Integrating congestion pricing and transit investment planning

This paper develops a mathematical model and solution procedure to identify an optimal zonal pricing scheme for automobile traffic to incentivize the expanded use of transit as a mechanism to stem congestion and the social costs that arise from that congestion. The optimization model assumes that there is a homogenous collection of users whose behavior can be described as utility maximizers and for which their utility function is driven by monetary costs. These monetary costs are assumed to be the tolls in place, the per mile cost to drive, and the value of their time. We assume that there is a system owner who sets the toll prices, collects the proceeds from the tolls, and invests those funds in transit system improvements in the form of headway reductions. This yields a bi-level optimization model which we solve using an iterative procedure that is an integration of a genetic algorithm and the Frank–Wolfe method. The method and solution procedure is applied to an illustrative example.     

A bi-level model of dynamic traffic signal control with continuum approximation

This paper proposes a bi-level model for traffic network signal control, which is formulated as a dynamic Stackelberg game and solved as a mathematical program with equilibrium constraints (MPEC). The lower-level problem is a dynamic user equilibrium (DUE) with embedded dynamic network loading (DNL) sub-problem based on the LWR model (Lighthill and Whitham, 1955; Richards, 1956). The upper-level decision variables are (time-varying) signal green splits with the objective of minimizing network-wide travel cost. Unlike most existing literature which mainly use an on-and-off (binary) representation of the signal controls, we employ a continuum signal model recently proposed and analyzed in Han et al. (2014), which aims at describing and predicting the aggregate behavior that exists at signalized intersections without relying on distinct signal phases. Advantages of this continuum signal model include fewer integer variables, less restrictive constraints on the time steps, and higher decision resolution. It simplifies the modeling representation of large-scale urban traffic networks with the benefit of improved computational efficiency in simulation or optimization. We present, for the LWR-based DNL model that explicitly captures vehicle spillback, an in-depth study on the implementation of the continuum signal model, as its approximation accuracy depends on a number of factors and may deteriorate greatly under certain conditions. The proposed MPEC is solved on two test networks with three metaheuristic methods. Parallel computing is employed to significantly accelerate the solution procedure.     

Revisiting Jiang’s dynamic continuum model for urban cities

Jiang et al. (Jiang, Y.Q., Wong, S.C., Ho, H.W., Zhang, P., Liu, R.X., Sumalee, A., 2011. A dynamic traffic assignment model for a continuum transportation system. Transportation Research Part B 45 (2), 343–363) proposed a predictive continuum dynamic user-optimaDUO-l to investigate the dynamic characteristics of traffic flow and the corresponding route-choice behavior of travelers. Their modeled region is a dense urban city that is arbitrary in shape and has a single central business district (CBD). However, we argue that the model is not well posed due to an inconsistency in the route-choice strategy under certain conditions. To overcome this inconsistency, we revisit the PDUO-C problem, and construct an improved path-choice strategy. The improved model consists of a conservation law to govern the density, in which the flow direction is determined by the improved path-choice strategy, and a Hamilton–Jacobi equation to compute the total travel cost. The simultaneous satisfaction of both equations can be treated as a fixed-point problem. A self-adaptive method of successive averages (MSA) is proposed to solve this fixed-point problem. This method can automatically determine the optimal MSA step size using the least squares approach. Numerical examples are used to demonstrate the effectiveness of the model and the solution algorithm.     

Numerical optimal control method for shockwaves reduction at stationary bottlenecks

The paper introduces an optimal control method for traffic management with variable speed limits. It consists of traffic flow dynamics prediction with a non‐linearized Lighthill–Whitham–Richards macroscopic traffic flow model, introduction of a cost functional, which enables stable shockwaves optimization, and numerical implementation of the optimization process with differential evolution. The method overcomes the discretization issues and provides speed limits that are in general not limited to small number of successive discrete points, i.e. variable message signs locations, nor in rounded speed limits. Performance of the method is demonstrated on a case study, which shows promising reduction of the backward moving shockwave that occurs because of a stationary bottleneck. Copyright © 2016 John Wiley & Sons, Ltd.     

Stochastic capacity expansion models for airport facilities

It is important and also challenging to plan airport facilities to meet future traffic needs in a rapidly changing environment, which is characterized by various uncertainties. One key issue in airport facility development is that facility performance functions (delay levels as functions of capacity utilization rates) are nonlinear, which complicates the solution method design. Potential demand fluctuations in a deregulated aviation market add another dimension to the decision making process. To solve this problem, a deterministic total cost minimization model is proposed and then extended into stochastic programs, by including uncertainties in traffic forecasts. After the exploration of properties of the delay cost function, an Outer-Approximation (OA) technique which is superior to the existing discrete approximation is designed. After model enhancements, an efficient solution framework based on the OA technique is used to solve the model to its global optimality by interactively generating upper and lower bounds to the objective. Computational tests demonstrate the validity of developed models and efficiency of proposed algorithms. The total cost is reduced by 18.8% with the stochastic program in the numerical example.     

Optimal deployment of emergency rescue stations in an urban transportation corridor

This paper addresses the deployment issue of emergency rescue stations in an urban transportation corridor, with an aim to effectively reduce the casualties in traffic accidents. On the basis of urban population density, an accident rate distribution function for a corridor is first presented and calibrated, and a damage cost function is proposed to capture the correlation between rescue time and deteriorating health condition of injured passengers. A continuum model is then developed for determining the optimal number and locations of the rescue stations along the corridor and the medical service resource distribution at rescue stations subject to a capital budget constraint. The solution properties of the proposed model are explored analytically. Numerical examples are provided to show the effects of population density, urban form and different deployment schemes (even and uneven) on the rescue station locations. A case study of Wuhan China is employed to illustrate the effectiveness of the proposed methodology in improving the performance of the emergency rescue system.

     

Real-time energy-efficient traffic control via convex optimization

This article proposes a macroscopic traffic control strategy to reduce fuel consumption of vehicles on highways. By implementing Greenshields fundamental diagram, the solution to Moskowitz equations is expressed as linear functions with respect to vehicle inflow and outflow, which leads to generation of a linear traffic flow model. In addition, we build a quadratic cost function in terms of vehicle volume to estimate fuel consumption rate based on COPERT model. A convex quadratic optimization problem is then formulated to generate energy-efficient traffic control decisions in real-time. Simulation results demonstrate significant reduction of fuel consumption on testing highway sections under peak traffic demands of busy hours.     

The treatment of uncertainty in the dynamic origin–destination estimation problem using a fuzzy approach

Regardless of existing types of transportation and traffic model and their applications, the essential input to these models is travel demand, which is usually described using origin–destination (OD) matrices. Due to the high cost and time required for the direct development of such matrices, they are sometimes estimated indirectly from traffic measurements recorded from the transportation network. Based on an assumed demand profile, OD estimation problems can be categorized into static or dynamic groups. Dynamic OD demand provides valuable information on the within-day fluctuation of traffic, which can be employed to analyse congestion dissipation. In addition, OD estimates are essential inputs to dynamic traffic assignment (DTA) models. This study presents a fuzzy approach to dynamic OD estimation problems. The problems are approached using a two-level model in which demand is estimated in the upper level and the lower level performs DTA via traffic simulation. Using fuzzy rules and the fuzzy C-Mean clustering approach, the proposed method treats uncertainty in historical OD demand and observed link counts. The approach employs expert knowledge to model fitted link counts and to set boundaries for the optimization problem by defining functions in the fuzzification process. The same operation is performed on the simulation outputs, and the entire process enables different types of optimization algorithm to be employed. The Box-complex method is utilized as an optimization algorithm in the implementation of the approach. Empirical case studies are performed on two networks to evaluate the validity and accuracy of the approach. The study results for a synthetic network and a real network demonstrate the robust performance of the proposed method even when using low-quality historical demand data.     

Study on road section environmental traffic capacity model and algorithm under double constraints

The coordinated development of city traffic and environment is a key research content in traffic field in twenty-first Century. Among them, road section environmental traffic capacity analysis is one of the important research issues. It can provide solid theoretical basis and reliable data support for road network traffic optimization control, road traffic pollution control and city traffic structure optimization. This paper analyzed main factors which impacted environmental traffic capacity from two aspects, including road capacity constraint conditions and road traffic pollution control constraint conditions. Then, road section environmental traffic capacity optimization model was established, and method of improved augmented Lagrange function was used to solve the model. Case study showed that, (1) The environmental traffic capacity optimal model and methodology were effective; (2) In order to ensure road section environmental traffic capacity greater than (or equal to) road capacity, some measures could be taken including adjusting motor vehicle type proportion as well as improving emission characteristics of motor vehicles exhausting pollutants.     

Genetic algorithm-based simulation optimization of the ALINEA ramp metering system: a case study in Atlanta

ABSTRACT

This paper presents a case study of the optimal ALINEA ramp metering system model of a corridor of the metro Atlanta freeway. Based on real-world traffic data, this study estimates the origin-destination matrix for the corridor. Using a stochastic simulation-based optimization framework that combines a micro-simulation model and a genetic algorithm-based optimization module, we determine the optimal parameter values of a combined ALINEA ramp metering system with a queue flush system that minimizes total vehicle travel time. We found that the performance of ramp metering with optimized parameters, which is very sensitive possibly because bottlenecks are correlated, outperforms the no control model with its optimized parameters in terms of reducing total travel time.     

High‐speed rail cost recovery time based on an integer optimization model

With increasing gasoline prices, electric high‐speed rail (HSR) systems represent one means to mitigate overexposure to volatile prices. However, additional research is needed related to funding this infrastructure. In this paper, we develop a new integer optimization model to address this problem and use a hypothetical case study to demonstrate the approach. The objective of the approach is to minimize the time period in which the cost of HSR construction and operation can be recovered. This is an iterative process based on an integer optimization model, whose objective function is to determine the optimum recovery time (ORT), by setting the HSR ticket price and frequency. Embedded in the optimization model is a multinomial logit model for calculating the demand for HSR as a function of these decision variables, thus capturing the effects of level of service on market share. In particular, the optimization model accounts for the role of different types of subsidies toward HSR construction (one‐time subsidies at construction, annual subsidies, and subsidies depending on frequency). This method can also help determine whether an HSR system should be built or how much subsidy should be provided given a fixed expected cost recovery time. By integrating the logit model into the objective function evaluation, the effects of ticket price and service frequency on service demand can be directly captured. Copyright © 2014 John Wiley & Sons, Ltd.     

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.     

Optimal tolls for multi-class traffic: Analytical formulations and policy implications

This paper puts together an analytical formulation to compute optimal tolls for multi-class traffic. The formulation is comprised of two major modules. The first one is an optimization component aimed at computing optimal tolls assuming a Stackelberg game in which the toll agency sets the tolls, and the equilibrating traffic plays the role of the followers. The optimization component is supported by a set of cost models that estimate the externalities as a function of a multivariate vector of traffic flows. These models were estimated using Taylor series expansions of the output obtained from traffic simulations of a hypothetical test case. Of importance to the paper is the total travel time function estimated using this approach that expresses total travel time as a multivariate function of the traffic volumes. The formulation presented in the paper is then applied to a variety of scenarios to gain insight into the optimality of current toll policies. The optimal tolls are computed for two different cases: independent tolls, and tolls proportional to passenger car equivalencies (PCE).The numerical results clearly show that setting tolls proportional to PCEs leads to lower values of welfare that are on average 15% lower than when using independent tolls, though, in some cases the total welfare could be up to 33% lower. This is a consequence of two factors. First, the case of independent tolls has more degrees of freedom than the case of tolls proportional to PCEs. Second, tolls proportional to PCEs do not account for externalities other than congestion, which is likely to lead to lower welfare values.The analytical formulations and numerical results indicate that, because the total travel time is a non-linear function of the traffic volumes, the marginal social costs and thus the optimal congestion tolls also depend on the traffic volumes for each vehicle class. As a result of this, for the relatively low volumes of truck traffic observed in real life, the optimal congestion tolls for trucks could indeed be either lower or about the same as for passenger cars. This stand in sharp contrast with what is implied in the use of PCEs, i.e., that the contribution to congestion are constant. This latter assumption leads to optimal truck congestion tolls that are always proportional to the PCE values.The comparison of the toll ratios (truck tolls divided by passenger car tolls) for both observed and optimal conditions suggests that the tolls for small trucks are about the right level, maybe a slightly lower than optimal. However, the analysis of the toll ratio for large trucks seems to indicate a significant overcharge. The estimates show that the average observed toll ratio for large trucks is even higher than the maximum optimal toll ratio found in the numerical experiments. This suggests that the tolls for large trucks are set on the basis of revenue generation principles while the passenger car tolls are being set based on a mild form of welfare maximization. This leads to a suboptimal cross-subsidization of passenger car traffic in detriment of an important sector of the economy.     

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.     

Optimization of mainline traffic via an adaptive co-ordinated ramp-metering control model with dynamic OD estimation

Frequently implemented at freeway accesses to streamline traffic, ramp-metering control strategy is often implemented during rush hours in heavily congested areas. This paper presents a novel ramp-metering control model capable of optimizing mainline traffic by providing metering rates for accesses within the control segments. Based on Payne's continuum traffic stream model, a linear dynamic model with a quadratic objective function is constructed for integrated-responsive ramp-metering control. Incorporating on-line origin–destination (OD) estimation of co-ordinated interchanges into the proposed model increases efficiency of the control. In addition, an iterative algorithm is proposed to obtain the optimal solution. Simulation results demonstrate the robustness of the proposed model and its ability to streamline freeway traffic while avoiding traffic congestion.     

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.     

Speed-flow relations and cost functions for congested traffic: Theory and empirical analysis

A dynamic ‘car-following’ extension of the conventional economic model of traffic congestion is presented, which predicts the average cost function for trips in stationary states to be significantly different from the conventional average cost function derived from the speed-flow function. When applied to a homogeneous road, the model reproduces the same stationary state equilibria as the conventional model, including the hypercongested ones. However, stability analysis shows that the latter are dynamically unstable. The average cost function for stationary state traffic coincides with the conventional function for non-hypercongested traffic, but rises vertically at the road’s capacity due to queuing, instead of bending backwards. When extending the model to include an upstream road segment, it predicts that such queuing will occur under hypercongested conditions, while the general shape of the average cost function for full trips does not change, implying that hypercongestion will not occur on the downstream road segment. These qualitative predictions are verified empirically using traffic data from a Dutch bottleneck. Finally, it is shown that reduced-form average cost functions, that relate the sum of average travel cost and average schedule delay costs to the number of users in a dynamic equilibrium, certainly need not have the intuitive convex shape, but may very well be concave – despite the fact that the underlying speed-flow function may be convex.     

The impact of source terms in the variational representation of traffic flow

This paper revisits the variational theory of traffic flow, now under the presence of continuum lateral inflows and outflows to the freeway. It is found that a VT solution apply only in Eulerian coordinates when source terms are exogenous, but not when they are a function of traffic conditions, e.g. as per a merge model. In discrete time, however, these dependencies become exogenous, which allowed us to propose improved numerical solution methods. In space-Lagrangian and time-Lagrangian coordinates, VT solutions may not apply even if source terms are exogenous.     

Morning commute in a single-entry traffic corridor with no late arrivals

This paper analyzes a model of early morning traffic congestion, that is a special case of the model considered in Newell (1988). A fixed number of identical vehicles travel along a single-lane road of constant width from a common origin to a common destination, with LWR flow congestion and Greenshields’ Relation. Vehicles have a common work start time, late arrivals are not permitted, and trip cost is linear in travel time and time early. The paper explores traffic dynamics for the social optimum, in which total trip cost is minimized, and for the user optimum, in which no vehicle’s trip cost can be reduced by altering its departure time. Closed-form solutions for the social optimum and quasi-analytic solutions for the user optimum are presented, along with numerical examples, and it is shown that this model includes the bottleneck model (with no late arrivals) as a limit case where the length of the road shrinks to zero.     

Traffic assignment considering air quality

This paper presents a methodology of assigning traffic in a network with the consideration of air quality. Traffic assignment is formulated as an optimization problem considering travel cost and on-road emissions. It introduces a cell-based approach to model emission concentrations so that either the average or maximum emissions in a network can be considered in the optimization process. The emissions in a cell are modeled taking into consideration the influence of the emission sources from all cells in the network. A case study demonstrates that minimizing travel cost and reducing air pollutants may not be always achieved simultaneously. The traffic assignment procedure can effectively reduce emission concentrations at those locations with the worst air quality conditions, with only a marginal increase in travel time and average emission concentration in the network.