Search

A paper published in 1983 in this journal by A. de Palma et at. uses a deterministic queueing supply model in combination with a random utility demand model to predict the pattern of traffic flows during a peak period. Two different versions of the supply model are included, a "basic model" which is identical to the supply model used by a number of other authors investigating the same general problem (e.g., M. J. Smith, 1984), and a more complicated "extended model." As detailed below, there is a mathematical discrepancy in the analysis. Because of this discrepancy, some of the conclusions about the traffic flow pattern in the case of the extended model are incorrect and all are unproven. For the simpler-and seemingly more realistic-basic model the discrepancy vanishes and the conclusions remain valid. [ABSTRACT FROM AUTHOR]

Microscopic traffic flow models enable predictions of traffic operations, which allows traffic engineers to assess the efficiency and safety effects of roadway designs. Modeling vehicle trajectories inside intersections is challenging because there is an infinite number of possible paths in a two-dimensional space, and drivers can simultaneously adapt their speeds as well. To date, human driver models for simultaneous longitudinal and lateral vehicle control based on the infrastructure characteristics and interactions with other drivers inside an intersection are still lacking. The contribution of this paper is threefold. First, it proposes an integrated microscopic traffic flow model to describe human-driven vehicle maneuvers under interactions. Drivers plan their heading and acceleration in the predicted future to minimize costs representing undesirable situations. The model works with a joint optimization for an interaction cost term. The weights associated with the interaction cost reflect how selfish or altruistic drivers are. Second, the proposed model endogenously gives the order of vehicles in case of crossing paths. Third, the paper develops a clustered validation method for microscopic traffic flow models with interacting vehicles, which account for interdriver variations. Results show that the model can accurately describe vehicle passing orders of interacting maneuvers, paths, and speeds against empirical data. The model can be applied to assess various intersection designs. Funding: This work was supported by the National Natural Science Foundation of China [Grants 71971140 and 52122215] and the Natural Science Foundation of Shanghai [Grant 20ZR1439300]. [ABSTRACT FROM AUTHOR]

Since advanced traveler information and traffic management systems have become popular, it is vital to capture the joint impact of various strategies on transportation systems. Developing analytical models to incorporate traffic dynamics and travel behavior is challenging. Based on observation of the heteroscedasticity of the simulation noise in the stochastic simulator, this paper develops the Bayesian stochastic Kriging (BSK) model to adapt for the heteroscedastic noise and metamodel parameter uncertainty in a Bayesian framework, which enhances the existing surrogate-based optimization methods. This paper presents a metamodel for large scale simulation-based freeway traffic management optimization problems. Simulation-based optimization combines the advantages of simulation models and mathematical optimization methods. The parameter estimation of the BSK model is accomplished by the Bayesian inference. The proposed methodology enables the efficient use of large scale high-resolution traffic simulation models for simulation-based optimization, while accounting for travelers' behavioral responses to information provision. We demonstrate the advantages of BSK compared to other existing metamodels using a numerical example of a synthetic network and a mathematical example. In a work zone scenario on a real-world freeway/arterial corridor of I-270 and MD-355 in the State of Maryland, the BSK model is applied to the freeway traffic management via optimizing the high-occupancy/toll rate and deploying dynamic message signs. Field traffic measurements by loop/microwave detections are used to calibrate travel demand and to supply the simulation parameters. The optimization results are promising in reducing the corridor-wide travel delay and enhancing the vehicle throughput. The online appendix is available at https://doi.org/10.1287/trsc.2018.0819. [ABSTRACT FROM AUTHOR]

Road traffic exhaust emission predictions are used to inform transport policy and investment decisions aimed at reducing emissions and achieving sustainable mobility. Emission predictions are also used as inputs when modeling air quality and human exposure to traffic-related air pollutants. To be effective, such policies and/or integration must be based on robust models that not only provide point-based predictions but also inform these with an interval of confidence that properly accounts for the propagation of uncertainties through the complex chain of models involved. This paper develops a data-driven methodological framework that enables calculating the uncertainty in average speed–based emission predictions induced by uncertainty in its traffic data inputs, which are most often predictions (or outputs) of traffic flow models. An ensemble-based optimisation approach is used to estimate both calibration and validation errors arising from uncertainty in the structure and parameterisation of the cell transmission model, a discretised first-order macroscopic traffic flow model that is often integrated with average speed–based emission models. A Monte Carlo sampling approach is proposed to propagate the uncertainty in traffic flow inputs to emission predictions. To ensure transferability of findings, this methodology has been tested using multiple real data sets on three motorway road networks, one of which operates under variable speed limits. The online appendix is available at https://doi.org/10.1287/trsc.2017.0787. [ABSTRACT FROM AUTHOR]

This paper presents the formulation of a new optimization problem designated as the express minibus problem, which intends to form small groups of clients with compatible boarding/exiting points in time and space for a new type of urban mobility service. This new transport option, as a competitive alternative to the private car, aims to provide almost direct services between dispersed demand poles in places where high-capacity and efficient public transport options are scarce, thus combining the major strengths of both public transport and private vehicles. Conventional public transport systems can present efficient space and energy consumption, whereas private vehicles have high levels of flexibility, are fast, and are always available. The proposed algorithm aims at assessing the potential demand of this new service by developing a clustering algorithm in which the groups of clients formed for each minibus route should present the following characteristics: there is a small number of boarding and exiting points, where in each point there is only boarding or alighting; boarding points should be close to each other, as well as the exiting points; there must be a reasonable distance between the last boarding point and the first exiting point; the average load factor must be high; and for all clients the overall detour time relative to the direct service should be small. This paper presents the rationale and structure of the clustering algorithm, followed by an application for the Lisbon metropolitan area during the morning peak, which could be adapted to the afternoon peak with some slight modifications. [ABSTRACT FROM AUTHOR]

This paper evaluates the robustness of a railway network with respect to operational delays. It assumes that trains in the network operate on fixed routes and with reference to a timetable. A stochastic delay propagation model is proposed for identifying primary (externally imposed) delays and for computing the resultant secondary (knock-on) delays. Delay probability distributions are computed for each train at each station on its journey, using timetable and infrastructure data for identifying potential station resource conflicts with other trains. The delay predictions are used to evaluate schedule robustness using two newly proposed metrics. Individual robustness measures the ability of trains to limit the adverse effects of their own primary delays. On the other hand, collective robustness measures the ability of the network as a whole, to limit the knock-on effects of primary delays imposed on a small fraction of trains. The two metrics provide stochastic guarantees on the punctuality of trains when the published schedule is put in operation. The applicability of the proposed methodology is validated using empirical data from a portion of the Indian Railways network, containing more than 38,000 train arrival/departure records. While a railway network is used as a case study, the same ideas can be applied to any scheduled transportation network. [ABSTRACT FROM AUTHOR]

Presents a response by C. Hendrickson and G. Kocur to a letter to the editor about their article "Schedule Delay and Departure Time Decisions in a Deterministic Model," in the 15th vol. of the journal "Transportation Science."

Presents a letter to the editor in response to the article "Schedule Delay and Departure Time Decisions in a Deterministic Model," by C. Hendrickson and G. Kocur, published in the 15th vol. of the journal "Transportation Science."

Transportation agencies often resort to the use of traffic simulation models to evaluate the impacts of changes in network design or network operations. They often have multiple traffic simulation tools that cover the network area where changes are to be made. These multiple simulators may differ in their modeling assumptions (e.g., macroscopic versus microscopic), in their reliability (e.g., quality of their calibration), as well as in their modeling scale (e.g., city-scale versus regional-scale). The choice of which simulation model to rely on, let alone of how to combine their use, is intricate. A larger-scale model may, for instance, capture more accurately the local-global interactions; yet may do so at a greater computational cost. This paper proposes an optimization framework that enables multiple simulation models to be jointly and efficiently used to address continuous urban transportation optimization problems. We propose a simulation-based optimization algorithm that embeds information from both a high-accuracy low-efficiency simulator and a low-accuracy high-efficiency simulator. At every iteration, the algorithm decides which simulator to evaluate. This decision is based on an analytical approximation of the accuracy loss as a result of running the lower-accuracy model. We formulate an analytical expression that is based on a differentiable and computationally efficient to evaluate traffic assignment model. We evaluate the performance of the algorithm with a traffic signal control problem on both a small network and a city network. We show that the proposed algorithm identifies signal plans with excellent performance, and can do so at a significantly lower computational cost than when systematically running the high-accuracy simulator. The proposed methodology contributes to enable large-scale high-resolution traffic simulation models to be used efficiently for simulation-based optimization. More broadly, it enables the use of multiple simulation models that may differ, for instance, in their scale, their resolution, or their computational costs, to be used jointly for optimization. [ABSTRACT FROM AUTHOR]

Delay imposed on buses is witnessed at isolated signalized intersections, as part of the delay is created due to bus and car interactions at the signalized approaches. Inexpensive solutions that do not involve new infrastructure are the most desired. Toward reducing person delay, presignal lights are installed at the upstream of the intersection. Presignal is a control tool that can manage the interaction and space conflict between cars and buses at the mixed lanes, located after the presignals, approaching the intersection. This paper presents an optimal presignal control policy that determines signal settings based on minimization of total person-time spent. The developed model is comprised of a simplified signalized intersection with one approach, where two presignal lights are located: one for bus lane and one for car lane. A continuous-time model is first developed to describe the queue dynamics for the mixed lanes after the presignals and the bus and car lanes before the presignals. The optimal solutions are derived analytically via the Pontryagin maximum principle, and the optimal presignal control policy is determined and synthesized. The derived analytical solutions are verified through the use of the optimal control software, DIDO, which uses an advanced optimization method and solves complex dynamic optimization problems without prior knowledge of the analytical computations or the solution. Several examples are used to test and analyze the derived solutions. Finally, the microscopic simulation software AIMSUN is used to test, assess, and evaluate the performance of the proposed optimal control policy in a more realistic traffic condition, where stochastic arrivals are incorporated. Supplemental Material: The online appendix is available at https://doi.org/10.1287/trsc.2022.1172. [ABSTRACT FROM AUTHOR]

This paper presents a case study of real-time traffic state estimation. The adopted general approach to the design of universal traffic state estimators for freeway stretches is based on stochastic macroscopic traffic flow modeling and extended Kalman filtering, which are outlined in the paper. The reported investigations were conducted by use of eight-hour traffic measurement data collected from a freeway stretch of 4.1 km close to Munich, Germany. Some key issues are carefully investigated, including the tracking capability of the designed traffic state estimator, significance of the online model parameter estimation, sensitivity of the estimator to the initial values of the estimated model parameters as well as to the related noise standard deviation values, and the capability of the estimator to handle biased flow measurements. The achieved results are quite satisfactory. [ABSTRACT FROM AUTHOR]

Observations of freeway traffic flow are usually quite scattered about an underlying curve when plotted versus density or occupancy. Although increasing the sampling intervals can reduce the scatter, whenever an experiment encompasses a rush hour with transitions in and out of congestion, some outlying data stubbornly remain beneath the ‘equilibrium’ curve. The existence of these nonequilibrium points is a poorly understood phenomenon that appears to contradict the simple kinematic wave (KW) model of traffic flow. This paper provides a tentative explanation of the phenomenon, based on experimental evidence. The evidence was a FIFO queue that grew and receded over two detector stations, generating typical flow-density scatter plots at both locations. The locations were far from other interacting traffic streams. The data revealed that a transition zone where vehicles decelerated gradually existed immediately behind the queue. The transition zone was quite wide (about 1 km at both locations), moved slowly (approximately with the ‘shock’ velocity of KW theory), and as a result spent many minutes over each detector station. Disequilibrium flow-density points arose only when the transition zone was over the detectors, suggesting that the transition zone explains their occurrence. The disequilibrium points drifted gradually from one branch of the curve to the other, as KW theory would have predicted if ‘shocks’ had a characteristic width equal to the dimension of the transition zone. Nothing was found in the data to contradict this view. This paper also shows that in our case, if one neglects the shocks' physical dimension, the position of every vehicle can be predicted with KW theory to within approximately five vehicle spacings. Thus, it appears that KW theory can predict rather accurately traffic behavior at the back of FTFO queues, i.e., when the lanes are equally attractive to all drivers. We end with a discussion offering some perspective on how the findings of this paper related to the traffic thinking found in the current literature. [ABSTRACT FROM AUTHOR]

A simple yet efficient traffic flow model, in particular one that describes vehicle longitudinal operational control and further characterizes a traffic flow fundamental diagram, is always desirable. Though many models have been proposed in the past with each having its own merits, research in this area is far from conclusive. This paper contributes a new model, i.e., the longitudinal control model, to the arsenal with a unique set of properties. The model is suited for a variety of transportation applications, among which a concrete example is provided in this paper. [ABSTRACT FROM AUTHOR]

This paper is concerned with the modeling of the Dynamic Traffic Assignment Problem (DTAP) for predicting the flows of urban transportation networks, mainly at peak periods. During the past 40 years, most of the research has been for the Static Traffic Assignment Problem (STAP) where it is assumed that demand is constant over time. This assumption is realistic for the analysis of intercity freight transportation networks over long periods of time, but it does not hold in an urban area, for simulating the flow variations during short periods (peak hours). Hence, during the past 20 years, the interest to the DTAP has been increasing. The seventies have been a transition period between heuristic models (where the demand is assigned to instantaneous minimum cost paths), and optimization models that take into account the demand over the whole study horizon of time, but all of them incorporate important limitations (only one destination; unrealistic conditions on the cost functions so that the flow "reaches" the destination; possible violation of the link capacities; etc.). In this paper, we propose a Dynamic Traffic Assignment Model which is mainly based on the following assumption: the time spent by a vehicle on a link may be decomposed into a fixed travel time plus a waiting time. The fixed travel time corresponds to the free or uncongested travel time over the link. Then the vehicle is put in an exit queue (which resides on the same link) until it becomes possible to enter a forward link; this decision is based on the link costs and their capacities. We show that this model leads to a network structure (a temporal expansion of the base network, including the queues) and therefore the DTAP may be viewed as a "simple" STAP over the expanded network. Hence, all the theories... [ABSTRACT FROM AUTHOR]

Queueing because of congestion is an important aspect of road traffic. This paper provides a novel threshold queue that models the empirical shape of the fundamental diagram. In particular, we show that our threshold queue with two service phases captures the capacity drop that is eminent in the fundamental diagram of modern traffic. We use measurements on a Danish highway to illustrate that our threshold queue is indeed capable of capturing the fundamental diagram of real-world traffic systems. We furthermore indicate the modelling power of our threshold queue via a sensitivity study showing that our model is able to capture a wide range of shapes for the fundamental diagram. The online appendix is available at https://doi.org/10.1287/trsc.2018.0850. [ABSTRACT FROM AUTHOR]

Ride sharing has been widely acknowledged as an effective solution for reducing travel costs, congestion, and pollution. This paper considers the ride-sharing problem of the scheduled commuter and business traffic within a closed community of companies that agree to share the calendars of their employees. We propose a formulation in the form of a general integer linear program (ILP) for the aforementioned ride-sharing problem, which incorporates return restrictions to satisfy the business needs, as well as meeting points and the option for riders to transfer between drivers. All the instances with 40 and 60 participants and most of the instances with 80 participants can be solved to optimality within a time limit of two hours. Using instances of up to 100 participants, the ILP can be solved with a gap of no more than 1.8% within the time limit. Because of the high computational complexity, we develop a constructive heuristic that is based on the savings concept. This heuristic is also able to combine ride sharing with the use of an external mobility service provider. Our numerical study shows that ride sharing can be an effective way of reducing the number of trips and vehicle miles. Particularly, ride sharing creates more benefits when the participation is high and when the origins and the destinations of the trips are more spatially concentrated. The results show that ride sharing can create up to 31.3% mileage savings and up to 28.7% reduction in the number of cars needed to fulfill employees' travel schedules. We also illustrate our model using a real-life ride-sharing problem of a Dutch consultancy and research firm. The online appendix is available at https://doi.org/10.1287/trsc.2018.0832. [ABSTRACT FROM AUTHOR]

In this paper, we present a cyclically time-expanded network model for simultaneous optimization of traffic assignment and traffic signal parameters, in particular, offsets, split times, and phase orders. Since travel times are of great importance for developing realistic solutions for traffic assignment and traffic signal coordination in urban road networks, we perform an extensive analysis of the model. We give an example showing that a linear time-expanded model can reproduce realistic nonconvex travel times especially for use with traffic signals and we verify this by simulation. Furthermore, we show how exact mathematical programming techniques—namely, mixed-integer linear programming—can be used for optimizing the control of traffic signals. We provide computational results for real-world instances and demonstrate the capabilities of the cyclically time-expanded model by simulation results obtained with state-of-the-art traffic simulation tools. [ABSTRACT FROM AUTHOR]

Traffic congestion in urban networks may lead to strong degradation in the utilization of the network infrastructure, which can be mitigated via suitable control strategies. This paper studies and analyzes the performance of an adaptive traffic-responsive strategy that controls the traffic light parameters in an urban network to reduce traffic congestion. A nearly optimal control formulation is adopted to avoid the curse of dimensionality occurring in the solution of the corresponding Hamilton–Jacobi–Bellman (HJB) optimal control problem. First, an (approximate) solution of the HJB is parametrized via an appropriate Lyapunov function; then, the solution is updated at each iteration in such a way to approach the nearly optimal solution, using a close-to-optimality index and information coming from the simulation model of the network (simulation-based design). Simulation results obtained using a traffic simulation model of the network Chania, Greece, an urban traffic network containing many varieties of junction staging, demonstrate the efficiency of the proposed approach, as compared with alternative traffic strategies based on a simplified linear model of the traffic network. It is shown that the proposed strategy can adapt to different traffic conditions and that low-complexity parametrizations of the optimal solution, a linear and a bimodal piecewise linear strategy, respectively, provide a satisfactory trade-off between computational complexity and network performance. [ABSTRACT FROM AUTHOR]

This paper investigates the cell-transmission model (CTM)-based single destination system optimum dynamic traffic assignment (SO-DTA) problem, focusing attention on a case where the cell properties are time-invariant. We show the backward propagation of congestion in CTM does not affect the optimal arrival flow pattern of SO-DTA, if the fundamental diagram is of triangular/trapezoidal shape as in the CTM. We mathematically prove that the set of earliest arrival flows (EAFs) not constrained by the traffic wave propagation equations obtained on the node-arc network without cell division is a subset of the SO-DTA. This finding leads to a new approach to the SO-DTA that solves the EAF. Such an EAF can be obtained by merely applying static flow techniques and turning the static flows into dynamic flows over time. Therefore, SO-DTA can theoretically be solved with a run time at the link level depending polynomially on log T . We use numerical examples to verify the results and report the computational benefits of the proposed method by solving SO-DTA on a real-world network. [ABSTRACT FROM AUTHOR]

This paper formulates an analytical stochastic network loading model. It is a stochastic formulation of the link transmission model (LTM), which itself is an operational formulation of Newell's simplified theory of kinematic waves. The proposed model builds on an existing initial model. It proposes a formulation with enhanced scalability. In particular, compared with the initial model, it has a complexity that is linear rather than cubic in the link's space capacity. This makes it suitable for large-scale network analysis. The model is validated versus a simulation-based implementation of the stochastic LTM. The proposed model yields significant gains in computational efficiency while preserving accuracy. The validation experiments illustrate how computational run times of the proposed model increase linearly with the link's space capacity, while the initial model has an exponential increase in run times. The proposed model yields accurate distributional approximations of the link's boundary conditions. It is used to address a probabilistic formulation of a citywide signal control problem. The model is shown to be robust to the quality of the initial signal plans. It yields signal plans that systematically outperform both initial plans, as well as a plan derived by widely used commercial signal control software. The model is suitable for large-scale network optimization. The online appendix is available at https://doi.org/10.1287/trsc.2017.0804. [ABSTRACT FROM AUTHOR]

If shipments have to be transported between many sources and sinks, direct connections from each source to each sink are often too expensive. Instead, a small number of nodes are upgraded to hubs that serve as transshipment points. All sources and sinks are connected to these hubs, so that only a few, strongly consolidated transport relations exist. While hubs and detours lead to additional costs, the savings from bundling shipments—i.e., economies of scale—usually outweigh these costs. Typical applications for hub networks are in cargo, air freight, and postal and parcel transport services. In this paper, we consider three classical and two recent formulations of single allocation hub location problems—i.e., hub location problems in which every source and sink is connected to exactly one hub. Solving larger instances of these problems to optimality is difficult because the inherent quadratic structure of the problem has to be linearized: This leads to a sharp rise in the number of variables. Our new approach relies on the fact that many instances—including the Civil Aeronautics Board and Australian Post data sets—have a Euclidean structure: The distances between the possible hub locations are Euclidean. This enables us to construct a new linearization together with a row generation procedure that solves instances of up to 200 nodes to optimality. For problems like the uncapacitated single allocation p-hub median problem and the uncapacitated single allocation hub location problem, we present the first optimal results for instances of this size. [ABSTRACT FROM AUTHOR]

China has recently developed a large-scale high-speed railway (HSR) network that not only revolutionizes the perception of long-haul transport but also fundamentally improves the emergency response capability of the country. This gives rise to a problem of scheduling a set of emergency trains within the predefined HSR timetable. According to different degrees of disturbance of the timetable, this paper identifies three kinds of solutions, named, ideal, quasi-ideal, and feasible solutions, to the problem. We define a "headroom" function for computing the maximum number of emergency trains that can be inserted between two adjacent regular trains without any disturbance, from which a linear algorithm for finding ideal solutions is derived. By identifying the scope of changes to each regular train, quasi-ideal and feasible solutions can be found based on the ideal solutions on a set of alternative timetables. Numerical experiments demonstrate that our method is very efficient for supporting near-immediate emergency responses. We have used the solution method to evaluate the emergency capacity of most HSR lines in China. In particular, we successfully applied the method to schedule emergency trains in the rescue operation of the 2015 Tianjin chemical explosion. The online appendix is available at https://doi.org/10.1287/trsc.2017.0794. [ABSTRACT FROM AUTHOR]

This note revisits a paper from Velan and Florian (Velan, S., M. Florian. 2002. A note on the entropy solutions of the hydrodynamic model of traffic flow. Transportation Sci. 36(4) 435-446) dealing with the entropy condition in traffic flow models. It aims to clarify the application of this condition for nondifferentiable fundamental diagrams and then to correct some misunderstandings that appear in the above-mentioned paper. This note clearly exhibits that the nonsmoothness of the fundamental diagram does not change the properties of the Lighthill-Whitham-Richards (LWR) solutions: (i) existence of a unique entropy solution and (ii) nonuniqueness of weak solutions. These precisions are important because piecewise linear fundamental diagrams appear to accurately fit with experimental observations and cannot be disproved on an alleged mathematical basis. [ABSTRACT FROM AUTHOR]

In this paper, congestion dynamics along crowded freeway corridors are modeled as a conservation law with a source term that is continuous in space. The source term represents the net inflow from ramps, postulated here as a location-dependent function of the demand for entering and exiting the corridor. Demands are assumed to be time-independent, which is appropriate for understanding the onset of congestion. Numerical and analytical results reveal the existence of four well-defined regions in time-space, two of which are transient. The conditions for the existence of congestion both in the freeway and in the on-ramps are identified, as well as the set of on-ramps that are most likely to become active bottlenecks. The results in this paper help explain the stochastic nature of bottleneck activation, and can be applied to devise effective system-wide ramp metering strategies that would prevent excessively long on-ramp queues. [ABSTRACT FROM AUTHOR]

In this paper we explicitly construct the entropy solutions for the Lighthill-Whitham-Richards (LWR) traffic flow model with a flow-density relationship which is piecewise quadratic, concave, but not continuous at the junction points where two quadratic polynomials meet, and with piecewise linear initial condition and piecewise constant boundary conditions. The existence and uniqueness of entropy solutions for such conservation laws with discontinuous fluxes are not known mathematically. We have used the approach of explicitly constructing the entropy solutions to a sequence of approximate problems in which the flow-density relationship is continuous but tends to the discontinuous flux when a small parameter in this sequence tends to zero. The limit of the entropy solutions for this sequence is explicitly constructed and is considered to be the entropy solution associated with the discontinuous flux. We apply this entropy solution construction procedure to solve four representative traffic flow cases, compare them with numerical solutions obtained by a high order weighted essentially nonoscillatory (WENO) scheme, and discuss the results from traffic flow perspectives. [ABSTRACT FROM AUTHOR]

By introducing the concept of speed elasticity of flow and density, this paper provides a generic characterization for a class of well-behaved equilibrium speed-flow curves that are differentiable and backward bending and possess monotone speed-density curves. We start with a comprehensive review on classical models, including Greenberg, Greenshields, and Underwood. A major limitation of these models is that the specification is uniquely determined by three road-specific parameters: the free-flow speed, the capacity flow, and the corresponding speed at the capacity flow, which makes the empirical application difficult due to lack of flexibility. Through a careful review of Del Castillo and Benitez [Del Castillo, J. M., F. G. Benitez. 1995. On the functional form of the speed-density relationship -- I: General theory, II: Empirical investigation. Transportation Res. Part B 29 373-406], we have provided a new characterization for the Newell-Frankin model and made a connection between the family of rational generating functions and the Greenshields-type models. Based on three primitive regularity conditions, we derive a generic characterization for well-behaved macroscopic equilibrium speed- flow curves that integrate all classical models. Using the generic characterization, we show that the equilibrium speed-flow curves derived from the car-following models can be classified as a two-parameter extension of the Greenshields-type model. We have also made an attempt in proposing a plausible rectification to the speed-flow models from the Highway Capacity Manual 2000 so that they possess the backward-bending property. A formal linkage between the generic characterization of speed-flow curves and the theory of congestion pricing is also established. [ABSTRACT FROM AUTHOR]

This paper deals with sensitivity analysis of static traffic user equilibrium problems. We apply some recently developed sensitivity analysis techniques for generalized equations to analyze the behavior of the equilibrium arc flow of such a problem when both the arc cost function and the travel demand vary. Our methods permit calculation of semiderivatives under general conditions and of derivatives under more restrictive conditions; we calculate the semiderivatives by solving a linear traffic user equilibrium problem and the derivatives by matrix multiplication together with the solution of a linear equation the dimension of which is at most the number of arcs. Three numerical examples show how to use these results in practice. [ABSTRACT FROM AUTHOR]

This paper deals with the fixed-cycle traffic-light (FCTL) queue, where vehicles arrive at an intersection controlled by a traffic light and form a queue. The traffic light alternates between green and red periods, and delayed vehicles are assumed to depart during the green period at equal time intervals. The key performance characteristic in the FCTL queue is the so-called mean overflow, defined as the mean queue length at the end of a green period. An exact solution for the mean overflow is available, but it has been considered to be of little practical value because it requires some numerical procedures. Therefore, most of the literature on the FCTL queue is about deriving approximations for the mean overflow. In deriving these approximations, most authors first approximate the FCTL queue by a bulk-service queue, approximate the mean overflow in the bulk-service queue, and use this as an approximation for the mean overflow in the FCTL queue. So far no quantitative comparison of both models has been given. We compare both models and assess the quality of the approximation for various settings of the parameter values. In this comparison and throughout the paper we do not restrict ourselves to Poisson arrivals, but consider a more general arrival process instead. We discuss the numerical issues that need to be resolved to calculate the exact expression for the mean overflow in both queues and show that clear computational schemes are available. Next, we present several bounds and approximations of the mean overflow that do not require numerical procedures. In particular, we derive a new approximation based on the heavy traffic limit and a scaling argument. We compare the new bounds and approximation with the existing ones. We elaborate on the impact of several parameters, like the length of the green and red period and the variance of the arrival distribution. [ABSTRACT FROM AUTHOR]

Insertion heuristics have proven to be popular methods for solving a variety of vehicle routing and scheduling problems. In this paper, we focus on the impact of incorporating complicating constraints on the efficiency of insertion heuristics. The basic insertion heuristic for the standard vehicle routing problem has a time complexity of O(n³). However, straightforward implementations of handling complicating constraints lead to an undesirable time complexity of O(n4. We demonstrate that with careful implementation it is possible, in most cases, to maintain the O⊃3 complexity or, in a few cases, increase the time complexity to O(n⊃3 log n). The complicating constraints we consider in this paper are time windows, shift time limits, variable delivery quantities, fixed and variable delivery times, and multiple routes per vehicle. Little attention has been given to some of these complexities (with time windows being the notable exception), which are common in practice and have a significant impact on the feasibility of a schedule as well as the efficiency of insertion heuristics. [ABSTRACT FROM AUTHOR]

This paper discusses the uniqueness of user equilibrium in transportation networks with heterogeneous commuters. Daganzo (1983) proved the uniqueness of (stochastic) user equilibrium when commuters have heterogeneous tastes over possible paths, but identical disutility functions from time costs. We first show, by example, that his result may not apply in general networks if disutility functions are allowed to differ. However, for "simple" transportation networks, we show that user equilibrium is always unique and weakly Pareto efficient (cf. the Braess example) for a general class of utility functions. We investigate whether this result applies to more general networks. We also show that user equilibrium is unique in a dynamic bottleneck model with a simple network. We discuss an interesting relationship between the following two problems: the existence of user equilibrium in a finite model and the uniqueness of user equilibrium in a continuum model. In the appendix, we also provide a proof of a slightly generalized version of Daganzo's theorem. [ABSTRACT FROM AUTHOR]

The queueing-theoretical model for stationary traffic flow developed in a former paper is extended and modified for nonstationary flow. In particular it is shown how speed-flow-density relationships under nonstationary conditions may deviate from those obtained for stationary conditions.It is shown how the wide scatter which is often observed with empirical speed-flow-density data can be explained by nonstationarity. Furthermore, hysteresis loops,which may show up in speed-flow-density relationships, are interpreted by means of nonstationarity. [ABSTRACT FROM AUTHOR]

Over recent years, increasing attention has been devoted to the problem of estimating Origin/Destination (O/D) matrices by using traffic counts, named in the following O/D Count Based Estimation (ODCBE) problem. These methods combine traffic flow measures with other available information to "correct" and improve an initial estimate of the O/D trip matrix. Virtually all models and procedures proposed in the literature are formulated as mathematical programming problems. Most ODCBE models use a relationship relating traffic counts to the unknown O/D matrix; this relationship is often in the form of an explicit estimate of the assignment matrix, i.e., of the fractions of O/D flows using each link of the network for which traffic counts are available. The computation of the assignment matrix is not trivial for congested networks, where travel costs and path choice fractions depend on flows. This problem has been dealt with in relatively few papers in the literature, usually formulated as a bilevel optimisation model under the assumption of a Deterministic User Equilibrium (DUE) assignment model. In this paper, the general within-day static ODCBE problem for congested networks is formulated as a fixed-point problem of an implicit function which results from the solution of a mathematical programming problem. In other words, the solution of the ODCBE problem is an O/D matrix that, once assigned to the network, reproduces flows and costs consistent with the values used to compute the assignment matrix. Fixed-point theorems and algorithms have been extended to the problem at hand. Different fixed-point algorithms, namely, Functional Iteration, Method of Successive Averages, and Method of Successive Averages with Decreasing Reinitialisation are proposed, and their performances are compared on a small test network. It has been verified that all algorithms converge to the same solution, though with different speeds. Furthermore, the fixed-point solution outperforms the... [ABSTRACT FROM AUTHOR]

Recently, Daganzo introduced the cell transmission model--a simple approach for modeling highway traffic flow consistent with the hydrodynamic model. In this paper, we use the cell transmission model to formulate the single destination System Optimum Dynamic Traffic Assignment (SO DTA) problem as a Linear Program (LP). We demonstrate that the model can obtain insights into the DTA problem, and we address various related issues, such as the concept of marginal travel time in a dynamic network and system optimum necessary and sufficient conditions. The model is limited to one destination and, although it can account for traffic realities as they are captured by the cell transmission model, it is not presented as an operational model for actual applications. The main objective of the paper is to demonstrate that the DTA problem can be modeled as an LP, which allows the vast existing literature on LP to be used to better understand and compute DTA. A numerical example illustrates the simplicity and applicability of the proposed approach. [ABSTRACT FROM AUTHOR]

Connected and automated vehicle (CAV) technology is providing urban transportation managers tremendous opportunities for better operation of urban mobility systems. However, there are significant challenges in real-time implementation as the computational time of the corresponding operations optimization model increases exponentially with increasing vehicle numbers. Following the companion paper (Chen et al. 2021), which proposes a novel automated traffic control scheme for isolated intersections, this study proposes a network-level, real-time traffic control framework for CAVs on grid networks. The proposed framework integrates a rhythmic control method with an online routing algorithm to realize collision-free control of all CAVs on a network and achieve superior performance in average vehicle delay, network traffic throughput, and computational scalability. Specifically, we construct a preset network rhythm that all CAVs can follow to move on the network and avoid collisions at all intersections. Based on the network rhythm, we then formulate online routing for the CAVs as a mixed integer linear program, which optimizes the entry times of CAVs at all entrances of the network and their time–space routings in real time. We provide a sufficient condition that the linear programming relaxation of the online routing model yields an optimal integer solution. Extensive numerical tests are conducted to show the performance of the proposed operations management framework under various scenarios. It is illustrated that the framework is capable of achieving negligible delays and increased network throughput. Furthermore, the computational time results are also promising. The CPU time for solving a collision-free control optimization problem with 2,000 vehicles is only 0.3 second on an ordinary personal computer. [ABSTRACT FROM AUTHOR]

Questions concerning when a road ceases to serve the public well or has failed are closely related to the ride quality of the road. The quantification of the rideability or serviceability of road deals with the human rating of ride quality. For the most thorough rating, a select panel of raters has been used to rate a road section after having either driven or ridden over the section. The average of the ratings may be called the present serviceability rating (PSR). Given a set of PSR covering a wide spectrum of roads of different surface characteristics, the essential question is how to explain the PSR in terms of the explanatory variables describing human sensitivity in some relevant functional form. It is apparent that a rater responds to the vibration environment in a moving vehicle induced by the longitudinal roughness of a road. This paper presents an analytical model connecting the characteristics of a road profile, and the dynamic response of a vehicle to the profile, to the human ratings of the ride quality. Analytical expressions for various dynamic indices in a moving vehicle are derived. Very good agreement between the model prediction and the ratings is demonstrated using actual field data. Obtaining a good model prediction would give the means of obtaining a rating of road quality comparable to that provided by experts, without the associated expense of employing such experts. [ABSTRACT FROM AUTHOR]

A bilevel programming approach is used to tackle an optimization problem for area traffic control and equilibrium flows. The signal timing plan is defined by common cycle time, and by starts and durations of greens. The system performance index is defined as the sum of a weighted linear combination of rate of delay and number of stops per unit time for all traffic streams, which is evaluated by the traffic model from TRANSYT. User equilibrium traffic assignment is formulated as a variational inequality problem. Approximate mathematical expressions for various components of the performance index and the average delay to a vehicle at the downstream junction in the TRANSYT model for both undersaturated and oversaturated links have been derived. For a locally optimal search, the gradient projection method is used in deciding whether feasible descent directions leading to a Karush-Kuhn-Tucker point, which is potentially a local optimum, can be identified. A global search heuristic is proposed in this paper by which successively better Karush-Kuhn-Tucker points can be found with reasonable computation effort. The mixed search procedure, including the locally optimal search and global search heuristic, is proposed. Encouraging results for Allsop and Charlesworth's network have confirmed that the approximately optimizing mixed search procedure in solving the area traffic control optimization problem can achieve substantially better results than does the nonoptimizing calculations of mutually consistent signal timings and link flows. [ABSTRACT FROM AUTHOR]

The paper studies the problem of predicting traffic equilibrium (TE) in a transportation network within the framework of decision making among discrete choices in a probabilistic and uncertain environment. Conventional approaches to predict TE typically assume that travel times are deterministic and perceived accurately by the travelers; and some new TE models have considered probabilistic travel times or inaccurate perceptions but not both. In our generalized model, which we refer to as GTESP, the travel time on each route is random and each traveler perceives, possibly inaccurately, a travel time probability distribution for each route which may vary from traveler to traveler Each traveler uses a disutility function of travel time to evaluate each route and chooses that route which minimizes his expected disutility. GTESP is difficult to solve for general nonlinear disutility functions. However, special cases—in particular when arc travel times are statistically independent and the disutility functions to evaluate route travel times are linear, exponential, or quadratic—are solvable, at least approximately. GTESP is general in the sense that most existing TE models can be shown to be special or limiting cases of GTESP. Furthermore, this paper demonstrates, with illustrative examples, that GTESP appears to capture travelers' risk-taking behavior more realistically than existing TE models. [ABSTRACT FROM AUTHOR]

For a predetermined set of an upper bound of link flows, this paper proposes a price-based congestion control scheme for achieving such a restraint target of traffic flow that evolves from day to day. On each day, drivers have to pay a toll selected from a feasible set. The tolls on each day are determined by the link flows and toll charges on the previous day and the predetermined upper bound of link flows. Several properties of the dynamical system model with the control scheme are analyzed, including the invariance of its evolutionary trajectories; the equivalence between its stationary state and user equilibrium under toll charge; the uniqueness, existence, and boundedness of its stationary state; and the convergence of its evolutionary trajectories. A special case of the model and implementation of the control scheme for several alternative targets are also given. Finally, application of the model to a traffic network is demonstrated with a numerical example. The study is helpful for better understanding the mechanism of congestion control under day-to-day traffic flow dynamics. [ABSTRACT FROM AUTHOR]

This paper introduces a variant of the vehicle routing problem adapted for bus-based, regional evacuation planning, where evacuees arrive at predetermined pickup locations at constant, location-specific rates. This arrival process more realistically portrays evacuee arrival behavior, presenting an important distinction from the current transit-based evacuation literature. In this problem, capacity-constrained buses are routed, potentially multiple times, to transport all evacuees to a depot/shelter such that the last pickup, and the end of the arrival process, occurs at a location-specific time, determined by risk considerations. The problem seeks to minimize the total waiting time at these locations (total exposure) and exploits efficiencies by allowing service choice. The structural properties of this problem guide the choice for two important strategic parameters: the maximum number of pickups allowed on each location and the fleet size. It is shown that, depending on the problem instance, increasing the maximum number of pickups may reduce both the fleet size requirement and the total exposure and that, past a certain threshold, there exists a maximum number of pickups (or a range of potential values, if the problem cannot be solved to optimality) that guarantees an efficient usage of the available fleet and equitable reductions in exposure across pickup locations. [ABSTRACT FROM AUTHOR]

Private enterprises and governments around the world use speed cameras to control traffic flow and limit speed excess. Cameras may be exposed to difficult weather conditions and typically require frequent maintenance. When deciding the order in which maintenance should be performed, one has to consider both the traveling times between the cameras and the traffic flow that each camera is supposed to monitor. In this paper, we study the problem of routing a set of technicians to repair cameras by minimizing the total weighted latency, that is, the sum of the weighted waiting times of each camera, where the weight is a parameter proportional to the monitored traffic. The resulting problem, called the weighted k-traveling repairman problem (wkTRP), is a generalization of the well-known traveling repairman problem and can be used to model a variety of real-world applications. To solve the wkTRP, we propose an iterated local search heuristic and an exact branch-and-cut algorithm enriched with valid inequalities. The effectiveness of the two methods is proved by extensive computational experiments performed both on instances derived from a real-world case study and on benchmark instances from the literature on the wkTRP and on related problems. [ABSTRACT FROM AUTHOR]

This paper presents an algorithm for the traffic assignment problem. The algorithm is characterized by the "origin-based" feature, which solves the user equilibrium flow that is restricted to a single-origin network and loops among origins to produce the all-origin to all-destination equilibrium flow. In contrast to most prior traffic assignment problem algorithms, our method maintains a general spanning tree rooted at each origin, where in-tree arcs can be directed either away from or toward the root. Leveraging an optimality condition in the cycle space, the algorithm uses the network simplex method to identify and cancel a set of negative cost cycles. Numerical experiments demonstrate that the algorithm can generate highly precise solutions with fast convergence on large-scale networks. [ABSTRACT FROM AUTHOR]

There has been extensive research on the optimal design of road congestion pricing schemes based on traffic network equilibrium models. Since travel demands are closely related to the locations of workplace and residence, it is of both theoretical and practical importance to extend the optimization approach to treat location choices as well as travel route choices. This paper addresses the problem of optimal location of housing supply and transportation network pricing in an integrated location and transportation model with heterogeneous households that have different values of travel time. In the model, housing exhibits external economies and diseconomies of scale, depending on the population density in residential zones. It is shown that in such a model the marginal cost pricing principle applied to internalize these externalities in general results in local optima of social surplus. Optimization algorithms based on sensitivity analysis are proposed to find combinations of housing supply patterns and road tolls that optimize social surplus under various conditions. A numerical example is given to illustrate the proposed method. The potential policy implications of the optimization approach are examined and compared with that of the marginal cost pricing principle. [ABSTRACT FROM AUTHOR]

The paper introduces a cutting-plane matheuristic for the design-balanced capacitated multicommodity network design problem, one of the premier formulations for the service network design problem with asset management concerns increasingly faced by carriers within their tactical planning processes. The matheuristic combines a cutting-plane procedure efficiently computing tight lower bounds and a variable-fixing procedure feeding a MIP solver. Learning mechanisms embedded into the cutting-plane procedure provide the means to identify promising variables and thus both reduce the dimension of the problem instance, making it addressable by a MIP solver, and guide the latter toward promising solution spaces. Extensive computational experiments show the efficiency of the proposed procedures in obtaining high-quality solutions, outperforming the current best methods from the literature. [ABSTRACT FROM AUTHOR]

Diverging junctions are important network bottlenecks, and a better understanding of diverging traffic dynamics has both theoretical and practical implications. In this paper, we present a new framework for constructing kinematic wave solutions to the Riemann problem of kinematic wave models of diverging traffic with jump initial conditions. Within this framework, the function space of weak solutions is enlarged to include interior states that occur with stationary discontinuities, and various discrete flux functions in cell transmission models of diverging traffic are used as entropy conditions to pick out unique physical solutions. Then in demand-supply space, we prove that the Riemann problem can be uniquely solved for existing discrete flux functions, in the sense that stationary states and, therefore, shock or rarefaction waves on all links, can be uniquely determined under given initial conditions. We show that the two diverge models by Lebacque and Daganzo are asymptotically equivalent. We also prove that the supply proportional and priority-based diverge models are locally optimal evacuation strategies. With numerical examples, we demonstrate the validity of the analytical solutions of interior states, stationary states, and corresponding kinematic waves. This study presents a unified framework for analyzing traffic dynamics arising at diverging junctions and could be helpful for developing emergency evacuation strategies. [ABSTRACT FROM AUTHOR]

In this paper we investigate a bottleneck model in which the capacity of the bottleneck is assumed stochastic and follows a uniform distribution. The commuters' departure time choice is assumed to follow the user equilibrium principle according to mean trip cost. The analytical solution of the proposed model is derived. Both the analytical and numerical results show that the capacity variability would indeed change the commuters' travel behavior by increasing the mean trip cost and lengthening the peak period. We then design congestion pricing schemes within the framework of the new stochastic bottleneck model, for both a time-varying toll and a single-step coarse toll, and prove that the proposed piecewise time-varying toll can effectively cut down, and even eliminate, the queues behind the bottleneck. We also find that the single-step coarse toll could either advance or postpone the earliest departure time. Furthermore, the numerical results show that the proposed pricing schemes can indeed improve the efficiency of the stochastic bottleneck through decreasing the system's total travel cost. [ABSTRACT FROM AUTHOR]

In traffic systems where driving is on the left, right-turning movements tend to be difficult to efficiently accommodate at signal controlled junctions. A hook turn is one potential solution for this. A hook turn is where a right turn is made from the nearside lane rather than an offside lane at a four-leg signalised junction. After entering the junction, the turning vehicle waits at a nearside position in front of the side road stop line, and then proceeds toward the exit arm when the side road signal turns green. The research described in this paper uses microscopic simulation modelling in an innovative way to compare the traffic performance of a hypothetical hook-turn junction with an equivalent conventional junction with opposed right turns. The simulation model evaluated traffic performance under various combinations of demand flow, turning proportions, and signal timings. It was found that hook turns reduced delays to through traffic from the same approach in nearly all cases. Overall junction performance depended on the scale of any increased delays to left-turning traffic and side road traffic resulting from the hook-turn movement. It is concluded that hook turns could be used much more widely than at present--including where driving is on the right--offering significant operational benefits in the right circumstances. [ABSTRACT FROM AUTHOR]

Convective weather is responsible for large delays and widespread disruptions in the U.S. National Airspace System, especially during summer. Traffic flow management algorithms require reliable forecasts of route blockage to schedule and route traffic. This paper demonstrates how raw convective weather forecasts, which provide deterministic predictions of the vertically integrated liquid (the precipitation content in a column of airspace) can be translated into probabilistic forecasts of whether or not a terminal area route will be blocked. Given a flight route through the terminal area, we apply techniques from machine learning to determine the likelihood that the route will be open in actual weather. The likelihood is then used to optimize terminalarea operations by dynamically moving arrival and departure routes to maximize the expected capacity of the terminal area. Experiments using real weather scenarios on stormy days show that our algorithms recommend that a terminal-area route be modified 30% of the time, opening up 13% more available routes that were forecast to be blocked during these scenarios. The error rate is low, with only 5% of cases corresponding to a modified route being blocked in reality, whereas the original route is in fact open. In addition, for routes predicted to be open with probability 0.95 or greater by our method, 96% of these routes (on average over time horizon) are indeed open in the weather that materializes. [ABSTRACT FROM AUTHOR]

This article introduces a game-theoretic approach for allocating protection resources among the components of a network so as to maximize its robustness to external disruptions. Specifically, we consider shortestpath networks where disruptions may result in traffic flow delays through the affected components or even in the complete loss of some elements. A multilevel program is proposed to identify the set of components to harden so as to minimize the length of the shortest path between a supply node and a demand node after a worst-case disruption of some unprotected components. An implicit enumeration algorithm is then developed to solve the multilevel problem to optimality. The approach is streamlined by solving the lower-level interdiction problem heuristically at each node of an enumeration tree and by using some variable fixing rules to reduce the dimension of the lower-level problems. A thorough computational investigation demonstrates that the proposed solution method is able to identify optimal protection strategies for networks of significant size. The paper is concluded with a study of the sensitivity of the solution approach to variations of the problem parameters such as the level of disruption and protective resources and the distribution of the arc lengths and delays. [ABSTRACT FROM AUTHOR]

In the 1960s, Braess showed that the overall system performance of a transportation network can be degraded when a new link is added to the network, given that travelers choose their routes based on the user equilibrium (UE) principle. This phenomenon is often referred to as Braess' paradox (BP). The original five-link BP network has been studied extensively with static link performance functions. In this paper, we revisit the original BP network with a dynamic point-queue model and examine whether the results from the static model would hold for the case with time-dependent queues. For this purpose, we solve the BP problem with the consideration of dynamic queuing that leads the system to a steady state while satisfying the dynamic user equilibrium (DUE) condition at every instant. Our results indicate that the locations of congestion, or "hot spots," of the system are sensitive to the capacity of each link in an intricate manner. The "surprising result" reported in previous studies with link performance functions, that a system can spontaneously grow out of Braess' paradox if the demand is sufficiently high, does not occur with time-dependent queues. Instead, we show that queues in different stages have different impacts on the system performance. The implication of this result is discussed in the context of developing proactive dynamic traffic control strategies that can eliminate the negative impact of BP while keeping the system operating at the DUE condition. Even though this study focuses on the original five-link network, the results illustrate the potential pitfalls of extending insights developed from a static framework for dynamic traffic and the importance of studying the problem with a dynamic framework for real-time traffic control. [ABSTRACT FROM AUTHOR]