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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]

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]

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]

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]

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]

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 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]

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]

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]

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]

Queue overflow is a critical issue in developing queue prediction technologies for applications in Advanced Transportation Management Systems (ATMS). Conventional queue prediction methods, however, are limited to incident-free queue length prediction where traffic arrivals can be readily obtained using detectors. Despite the problems posed by queue overflow, studies addressing queue-overflow issues, or for predicting queue overflows beyond detectors, appear inadequate. This paper describes an advanced methodology which uses a stochastic system modeling approach and random processes for predicting queue lengths beyond detectors in real time. Lane changing is taken into account in developing the queue-overflow prediction model because lane changing accompanies queue overflow in most cases. A discrete-time, nonlinear stochastic system is specified for modeling the queues and lane changes beyond detectors during queue-overflow occurrence. The noise terms of the recursive equations of the model account for the effects of queues and a variety of arriving volumes on vehicular lane-changing maneuvers during queue-overflow occurrence. The unknown traffic arrivals beyond detectors are predicted employing random processes. In addition, a recursive estimation algorithm for predicting real-time queue overflows is developed utilizing the extended Kalman filtering technique. Preliminary test results indicate that the proposed methodology is promising for real-time prediction of queue overflows. The predicted queue overflows can be used not only in understanding the phenomenon of lane traffic patterns during queue-overflow occurrence, but also in developing related advanced technologies such as real-time road traffic congestion control and management systems. [ABSTRACT FROM AUTHOR]

The interdependence of the time-dependent behavior of traffic flows and tripmakers' departure time decisions is central to the analysis of congestion phenomena. The study of the day-to-day dynamics of this interaction in the field is hampered by the inability to obtain adequate data. This paper presents an experimental approach involving real commuters, whereby a traffic simulation model is used to predict congestion patterns under given departure distributions resulting from the actual decisions o[ the individual participants. These decisions are updated daily, in response to information on prior system performance predicted by the simulation model. The results of this experiment are described in this paper, with emphasis on the system's evolution and dynamic properties, particularly convergence. In addition, concentration and congestion patterns as well as the associated travel time variability are addressed. Initial insights into the processes underlying user behavior in this system are also presented. [ABSTRACT FROM AUTHOR]

One of the suggested techniques for reducing peak period traffic congestion is to flex work hours. If one is to predict the effect this work hour change shall have on the congestion, it is essential to understand how the peak traffic demand develops. However, there seem to be no existing theories explaining this process. In this paper, therefore, a mechanism by which commuters select their departure time from home is suggested and, based on this, a method is proposed for predicting the temporal distribution of traffic demand during the peak period. This should lead to the understanding of the effects of flexed work hours on the congestion. The model developed in this paper is based on the assumption that the commuters wish to arrive at work at a particular time without being delayed for too long in the system. A commuter therefore attaches cost to delays and also to early and late arrivals at work. This model proposes an iterative procedure by which to obtain the distribution of a commuter's departure time from home, assuming that he tries to minimize the total cost. [ABSTRACT FROM AUTHOR]

Paradoxes may occur when different traffic equilibrium models are applied starting from the same data. When in the traffic system "players" of different size are present, a Mixed Behavior Equilibrium can be stated. One should expect, by intuition, that total cost decreases with the reduction of noncooperative players on the network. This assumption does not hold in general. This paper provides numerical examples to show it The problem of investigating the relationship between different equilibrium models arises when one considers a strategy for rerouting vehicles in road networks, in order to reduce congestion Route Guidance Systems, for example). The importance of identifying paradoxical situations in such problems is briefly discussed. [ABSTRACT FROM AUTHOR]

The paper develops a dynamic model of peak period traffic congestion that considers a limited number of bottlenecks. The model predicts the temporal distribution of traffic volumes with an elastic demand model. In response to changes in the traffic conditions travelers can switch to a different mode, divert to an alternate route, or shift the trip forward or backward in time to avoid a long delay. A simple example would be the case of two parallel routes with travelers jointly selecting route and departure time. The choice of route and mode are dependent on travel times and travel costs. The choice of departure time is based on the trade-off between travel time and schedule delay which is the difference between the actual and the desired arrival times. The delays at the bottlenecks are modeled with a deterministic queueing model that determines waiting time as a function of the length of the queue at the time of arrival at the bottleneck. The day to day adjustment of the distribution of traffic is derived from a dynamic Markovian model The model is used to perform simulation experiments. The results demonstrate the response of the traffic conditions at the bottlenecks to a change in the system. The model is used to analyze the impacts of alternative pricing policies and preferential treatment of high occupancy vehicles. [ABSTRACT FROM AUTHOR]

In this paper, M/G/CIC state dependent queueing models are proposed for modeling and analyzing vehicular traffic flows. Congestion aspects of traffic flow are represented by introducing state dependent service rates as a function of number of vehicles on each road link. Analytical models for unidirectional and multisource flows are presented. Finally, queueing models to analytically determine the optimal capacity and performance measures of the road links are incorporated into a series of software programs available from the authors. [ABSTRACT FROM AUTHOR]

During the Moslem pilgrimage season the Jamarat bridge becomes congested with pilgrims, due to space and time constraints. This paper aims at developing a model for regulating pedestrian, flow into the bridge. The model may provide facility designers and managers with a quantitative tool for predicting the level of congestion at specific regions on the bridge given the specific demand flow data and a particular control strategy. Thus various alternatives for controlling the flow can be examined. The model is also a tool for determination of the optimal level of flow such that the number of persons in those specific regions does not exceed some predetermined limit. An optimization model is constructed and an example is included. [ABSTRACT FROM AUTHOR]

Motorists going through a bottleneck during the morning rush hour have to time their departure times to ensure they arrive to work at a reasonable time. Traffic and congestion levels at the bottleneck depend on the motorists' work schedule and the disutility of unpunctuality. This paper shows that, under certain conditions, there is only one equilibrium order of arrivals; an order under which motorists do not have an incentive to jockey for position in the queue. [ABSTRACT FROM AUTHOR]

The paper gives conditions which guarantee the existence of an equilibrium arrival pattern at a single bottleneck. In the model, the times at which a driver wishes to leave the bottleneck depend on the driver. The equilibrium queue length in this model always has a continuous time derivative everywhere. However, the slope of the equilibrium cumulative arrival distribution is discontinuous at the beginning and end of congestion. [ABSTRACT FROM AUTHOR]

In a noncongested transportation network where each user chooses his quickest route, the creation of an additional route between some origin-destination pair clearly cannot result in an increase in travel time to users traveling between that o-d pair. It seems reasonable to assume the same can be said of congested networks. In 1968, D. Braess presented a remarkable example demonstrating this is not the case: a new route can increase travel time for all. The present paper gives, under reasonable assumptions, necessary and sufficient conditions for "Braess' Paradox" to occur in a general transportation network. As a corollary, we obtain that Braess' Paradox is about as likely to occur as not occur. [ABSTRACT FROM AUTHOR]

The traffic assignment problem aims to calculate an equilibrium route flow vector, generally by seeking a zero of an appropriate objective function. If a continuous dynamical system follows a descent direction for this objective function at each nonequilibrium route flow vector, the system converges to equilibrium. It is shown that when this dynamical system is discretized with a fixed step length, the system eventually approaches close to equilibrium provided that the objective function is continuously differentiable and that the rate of descent is bounded below. The method of successive averages is widely used in traffic assignment; it has a decreasing step size at each iteration. With the same conditions as above, it is shown that the resulting dynamical system converges to equilibrium. In the steady-state model, the necessary conditions are shown to be satisfied, provided that the route cost vector is a continuously differentiable monotone function of the route flow vector. However, continuous differentiability of the cost function is shown not to hold in the dynamic queueing model. [ABSTRACT FROM AUTHOR]

We address the controversial issue of traffic flow modeling, whether first-order, second-order, or other traffic models are best supported by empirical facts and theoretical considerations. This is done by a critical discussion of the pros and cons of the different theoretical approaches and by the analysis of a large set of empirical data with new evaluation techniques. Specifically, we investigate characteristic properties of the congested traffic states on a 30-km-long stretch of the German freeway A5 near Frankfurt/Main. Among the approximately 245 breakdowns of traffic flow at several different bottlenecks in 165 days, we have identified five different kinds of spatiotemporal congestion patterns and their combinations. Based on an "adaptive smoothing method" for the visualization of detector data, we also discuss particular features of breakdowns, such as signs of unstable traffic flow and the "boomerang effect," which often seems to be caused by overtaking maneuvers of trucks. Controversial issues such as "synchronized flow" or stop-and-go waves are addressed as well. Our empirical results are compared with the implications of different theoretical concepts such as first-order traffic models and the phase diagram of congested traffic states predicted by some second-order models and the nonlocal, gas-kinetic based traffic model (GKT model). For a correct understanding of empirical observations such as the "general pattern," it is important to consider particularities such as the fact that off-ramps can act as bottlenecks, when activated by downstream on-ramp bottlenecks. As sequences of off- and on-ramps generate different congestion patterns than single on-ramps, they must be treated as interconnected bottlenecks. Furthermore, our empirical results question Kerner's three-phase theory. [ABSTRACT FROM AUTHOR]

A space-time network is developed that represents traffic flows over time for a capacitated road transportation system having one-way and two-way streets. Traffic signal lights are explicitly incorporated into the network structure so that total travel time is a piecewise linear convex function of the number of units traveling on the streets. Hence congestion effects are explicitly considered while maintaining the linear nature of the model. The first example presented has one source and one sink. There is a unimodal buildup of traffic at the source (say a factory) which enters the street network as quickly as its capacity permits and proceeds through the network, stopping at red lights when necessary, toward the sink (a residential area). Two efficient solution methods are used: a network flow solution suitable for a multiple-source single-destination network, and a shortest path solution suitable only for a single-source single-destination network. Computations show that the arrival rate has multiple peaks which are induced by the stop lights. The second example has multiple sources and one sink and gives similar results, except that the arrival rate has a single board peak which is due to the extreme symmetry of the constraints of the problem. [ABSTRACT FROM AUTHOR]