Distributed coordinated signal timing optimization in connected transportation networks

This paper presents a Distributed-Coordinated methodology for signal timing optimization in connected urban street networks. The underlying assumption is that all vehicles and intersections are connected and intersections can share information with each other. The novelty of the work arises from reformulating the signal timing optimization problem from a central architecture, where all signal timing parameters are optimized in one mathematical program, to a decentralized approach, where a mathematical program controls the timing of only a single intersection. As a result of this distribution, the complexity of the problem is significantly reduced thus, the proposed approach is real-time and scalable. Furthermore, distributed mathematical programs continuously coordinate with each other to avoid finding locally optimal solutions and to move towards global optimality. We proposed a real-time and scalable solution technique to solve the problem and applied it to several case study networks under various demand patterns. The algorithm controlled queue length and maximized intersection throughput (between 1% and 5% increase compared to the actuated coordinated signals optimized in VISTRO) and reduced travel time (between 17% and 48% decrease compared to actuated coordinated signals) in all cases.     

Dynamic traffic metering in urban street networks: Formulation and solution algorithm

Traffic metering offers great potential to reduce congestion and enhance network performance in oversaturated urban street networks. This paper presents an optimization program for dynamic traffic metering in urban street networks based on the Cell Transmission Model (CTM). We have formulated the problem as a Mixed-Integer Linear Program (MILP) capable of metering traffic at network gates with given signal timing parameters at signalized intersections. Due to the complexities of the MILP model, we have developed a novel and efficient solution approach that solves the problem by converting the MILP to a linear program and several CTM simulation runs. The solution algorithm is applied to two case studies under different conditions. The proposed solution technique finds solutions that have a maximum gap of 1% of the true optimal solution and guarantee the maximum throughput by keeping some vehicles at network gates and only allowing enough vehicles to enter the network to prevent gridlocks. This is confirmed by comparing the case studies with and without traffic metering. The results in an adapted real-world case study network show that traffic metering can increase network throughput by 4.9–38.9% and enhance network performance.     

Multi-agent model predictive control of signaling split in urban traffic networks

The operation of large dynamic systems such as urban traffic networks remains a challenge in control engineering to a great extent due to their sheer size, intrinsic complexity, and nonlinear behavior. Recently, control engineers have looked for unconventional means for modeling and control of complex dynamic systems, in particular the technology of multi-agent systems whose appeal stems from their composite nature, flexibility, and scalability. This paper contributes to this evolving technology by proposing a framework for multi-agent control of linear dynamic systems, which decomposes a centralized model predictive control problem into a network of coupled, but small sub-problems that are solved by the distributed agents. Theoretical results ensure convergence of the distributed iterations to a globally optimal solution. The framework is applied to the signaling split control of traffic networks. Experiments conducted with simulation software indicate that the multi-agent framework attains performance comparable to conventional control. The main advantages of the multi-agent framework are its graceful extension and localized reconfiguration, which require adjustments only in the control strategies of the agents in the vicinity.     

Dynamic system-optimal traffic assignment using a state space model

We propose a new mathematical formulation for the problem of optimal traffic assignment in dynamic networks with multiple origins and destinations. This problem is motivated by route guidance issues that arise in an Intelligent Vehicle-Highway Systems (IVHS) environment. We assume that the network is subject to known time-varying demands for travel between its origins and destinations during a given time horizon. The objective is to assign the vehicles to links over time so as to minimize the total travel time experienced by all the vehicles using the network. We model the traffic network over the time horizon as a discrete-time dynamical system. The system state at each time instant is defined in a way that, without loss of optimality, avoids complete microscopic detail by grouping vehicles into platoons irrespective of origin node and time of entry to network. Moreover, the formulation contains no explicit path enumeration. The state transition function can model link travel times by either impedance functions, link outflow functions, or by a combination of both. Two versions (with different boundary conditions) of the problem of optimal traffic assignment are studied in the context of this model. These optimization problems are optimal control problems for nonlinear discrete-time dynamical systems, and thus they are amenable to algorithmic solutions based on dynamic programming. The computational challenges associated with the exact solution of these problems are discussed and some heuristics are proposed.     

Selection of a trip table which reproduces observed link flows

In urban traffic management and planning, an important problem is estimating the number of drivers traveling between each origin-destination zone. We review a model due to Nguyen for estimating these numbers of drivers, based on counts of the traffic flows on each street, and develop an effective algorithm for solving it. The multiplicity of solutions of this model poses the additional question of which solution to use; we introduce a secondary optimization problem to overcome this difficulty. Efficient solution techniques are described for these problems and computational results are reported. It is noted that the most efficient solution methods involve user interaction to specify values of parameters which improve the convergence rates.     

Exploiting the fundamental diagram of urban networks for feedback-based gating

Traffic signal control for urban road networks has been an area of intensive research efforts for several decades, and various algorithms and tools have been developed and implemented to increase the network traffic flow efficiency. Despite the continuous advances in the field of traffic control under saturated conditions, novel and promising developments of simple concepts in this area remains a significant objective, because some proposed approaches that are based on various meta-heuristic optimization algorithms can hardly be used in a real-time environment. To address this problem, the recently developed notion of network fundamental diagram for urban networks is exploited to improve mobility in saturated traffic conditions via application of gating measures, based on an appropriate simple feedback control structure. As a case study, the proposed methodology is applied to the urban network of Chania, Greece, using microscopic simulation. The results show that the total delay in the network decreases significantly and the mean speed increases accordingly.     

Store-and-forward based methods for the signal control problem in large-scale congested urban road networks

The problem of designing network-wide traffic signal control strategies for large-scale congested urban road networks is considered. One known and two novel methodologies, all based on the store-and-forward modeling paradigm, are presented and compared. The known methodology is a linear multivariable feedback regulator derived through the formulation of a linear-quadratic optimal control problem. An alternative, novel methodology consists of an open-loop constrained quadratic optimal control problem, whose numerical solution is achieved via quadratic programming. Yet a different formulation leads to an open-loop constrained nonlinear optimal control problem, whose numerical solution is achieved by use of a feasible-direction algorithm. A preliminary simulation-based investigation of the signal control problem for a large-scale urban road network using these methodologies demonstrates the comparative efficiency and real-time feasibility of the developed signal control methods.     

Personalized real-time traffic information provision: Agent-based optimization model and solution framework

The advancement of information and communication technology allows the use of more sophisticated information provision strategies for real-time congested traffic management in a congested network. This paper proposes an agent-based optimization modeling framework to provide personalized traffic information for heterogeneous travelers. Based on a space–time network, a time-dependent link flow based integer programming model is first formulated to optimize various information strategies, including elements of where and when to provide the information, to whom the information is given, and what alternative route information should be suggested. The analytical model can be solved efficiently using off-the-shelf commercial solvers for small-scale network. A Lagrangian Relaxation-based heuristic solution approach is developed for medium to large networks via the use of a mesoscopic dynamic traffic simulator.     

Co-design of traffic network topology and control measures

The two main directions to improve traffic flows in networks involve changing the network topology and introducing new traffic control measures. In this paper, we consider a co-design approach to apply these two methods jointly to improve the interaction between different methods and to get a better overall performance. We aim at finding the optimal network topology and the optimal parameters of traffic control laws at the same time by solving a co-optimization problem. However, such an optimization problem is usually highly non-linear and non-convex, and it possibly involves a mixed-integer form. Therefore, we discuss four different solution frameworks that can be used for solving the co-optimization problem, according to different requirements on the computational complexity and speed. A simulation-based study is implemented on the Singapore freeway network to illustrate the co-design approach and to compare the four different solution frameworks.     

Network traffic flow optimization under performance constraints

In this paper, a model-based perimeter control policy for large-scale urban vehicular networks is proposed. Assuming a homogeneously loaded vehicle network and the existence of a well-posed Network Fundamental Diagram (NFD), we describe a protected network throughout its aggregated dynamics including nonlinear exit flow characteristics. Within this framework of constrained optimal boundary flow gating, two main performance metrics are considered: (a) first, connected to the NFD, the concept of average network travel time and delay as a performance metric is defined; (b) second, at boundaries, we take into account additional external network queue dynamics governed by uncontrolled inflow demands. External queue capacities in terms of finite-link lengths are used as the second performance metric. Hence, the corresponding performance requirement is an upper bound of external queues. While external queues represent vehicles waiting to enter the protected network, internal queue describes the protected network’s aggregated behavior.By controlling the number of vehicles joining the internal queue from the external ones, herewith a network traffic flow maximization solution subject to the internal and external dynamics and their performance constraints is developed. The originally non-convex optimization problem is transformed to a numerically efficiently convex one by relaxing the performance constraints into time-dependent state boundaries. The control solution can be interpreted as a mechanism which transforms the unknown arrival process governing the number of vehicles entering the network to a regulated process, such that prescribed performance requirements on travel time in the network and upper bound on the external queue are satisfied. Comparative numerical simulation studies on a microscopic traffic simulator are carried out to show the benefits of the proposed method.     

An optimization method for sustainable traffic control in urban areas

The optimization of traffic signalization in urban areas is formulated as a problem of finding the cycle length, the green times and the offset of traffic signals that minimize an objective function of performance indices. Typical approaches to this optimization problem include the maximization of traffic throughput or the minimization of vehicles’ delays, number of stops, fuel consumption, etc. Dynamic Traffic Assignment (DTA) models are widely used for online and offline applications for efficient deployment of traffic control strategies and the evaluation of traffic management schemes and policies. We propose an optimization method for combining dynamic traffic assignment and network control by minimizing the risk of potential loss induced to travelers by exceeding their budgeted travel time as a result of deployed traffic signal settings, using the Conditional Value-at-Risk model. The proposed methodology can be easily implemented by researchers or practitioners to evaluate their alternative strategies and aid them to choose the alternative with less potential risk. The traffic signal optimization procedure is implemented in TRANSYT-7F and the dynamic propagation and route choice of vehicles is simulated with a mesoscopic dynamic traffic assignment tool (DTALite) with fixed temporal demand and network characteristics. The proposed approach is applied to a reference test network used by many researchers for verification purposes. Numerical experiments provide evidence of the advantages of this optimization method with respect to conventional optimization techniques. The overall benefit to the performance of the network is evaluated with a Conditional Value-at-Risk Analysis where the optimal solution is the one presenting the least risk for ‘guaranteed’ total travel times.     

Approximate algorithms for the discrete network design problem

The discrete network design problem is one of finding a set of feasible actions (projects) from among a collection of possible actions, that when implemented, optimizes some objective function(s). This is a combinatorial optimization problem that is very expensive to solve exactly. This paper proposes two algorithms for obtaining approximate solutions to the discrete network design problem with much less computational effeort. The computational savings are achieved by approximating the original problem with a new formulation which is easier to solve. The first algorithm proposed solves this approximate problem exactly, while the second is even more efficient, but provides only a near-optimal solution to the approximate problem. Experience with test problems indicates that these approximations can reduce the computational effort by a factor of 3–5, with little loss in solution accuracy.     

Mapping evacuation risk on transportation networks using a spatial optimization model

The focus of this paper is on the development of a methodology to identify network and demographic characteristics on real transportation networks which may lead to significant problems in evacuation during some extreme event, like a wildfire or hazardous material spill. We present an optimization model, called the critical cluster model, that can be used to identify small areas or neighborhoods which have high ratios of population to exit capacity. Although this model in its simplest form is a nonlinear, constrained optimization problem, a special integer-linear programming equivalent can be formulated. Special contiguity constraints are needed to keep identified clusters spatially connected. We present details on how this model can be solved optimally as well as discuss computational experience for several example transportation networks. We describe how this model can be integrated within a GIS system to produce maps of evacuation risk or vulnerability. This model is now being utilized in several research projects, in Europe and the US.     

Equity-based timetable synchronization optimization in urban subway network

In the urban subway transportation system, passengers may have to make at least one transfer traveling from their origin to destination. This paper proposes a timetable synchronization optimization model to optimize passengers’ waiting time while limiting the waiting time equitably over all transfer station in an urban subway network. The model aims to improve the worst transfer by adjusting the departure time, running time, the dwelling time and the headways for all directions in the subway network. In order to facilitate solution, we develop a binary variables substitute method to deal with the binary variables. Genetic algorithm is applied to solve the problem for its practicality and generality. Finally, the suggested model is applied to Beijing urban subway network and several performance indicators are presented to verify the efficiency of suggested model. Results indicate that proposed timetable synchronization optimization model can be used to improve the network performance for transfer passengers significantly.     

Connectivity-based optimization of vehicle route and speed for improved fuel economy

Traditionally, vehicle route planning problem focuses on route optimization based on traffic data and surrounding environment. This paper proposes a novel extended vehicle route planning problem, called vehicle macroscopic motion planning (VMMP) problem, to optimize vehicle route and speed simultaneously using both traffic data and vehicle characteristics to improve fuel economy for a given expected trip time. The required traffic data and neighbouring vehicle dynamic parameters can be collected through the vehicle connectivity (e.g. vehicle-to-vehicle, vehicle-to-infrastructure, vehicle-to-cloud, etc.) developed rapidly in recent years. A genetic algorithm based co-optimization method, along with an adaptive real-time optimization strategy, is proposed to solve the proposed VMMP problem. It is able to provide the fuel economic route and reference speed for drivers or automated vehicles to improve the vehicle fuel economy. A co-simulation model, combining a traffic model based on SUMO (Simulation of Urban MObility) with a Simulink powertrain model, is developed to validate the proposed VMMP method. Four simulation studies, based on a real traffic network, are conducted for validating the proposed VMMP: (1) ideal traffic environment without traffic light and jam for studying the fuel economy improvement, (2) traffic environment with traffic light for validating the proposed traffic light penalty model, (3) traffic environment with traffic light and jam for validating the proposed adaptive real-time optimization strategy, and (4) investigating the effect of different powertrain platforms to fuel economy using two different vehicle platforms. Simulation results show that the proposed VMMP method is able to improve vehicle fuel economy significantly. For instance, comparing with the fastest route, the fuel economy using the proposed VMMP method is improved by up to 15%.     

Surrogate‐based optimization of cordon toll levels in congested traffic networks

The benefit, in terms of social surplus, from introducing congestion charging schemes in urban networks is depending on the design of the charging scheme. The literature on optimal design of congestion pricing schemes is to a large extent based on static traffic assignment, which is known for its deficiency in correctly predict travel times in networks with severe congestion. Dynamic traffic assignment can better predict travel times in a road network, but are more computational expensive. Thus, previously developed methods for the static case cannot be applied straightforward. Surrogate‐based optimization is commonly used for optimization problems with expensive‐to‐evaluate objective functions. In this paper, we evaluate the performance of a surrogate‐based optimization method, when the number of pricing schemes, which we can afford to evaluate (because of the computational time), are limited to between 20 and 40. A static traffic assignment model of Stockholm is used for evaluating a large number of different configurations of the surrogate‐based optimization method. Final evaluation is performed with the dynamic traffic assignment tool VisumDUE, coupled with the demand model Regent, for a Stockholm network including 1240 demand zones and 17 000 links. Our results show that the surrogate‐based optimization method can indeed be used for designing a congestion charging scheme, which return a high social surplus. Copyright © 2016 John Wiley & Sons, Ltd.     

Global optimization methods for the discrete network design problem

This paper addresses the discrete network design problem (DNDP) with multiple capacity levels, or multi-capacity DNDP for short, which determines the optimal number of lanes to add to each candidate link in a road network. We formulate the problem as a bi-level programming model, where the upper level aims to minimize the total travel time via adding new lanes to candidate links and the lower level is a traditional Wardrop user equilibrium (UE) problem. We propose two global optimization methods by taking advantage of the relationship between UE and system optimal (SO) traffic assignment principles. The first method, termed as SO-relaxation, exploits the property that an optimal network design solution under SO principle can be a good approximate solution under UE principle, and successively sorts the solutions in the order of increasing total travel time under SO principle. Optimality is guaranteed when the lower bound of the total travel time of the unexplored solutions under UE principle is not less than the total travel time of a known solution under UE principle. The second method, termed as UE-reduction, adds the objective function of the Beckmann-McGuire-Winsten transformation of UE traffic assignment to the constraints of the SO-relaxation formulation of the multi-capacity DNDP. This constraint is convex and strengthens the SO-relaxation formulation. We also develop a dynamic outer-approximation scheme to make use of the state-of-the-art mixed-integer linear programming solvers to solve the SO-relaxation formulation. Numerical experiments based on a two-link network and the Sioux-Falls network are conducted.     

Cooperative traffic control of a mixed network with two urban regions and a freeway

Currently most optimization methods for urban transport networks (i) are suited for networks with simplified dynamics that are far from real-sized networks or (ii) apply decentralized control, which is not appropriate for heterogeneously loaded networks or (iii) investigate good-quality solutions through micro-simulation models and scenario analysis, which make the problem intractable in real time. In principle, traffic management decisions for different sub-systems of a transport network (urban, freeway) are controlled by operational rules that are network specific and independent from one traffic authority to another. In this paper, the macroscopic traffic modeling and control of a large-scale mixed transportation network consisting of a freeway and an urban network is tackled. The urban network is partitioned into two regions, each one with a well-defined Macroscopic Fundamental Diagram (MFD), i.e. a unimodal and low-scatter relationship between region density and outflow. The freeway is regarded as one alternative commuting route which has one on-ramp and one off-ramp within each urban region. The urban and freeway flow dynamics are formulated with the tool of MFD and asymmetric cell transmission model, respectively. Perimeter controllers on the border of the urban regions operating to manipulate the perimeter interflow between the two regions, and controllers at the on-ramps for ramp metering are considered to control the flow distribution in the mixed network. The optimal traffic control problem is solved by a Model Predictive Control (MPC) approach in order to minimize total delay in the entire network. Several control policies with different levels of urban-freeway control coordination are introduced and tested to scrutinize the characteristics of the proposed controllers. Numerical results demonstrate how different levels of coordination improve the performance once compared with independent control for freeway and urban network. The approach presented in this paper can be extended to implement efficient real-world control strategies for large-scale mixed traffic networks.     

Global optimization method for network design problem with stochastic user equilibrium

In this paper, we consider the continuous road network design problem with stochastic user equilibrium constraint that aims to optimize the network performance via road capacity expansion. The network flow pattern is subject to stochastic user equilibrium, specifically, the logit route choice model. The resulting formulation, a nonlinear nonconvex programming problem, is firstly transformed into a nonlinear program with only logarithmic functions as nonlinear terms, for which a tight linear programming relaxation is derived by using an outer-approximation technique. The linear programming relaxation is then embedded within a global optimization solution algorithm based on range reduction technique, and the proposed approach is proved to converge to a global optimum.