing parameters can quickly converge, while DTA's route switching model predominately determines and typically requires more iterations to reach a stable condition. A real‐world work zone case study illustrates how this application can be used to assess impacts of road construction or traffic incident events that disrupt normal traffic operations and cause route switching on multiple analysis levels. Copyright © 2014 John Wiley & Sons, Ltd.     

Evaluating the impacts of urban corridor traffic signal optimization on vehicle emissions and fuel consumption

This study investigates the impacts of traffic signal timing optimization on vehicular fuel consumption and emissions at an urban corridor. The traffic signal optimization approach proposed integrates a TRANSIMS microscopic traffic simulator, the VT-Micro model (a microscopic emission and fuel consumption estimation model), and a genetic algorithm (GA)-based optimizer. An urban corridor consisting of four signalized intersections in Charlottesville, VA, USA, is used for a case study. The result of the case study is then compared with the best traffic signal timing plan generated by Synchro using the TRANSIMS microscopic traffic simulator. The proposed approach achieves much better performance than that of the best Synchro solution in terms of air quality, energy and mobility measures: 20% less network-wide fuel consumption, 8–20% less vehicle emissions, and nearly 27% less vehicle-hours-traveled (VHT).     

A dual control approach for repeated anticipatory traffic control with estimation of network flow sensitivity

This paper investigates a strategic signal control, which anticipates travelers' route choice response and determines signal timings to optimize network‐wide objectives. In general traffic assignment models are used for anticipating this route choice response. However, model‐reality mismatch usually brings suboptimal solutions to the real system. A repeated anticipatory control resolves the suboptimality and addresses the modeling error by learning from information on model bias. This paper extends the repeated control approach and focuses on the estimation of flow sensitivity as well as its influence on control, which is a crucial issue in implementation of model bias correction. The main objective of this paper is first to analyze the estimation error in the real flow derivative that is estimated from noisy measurements. A dual control method is then presented, improving both optimization objective function and derivative estimation during the control process. The proposed dual algorithm is tested on a simple network as well as on a midsize network. Numerical examples confirm the reliable performance of the new reality‐tracking control strategy and its ability to identify (local) optimal solutions on real traffic networks. Copyright © 2016 John Wiley & Sons, Ltd.     

A solution algorithm for a dynamic deterministic user equilibrium assignment model with departure time choice

Abstract

A route-based combined model of dynamic deterministic route and departure time choice and a solution method for many origin and destination pairs is proposed. The divided linear travel time model is used to calculate the link travel time and to describe the propagation of flow over time. For the calculation of route travel times, the predictive ideal route travel time concept is adopted. Solving the combined model of dynamic deterministic route and departure time choice is shown to be equivalent to solving simultaneously a system of non-linear equations. A Newton-type iterative scheme is proposed to solve this problem. The performance of the proposed solution method is demonstrated using a version of the Sioux Falls network. This shows that the proposed solution method produces good equilibrium solutions with reasonable computational cost.