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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]

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]

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]

The contribution of the paper is a complete analysis of the sensitivity of elastic demand traffic (Wardrop) equilibria. The existence of a directional derivative of the equilibrium solution (link flow, least travel cost, demand) in any direction is given a characterization, and the same is done for its gradient. The gradient, if it exists, is further interpreted as a limiting case of the gradient of the logit-based SUE solution, as the dispersion parameter tends to infinity. In the absence of the gradient, we show how to compute a subgradient. All these computations (directional derivative, (sub) gradient) are performed by solving similar traffic equilibrium problems with affine link cost and demand functions, and they can be performed by the same tool as (or one similar to) the one used for the original traffic equilibrium model; this fact is of clear advantage when applying sensitivity analysis within a bilevel (or mathematical program with equilibrium constraints, MPEC) application, such as for congestion pricing, OD estimation, or network design. A small example illustrates the possible nonexistence of a gradient and the computation of a subgradient. [ABSTRACT FROM AUTHOR]

Recently, extensive studies have been conducted on the computational methods of sensitivity analysis for the Wardropian equilibrium modeling of traffic networks and their applications. But the same problems in the context of the stochastic user equilibrium modeling seem not to have been addressed. In this paper, we present a method for sensitivity analysis for network flows at stochastic user equilibrium. Our method is developed from a dual formulation of the stochastic user equilibrium analysis. By adopting Dial's algorithm for stochastic traffic assignment, we are able to formulate a computationally efficient link-based algorithm for the sensitivity analysis. Since the Wardropian equilibrium in a traffic network is an extreme case of stochastic user equilibrium with θ → ∞, θ being a dispersion parameter in the expected utility function for stochastic route choice, the method presented here can also be used for sensitivity analysis of the Wardropian equilibrium by setting θ large enough. [ABSTRACT FROM AUTHOR]

This paper contains a quantitative evaluation of probabilistic traffic assignment models and proposes an alternate formulation. First, the concept of stochastic-user-equilibration (S-U-E) is formalized as an extension of Wardrop's user-equilibration criterion. Then, the stochastic-network-loading (S-N-L) problem (a special case of S-U-E for networks with constant link costs) is analyzed in detail and an expression for the probability of route choice which is based on two general postulates of user behavior is derived. The paper also discusses the weaknesses of existing S-N-L techniques (with special attention paid to Dial's multipath method) and compares them to the suggested approach. The proposed model seems reasonable and does not exhibit the inherent weaknesses of the logit model when applied to sets of routes which overlap heavily. The discussion is supported by several numerical examples on small contrived networks. The paper concludes with the discussion of two techniques that can be used to approximate the link flows resulting from the proposed model in large networks. [ABSTRACT FROM AUTHOR]

A pavement deterioration model predicts the performance of a pavement over time as a function of traffic, pavement characteristics and environmental factors. The most important performance characteristics of a pavement are its ability to bear traffic loads and its ability to provide a smooth ride. However, there is no unambiguous approach to directly measure these performance characteristics. Therefore, we consider pavement performance to be unobservable. The problem of designing pavement deterioration models is the problem of defining the above unobservable characteristics in terms of what is observed, i.e., in terms of measured extents and severities of different damage components. The methodology presented in this paper describes a statistical technique to estimate latent pavement performance from observed pavement damage. No constraints are placed on the number or type of measurements required, so the methodology is flexible enough to include different measurement techniques and data collection strategies. The estimation procedure simultaneously fits a deterioration model and a performance index calibration model to data, thereby producing much better fits to data than traditional deterioration models. The methodology presented in this paper will be useful for deriving more realistic predictive models of pavement deterioration and for defining better data collection strategies. [ABSTRACT FROM AUTHOR]

This paper presents a theory of traffic equilibrium which involves responsive signal control policies; in this theory drivers' route choices and the control policy's choice of green times are treated in a symmetrical manner. The central theme of the paper is the iterative optimization assignment algorithm. This algorithm may be considered as a means of calculating equilibria which are consistent with a given responsive control policy. But it may also be regarded as a highly idealized model of the day to day dynamics of drivers' route choices when a responsive signal setting policy is employed; on "day" 1 the signals are held fixed and drivers settle down to an equilibrium flow pattern, on "day 2" the flow pattern is held fixed and the signals are updated according to the control policy for the fixed flow pattern, on "day" 3 the signals are held fixed and drivers settle down to an equilibrium flow pattern.... We state natural but strong conditions on the responsive control policy which guarantee that this algorithm is bound to converge to a convex set of (flow, control) pairs such that (i) the flow is a user equilibrium and (ii) the control parameters satisfy the responsive control policy; and we give a proof of convergence under these conditions--we do not seek to minimize total travel cost. Our conditions involve the delay or cost formula used; with the BPR cost formula, modified in a natural way to allow for green times, the traditional policy of choosing control parameters which minimize delay for the observed traffic pattern does satisfy these conditions in full. However, with Webster's delay formula traditional control policies are a long way... [ABSTRACT FROM AUTHOR]

The average time a driver has to wait before he can cross two major streams has been a major performance indicator for unsignalized intersections. The equations presented in this paper give an estimate of this average delay as a function of the average delay to isolated minor stream vehicles (Adams' delay) and the degree of saturation of the minor stream (minor stream entry flow/ maximum entry flow) and a form factor (which quantifies the effect of queueing in the minor stream). It was assumed that drivers were consistent and homogeneous and that headways in each major stream were independent of other headways in the same stream and in the other stream. Although the concepts were described in general terms, equations for the maximum minor stream entry flow and Adams' delay were developed assuming that the headways in the major stream to have a dichotomized distribution as given by R. J. Cowan in 1975. Tanner's equations can be used to calculate the form factor when there is a single major stream and when the minor stream headways are Poissonian. For other conditions, a computer simulation program was used to give estimates of the form factor which give satisfactory estimates of average delay for practical purposes. The discussion in this paper indicates that the degree of bunching in the major streams has a major effect of Adams' delay, average delay and the maximum minor stream entry flow. [ABSTRACT FROM AUTHOR]

This paper proposes different "dynamic" estimators using time-varying traffic counts to obtain (discrete) time-varying OD flows or average OD flows. All the estimators can combine counts with other available information, e.g., out-dated matrices and surveys, on a general network and can be formulated as optimization problems. In the case of time-varying OD flows, two types of estimators are proposed. Simultaneous estimators produce joint estimates of the whole set of OD matrices, one for each time slice, whereas sequential estimators produce a sequence of OD estimates for successive time slices. A particular type of simultaneous and sequential estimator (namely Generalized Least Squares) was tested on the Italian Brescia-Padua motorway for which "true" OD flows over a whole day were available. Results were generally satisfactory, showing that also in the "no a priori information" case significant estimates could be obtained. [ABSTRACT FROM AUTHOR]

In this paper a restriction (simplicial decomposition) strategy is employed to efficiently implement a modified Newton method to solve the general asymmetric network equilibrium problem. Implementation details are discussed. Numerical results on one small-scale and one medium-scale problem, with varying asymmetry levels, are presented. Performance o[ the algorithms with respect to the asymmetry level of the cost mapping is assessed. [ABSTRACT FROM AUTHOR]

In this paper, a model is described that will under certain circumstances yield the most likely origin-destination matrix which is consistent with measurements of link traffic volumes. Given knowledge of the proportionate usage of each link by the traffic between each zone pair, the model parameters scale each element of a prior estimate of the origin-destination matrix up or down so that the measurements of link traffic volumes are reproduced. The fitted values are shown by example to be invariant to the application of uniform scaling to the prior estimates. A Newton model fitting procedure is out- lined. In reality, measurements of link traffic volumes are random variables and the proportionate usage of links by the traffic for each zone pair is not known with certainty. An expression is derived for the variances and covariances of the logarithms of the fitted values in terms of the variances and covariances of the measured link volumes, taking the proportionate usage of links as given. The expression permits the calculation of asymmetric confidence intervals for the elements of the fitted origin-destination matrix. [ABSTRACT FROM AUTHOR]

Existing methods of estimating section (link) density on freeways from data provided by electronic presence (loop) detectors typically require extensive knowledge or strong assumptions on prevailing flow conditions, such as homogeneity. Consequently, these methods are known to produce poor estimates in inhomogeneous conditions, or when a priori knowledge of traffic conditions is not available. In this paper, a new data processing approach is presented which estimates density well over a wide range of traffic conditions. It does this by detecting spatially inhomogeneous traffic conditions and compensating the density estimation algorithm appropriately. The data processing algorithm is computationally simple, is not flow-level dependent, does not require any a priori knowledge of traffic conditions on the road and is insensitive to the types of uncertainty found in detector data. The algorithm uses both flow and occupancy data from adjacent detector stations to track the density on a link. A scalar Kalman filter formulation is used to provide the desired density estimate. The simplicity of the filter algorithm is achieved by using a scalar Generalized Likelihood Ratio (GLR) event detection algorithm to compensate the filter for spatially inhomogeneous conditions. Performance of the algorithm is demonstrated with a microscopic freeway simulation. [ABSTRACT FROM AUTHOR]

The movement of traffic past a point is compared to the output of a queuing system having random input. A generalization of the queue output model leads to a suitable headway model: this model is a mixture of two distributions, representing following and nonfollowing headways, in appropriate proportions. This model is compared with, several others that have been suggested; when used with a lognormal distribution of following headways, it gives the best overall fit to data from the M4 motorway, England, and two-way roads in Indiana, USA. For each site, the parameters of the following headway distribution can be assumed constant. The mean following headways are 1.3 sec and 1.6 sec for the M4 fast and slow lanes respectively, and 2 sec for the Indiana sites. The standard deviation of logarithms of following headways is 0.4 for both M4 lanes and 0.45 for the Indiana sites. For most samples, the reciprocal of the mean interbunch gap λ can be approximated by λ = λ* - ½λ*&frac32;, where λ* is the flow rate, and the proportion of the following vehicles ψ can be approximated by ψ = ρ -- ½ (ρ- 1) λ*&frac32;, where ρ is the traffic intensity. [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]

The modeling of traffic control systems for solving such problems as surface street signalization, dynamic traffic assignment, etc., typically results in the appearance of a conditional function. For example, the consistent representation of the outflow discharge at an approach of a signalized intersection implies a function that is conditional on the signal indication and the prevailing traffic conditions. Representing such functions by some sort of constraint(s), ideally linear, so as to be considered in the context of a mathematical programming problem, is a nontrivial task, most often resolved by adopting restrictive assumptions regarding real-life process behavior. To address this general problem, we develop two methodologies that are largely based on analogies from mathematical logic that provide a practical device for the transformation of a specific form of a linear conditional piecewise function into a mixed integer model (MIM), i.e., a set of mixed-integer linear inequality constraints. We show the applicability of these methodologies to transforming into a MIM virtually every possible conditional piecewise function that can be found when one is modeling transportation systems based on the widely adopted dispersion-and-store and cell transmission traffic flow models, as well as to analyzing existing MIMs for identifying and eliminating redundancies. [ABSTRACT FROM AUTHOR]

We present and analyse a model of the combined choice of departure time and route in a congested road network. Using the property of equilibrium solutions that for each origin-destination pair the total cost associated with travel is identical for all travellers, we establish a general result that elates assignments to various components of cost. The analysis is developed to include time-varying tolls and to establish a formula that will induce any specified in flow profile as an equilibrium. We introduce an iteration operator to calculate equilibrium in flow profiles, and present the results of example calculations for a range of test problems. [ABSTRACT FROM AUTHOR]

The multiclass network equilibrium problem is expressed in general as a nonmonotone, asymmetric, variational inequality problem. We show that in spite of the nonmonotonicity of the cost operator, the problem may actually satisfy a weaker property, induced by the hierarchical nature of the travel cost interactions. This property allows a natural decomposition approach, not otherwise available, that admits provably convergent algorithms. We present one such algorithm, easily implementable using a solver for the single-class network equilibrium problem, together with a convergence proof. [ABSTRACT FROM AUTHOR]

An interactive computer-based model is described which permits a reasonable assessment of the decrease in the number of vehicle miles driven when one or several lanes of a freeway are devoted to the exclusive use of "carpools": vehicles carrying at least a specified number of people. The vehicle miles driven are obtained by finding the equilibrium distribution of pool sizes as a function of distance driven, on both regular and priority lanes. A simple but believable economic model incorporating the cost of time and the "utility" of having a vehicle for one's exclusive use is the basis for determining what individuals will do in their self-interest. The economic model is partly verified using existing pooling data without priority lanes. The idea of the priority lane or lanes is, of course, that they move faster than the regular lanes. However, an attractive feature of the priority lane concept is that, in typical cases, traffic flow is actually improved even for those who choose not to pool. Simple runs of the model show that in some cases it can be better for all concerned if two lanes are reserved for carpools rather than one lane, and if vehicles with two occupants are allowed to use the priority lanes rather than requiring three occupants. A 12.5-mi stretch of the Santa Monica Freeway in the Los Angeles area is used as a computational example for the theory. Further refinements to the model are suggested. [ABSTRACT FROM AUTHOR]

Flows of convoy-type traffic through networks whose arcs are characterized by both travel times and flowrate constraints are investigated. Suggested here, in particular, is the notion of a 'flowrate-constrained fastest path'- a path by means of which the entirety of a volume of traffic, initially located at a source node, can arrive at a sink in as short a time as possible when all traffic must flow along the same path and rates of flow along arcs are limited by flowrate constraints. Unlike the usual fastest path problems (those in networks without flowrate constraints), flowrate-constrained fastest times and paths both depend, in general, upon the initial volume of traffic at the source node. Several theorems about flowrate-constrained fastest times and paths are stated and proved; it is shown, for example, that such paths are independent of source volume whenever this volume is sufficiently large. Two algorithms for finding flowrate-constrained fastest tunes and paths are given. [ABSTRACT FROM AUTHOR]