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This paper develops a continuous approximation model for analyzing the spatial distribution of traffic flow in the presence of a barrier to travel. The traffic flow density is derived for a rectangular city with a grid road network and a rectangular barrier. The traffic flow density describes traffic flow as a function of position and provides a fundamental understanding of the effect of the barrier. The analytical expression for the traffic flow density demonstrates how the location and shape of the barrier affect the spatial distribution of traffic flow. The effect of the shape of the city is also examined. The model is useful for transportation and logistics problems with barriers. [ABSTRACT FROM AUTHOR]

We study a double-ended queue consisting of two classes of customers. Whenever there is a pair of customers from both classes, they are matched and leave the system. The matching is instantaneous following the first-come-first-match principle. If a customer cannot be matched immediately, he/she will stay in a queue. We also assume customers are impatient with generally distributed patience times. Under suitable heavy traffic conditions, we establish simple linear asymptotic relationships between the diffusion-scaled queue length process and the diffusion-scaled offered waiting time processes and show that the diffusion-scaled queue length process converges weakly to a diffusion process that admits a unique stationary distribution. [ABSTRACT FROM AUTHOR]

Arrival processes to service systems often display fluctuations that are larger than anticipated under the Poisson assumption, a phenomenon that is referred to as overdispersion. Motivated by this, we analyze a class of discrete-time stochastic models for which we derive heavy-traffic approximations that are scalable in the system size. Subsequently, we show how this leads to novel capacity sizing rules that acknowledge the presence of overdispersion. This, in turn, leads to robust approximations for performance characteristics of systems that are of moderate size and/or may not operate in heavy traffic. [ABSTRACT FROM AUTHOR]

Highlights • We propose a lane choice model that tractably evaluates the utility across all routes. • We solve the dynamic pricing problem using the value function approximation method. • The proposed algorithm outperforms heuristics based on feedback control. Abstract Priced managed lanes are increasingly being used to better utilize the existing capacity of the roadway to relieve congestion and offer reliable travel time to road users. In this paper, we investigate the optimization problem for pricing managed lanes with multiple entrances and exits which seeks to maximize the revenue and minimize the total system travel time (TSTT) over a finite horizon. We propose a lane choice model where travelers make online decisions at each diverge point considering all routes on a managed lane network. We formulate the problem as a deterministic Markov decision process and solve it using the value function approximation (VFA) method for different initializations. We compare the performance of the toll policies predicted by the VFA method against the myopic revenue policy which maximizes the revenue only at the current timestep and two heuristic policies based on the measured densities on the managed and general purpose lanes (GPLs). We test the results on four different test networks. The primary findings from our research suggest the usefulness of the VFA method for determining dynamic tolls. The best-found objective value from the method at its termination is better than other heuristics for all test networks with average improvements in the objective ranging between 10% and 90% for revenue maximization and 0–27% for TSTT minimization. Certain VFA initializations obtain best-found toll profiles within first 5–50 iterations which warrants computational time savings. Our findings also indicate that the revenue-maximizing optimal policies follow the "jam-and-harvest" behavior where the GPLs are pushed towards congestion in the earlier time steps to generate higher revenue in the later time steps, a characteristic not observed for the policies minimizing TSTT. [ABSTRACT FROM AUTHOR]

Abstract This paper investigates the dynamic user equilibrium (DUE) on a single origin-destination pair with two alternative routes, a freeway with a fixed capacity and the surrounding city-streets network, modeled with a network macroscopic fundamental diagram (NMFD). We find using suitable transformations that only a single network parameter is required to characterize the DUE solution, the freeway to NMFD capacity ratio. We also show that the stability and convergence properties of this system are captured by the constant demand case, which corresponds to an autonomous dynamical system that admits analytical solutions. This solution is characterized by two critical accumulation values that determine if the steady state is in free-flow or gridlock, depending on the initial accumulation. Additionally, we also propose a continuum approximation to account for the spatial evolution of congestion, by including variable trip length and variable NMFD coverage area in the model. It is found that gridlock cannot happen and that the steady-state solution is independent of surface network parameters. These parameters do affect the rate of convergence to the steady-state solution, but convergence rates appear virtually identical when time is expressed in units of the NMFD free-flow travel time. [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]

We present a novel data-driven approach to populate virtual road networks with realistic traffic flows. Specifically, given a limited set of vehicle trajectories as the input samples, our approach first synthesizes a large set of vehicle trajectories. By taking the spatio-temporal information of traffic flows as a 2D texture, the generation of new traffic flows can be formulated as a texture synthesis process, which is solved by minimizing a newly developed traffic texture energy. The synthesized output captures the spatio-temporal dynamics of the input traffic flows, and the vehicle interactions in it strictly follow traffic rules. After that, we position the synthesized vehicle trajectory data to virtual road networks using a cage-based registration scheme, where a few traffic-specific constraints are enforced to maintain each vehicle's original spatial location and synchronize its motion in concert with its neighboring vehicles. Our approach is intuitive to control and scalable to the complexity of virtual road networks. We validated our approach through many experiments and paired comparison user studies. [ABSTRACT FROM AUTHOR]

This paper presents an innovative design method for determining lateral clearance needs on a spiraled horizontal curve to satisfy sight distance requirements. The roadside lateral clearance is represented by a spiraled horizontal curve that is easy to implement in practice. The design parameters were determined. The characteristics of the corresponding lateral offsets were explored for the influential roadway factors, including required sight distance or design speed, curve radius, curve length, spiral curve length, and station location expressed in fraction of sight distance. The results show that ratio of spiral curve length to required sight distance is the major factor that affects the ratio of the lateral offset to the maximum offset at a circular curve. A single design chart and a design table also are provided as alternative design tools to determine the offset for a specific obstruction location. The proposed design method not only greatly improves the AASHTO approximate approach, but also provides an alternative approach to improving design consistency on horizontal alignments. This paper complements another paper on lateral clearance needs for simple horizontal curves. DOI: 10.1061/JTEPBS.0000046. [ABSTRACT FROM AUTHOR]

We consider the problem of estimating the parameters of a linear univariate autoregressive (AR) model with sub-Gaussian innovations from a limited sequence of consecutive observations. Assuming that the parameters are compressible, we analyze the performance of the $\ell _1$ -regularized least squares as well as a greedy estimator of the parameters and characterize the sampling tradeoffs required for stable recovery in the nonasymptotic regime. In particular, we show that for a fixed sparsity level, stable recovery of AR parameters is possible when the number of samples scale sublinearly with the AR order. Our results improve over existing sampling complexity requirements in AR estimation using the Lasso, when the sparsity level scales faster than the square root of the model order. We further derive sufficient conditions on the sparsity level that guarantee the minimax optimality of the $\ell _1$-regularized least squares estimate. Applying these techniques to simulated data as well as real-world datasets from crude oil prices and traffic speed data confirm our predicted theoretical performance gains in terms of estimation accuracy and model selection. [ABSTRACT FROM PUBLISHER]

Link traffic flow models are widely used in networking loading model studies. A section based method is developed for supporting analysis of link flows with kinematic waves. We consider the shock surface between free traffic and congested traffic, divide the link into two dynamic sections with different traffic states and present a section based link flow model (STM) to simulate the link flow in traffic network. The computing performance of STM is evaluated and the quality of the presented approximation procedure is tested against the results of the cell transmission model and link transmission model. The results show that the STM presented in this paper yields better approximations of analytical results compared to cell transmission model and can capture the queue propagation without extra model improvement compared to link transmission model. [ABSTRACT FROM AUTHOR]

This paper is motivated by recent results in the design of signal plans for Manhattan that highlight the importance of providing signal control algorithms with an analytical description of between-link dependencies. This is particularly important for congested networks prone to the occurrence of spillbacks. This paper formulates a probabilistic network model that proposes an aggregate description of the queue-length, and then approximates the joint aggregate queue-length distribution of subnetworks. The goal is to model between-queue dependencies beyond first-order moments, yet to do so in a tractable manner such that these techniques can be used for optimization purposes. This paper models an urban road network as a finite space capacity Markovian queueing network. Exact evaluation of the stationary joint queue-length distribution of such a network with arbitrary size and topology can be obtained numerically. Nonetheless, the main challenge to such an approach remains the dimensionality of the network state space, which is exponential in the number of queues. This paper proposes to address the dimensionality issue by: 1) describing the state of the network aggregately, and 2) decomposing the network into overlapping subnetworks. We propose an analytical approximation of the stationary aggregate joint queue-length distribution of a subnetwork. The model consists of a system of nonlinear equations with a dimension that is linear, instead of exponential, in the number of queues and that is independent of the space capacity of the individual queues. The method is derived for tandem Markovian finite capacity queueing networks. The proposed model is computationally tractable and scalable, it can be efficiently used for the higher-order distributional analysis of large-scale networks. The model is validated versus simulation estimates and versus other decomposition methods. We then use it to address an urban traffic control problem. We show the added value of accounting for higher-order spatial between-queue dependency information in the control of congested urban networks. [ABSTRACT FROM AUTHOR]

Compared with path-based day-to-day (DTD) traffic evolution models, link-based DTD traffic evolution models are easier to calibrate and validate. However, the inherent network loading sub-problem in link-based DTD models induces high computational burden which precludes their broad practical applicability. To address this challenge, this study proposes three approximation models for the DTD traffic flow evolution process based on the sensitivity analysis of the network loading sub-problem in a link-based DTD model. In particular, a first-order approximation (FOA) model is formulated based on the derivative of link flow solutions with respect to perturbations on network characteristics. To improve the approximation accuracy of the FOA model, a second-order approximation (SOA) model and a variable reduced approximation (VRA) model are developed. The applicability conditions of the proposed approximation models are derived. A small numerical example demonstrates that the FOA model performs well when perturbations are small and the approximation accuracy reduces as the scale of perturbations increases. The SOA and VRA models can improve the approximation accuracy of the FOA model, at the cost of computing the second-order derivative and the reference link flow pattern, respectively. [ABSTRACT FROM AUTHOR]

The Totally Asymmetric Simple Exclusion Process (TASEP) is studied on open long chains with a shunted section between two simple chain segments in the maximum current phase. The reference case, when the two branches are chosen with equal probability, is considered. The conditions for the occurrence of traffic jams and their properties are investigated both within the effective rates approximation and by extensive Monte Carlo simulations for arbitrary length of the shortcut. Our main results are: (1) For any length of the shortcut and any values of the external rates in the domain of the maximum current phase, there exists a position of the shortcut where the shunted segment is in a phase of coexistence with a completely delocalized domain wall; (2) The main features of the coexistence phase and the density profiles in the whole network are well described by the domain wall theory. Apart from the small inter-chain correlations, they depend only on the current through the shortcut; (3) The model displays unexpected features: (a) the current through the longer shunted segment is larger than the current through the shortcut, and (b) the delocalized domain wall in the coexistence phase of the long shunted segment induces similar behavior even in shortcuts containing a small number of sites; (4) From the viewpoint of vehicular traffic, most comfortable conditions for the drivers are provided when the shortcut is shifted downstream from the position of coexistence, when both the shunted segment and the shortcut exhibit low-density lamellar flow. Most unfavorable is the opposite case of upstream shifted shortcut, when both the shunted segment and the shortcut are in a high-density phase describing congested traffic of slowly moving cars. The above results are relevant also to phenomena like crowding of molecular motors moving along twisted protofilaments. [ABSTRACT FROM AUTHOR]

This paper presents two modeling approaches for median-type facility location design under elastic customer demand and traffic equilibrium in a continuous space. The first approach, following the continuum approximation scheme, builds upon the special case of an infinite homogeneous plane where traffic equilibrium can be described by an ordinary differential equation. The solution to this homogeneous case, sometimes in a closed form, is then used to develop approximate solutions to more general cases (e.g., those in a heterogeneous space). This model provides a computationally efficient way to obtain managerial insights and near-optimal solutions, especially for large problem instances. We also develop a more traditional discrete location model in the form of a mixed-integer program, which builds directly upon a nonlinear partial differential equation description of customer traffic equilibrium. We develop a Lagrangian relaxation based solution approach with an embedded finite-element method subroutine, to separate and solve the location decisions as well as the traffic equilibrium. Numerical experiments are conducted to illustrate applicability of the proposed models and to compare performance of the two complementing modeling approaches. [ABSTRACT FROM AUTHOR]

This paper investigates at an aggregated (macroscopic) scale the effects of route patterns on a road network. Four main variables are considered: the production, the mean speed, the outflow and the mean travel distance. First, a simple network with heterogeneous travel distances between origins and destinations is studied by simulation. It appears that the mean travel distance is not only very sensitive to the changes in the origin–destination (OD) matrix but also to the internal traffic conditions within the network. When this distance is assumed constant as usual in the literature, significant errors may appear when estimating the outflow at the network perimeter. The OD matrix also modifies the shape of the macroscopic fundamental diagram (MFD) to a lesser extend. Second, a new modeling framework is proposed to account for multiple macroscopic routes within reservoirs (spatial aggregates of road network) in the context of MFD simulation. In contrast to existing works, partial accumulations are defined per route and traffic waves are tracked at this level. This leads to a better representation of wave propagation between the reservoir frontiers. A Godunov scheme is combined to a HLL Riemann approximate solver in order to derive the model numerical solutions. The accuracy of the resulting scheme is assessed for several simple cases. The new framework is similar to some multiclass models that have been elaborated in the context of link traffic dynamics. [ABSTRACT FROM AUTHOR]

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

This article examines the application of a path-based algorithm to the static and fixed demand asymmetric traffic assignment problem. The algorithm is of the simplicial decomposition type and it solves the equilibration or master problem step by means of five existing projection methods for variational inequality problems to evaluate their performance on real traffic networks. The projection methods evaluated are: (1) a cost approximation-based method for minimizing the Fukushima's gap function, (2) the modified descent method of Zhu and Marcotte (), (3) the double projection method of Khobotov () and three of its recently developed variants (Nadezhkina and Takahashi, ; Wang et al., ; and He et al., 2012); (4) the method of Solodov and Svaiter (); and (5) the method of Solodov and Tseng (). These projection methods do not require evaluation of the Jacobians of the path cost functions. The source for asymmetries are link costs with interactions, as in the case of priority ruled junctions. The path-based algorithm has been computationally tested using the previous projection methods on three medium to large networks under different levels of congestion and the computational results are presented and discussed. Comparisons are also made with the basic projection algorithm for the fixed demand asymmetric traffic assignment problem. Despite the lack of monotonicity properties of the test problems, the only method that failed to converge under heavy congestion levels was the basic projection algorithm. The fastest convergence was obtained in all cases solving the master problem step using the method of He et al. (2012), which is a variant of Khobotov's method. [ABSTRACT FROM AUTHOR]

This paper derives a five-parameter social force car-following model that converges to the kinematic wave model with triangular fundamental diagram. Analytical solutions for vehicle trajectories are found for the lead-vehicle problem, which exhibit clockwise and counter-clockwise hysteresis depending on the model’s parameters and the lead vehicle trajectory. When coupled with a stochastic vehicle dynamics module, the model is able to reproduce periods and amplitudes of stop-and-go waves, as reported in the field. The model’s stability conditions are analysed and its trajectories are compared to real data. [ABSTRACT FROM AUTHOR]

Real-time coordinated traffic management strategies that benefit from parsimonious models with aggregated network dynamics, provide a new generation of smart hierarchical strategies to improve network capacity and performance. However, this raises the question of route choice behavior in case of heterogeneous urban networks, where different parts of the city are subject to different types of control. Traffic equilibrium phenomena have not been thoroughly investigated in these models. Approximate traffic equilibrium conditions can be integrated within the parsimonious traffic models to develop regional routing strategies, while detailed route choice strategies can be incorporated at a later stage in a hierarchical framework. In this study, we develop an aggregated and approximate dynamic traffic assignment (DTA) procedure to be incorporated in the macroscopic fundamental diagram (MFD) dynamics, and establish dynamic stochastic user equilibrium (DSUE) conditions. The methodology consists of two main components; stochastic network loading and a fixed-point solution method. Loading procedure is designed to handle stochastic components in the model such as trip length uncertainty, variation of speeds across the links, perception error of travelers. The results taken from this procedure are averaged through the well-known method of successive averages (MSA) to reach fixed-point solution for the system. Real-time route guidance strategies can be revisited towards a “system of systems” approach. [ABSTRACT FROM AUTHOR]

Over the past few years, much attention has been paid to computing flows for multi-class network equilibrium models that exhibit uniqueness of the class flows and proportionality (Bar-Gera et al., 2012). Several new algorithms have been developed such as bush based methods of Bar-Gera (2002), Dial (2006), and Gentile (2012) that are able to obtain very fine solutions of network equilibrium models. These solutions can be post processed (Bar-Gera, 2006) in order to ensure proportionality and class uniqueness of the flows. Recently developed, the TAPAS, algorithm (Bar Gera, 2010) is able to produce solutions that have proportionality embedded, without requiring post processing. It was generally accepted that these methods for solving UE traffic assignment are the only way to obtain unique path and class link flows. The purpose of this paper is to show that the linear approximation method and some of its variants satisfy these conditions as well. In addition, some analytical results regarding the relation between steps of the linear approximation algorithm and the path flows entropy are presented. [ABSTRACT FROM AUTHOR]

The California Complete Streets Act of 2008 requires local governments to update general plans so that new construction or modification of roadways considers all transportation modes, which include but are not limited to walking, cycling, and driving. This work evaluates the effect of a complete street retrofit on Ocean Park Boulevard (hereafter referred to as “the retrofit”) in Santa Monica, California, in terms of the street use by different transportation modes and corresponding ultrafine particle (UFP) and fine particle (PM 2.5 ) concentrations. After subtracting background concentrations, UFP decreased after the retrofit by 4200 particles cm −3 while PM 2.5 had no statistically significant change. The emission-weighted traffic volume, an index used to account for flows of vehicles with different pollutant-emitting capacities, decreased 26%, which may explain why UFP reductions were observed while total traffic flow remained the same. The number of pedestrians increased by 37% compared to pre-retrofit conditions and the number of cyclists remained approximately the same. Although no causality could be reached, this study observed improved air quality on street after retrofit. Nonetheless, a full evaluation of the health impacts of the retrofit requires further information about how travel behavior, not just traffic, has changed. [ABSTRACT FROM AUTHOR]

In this paper, we analyze the end-to-end delay performance of a tandem queueing system with mobile queues. Due to state-space explosion, there is no hope for a numerical exact analysis for the joint-queue-length distribution. For this reason, we present an analytical approximation that is based on queue-length analysis. Through extensive numerical validation, we find that the queue-length approximation exhibits excellent performance for light traffic load. [ABSTRACT FROM PUBLISHER]

Highlights: [•] A common numerical framework for second-order traffic flow models is presented. [•] The ow models are written in conservation or balance law form. [•] The relaxation approximation transforms the nonlinear systems to semi-linear ones. [•] High-resolution finite volume discretizations (in space and time) are utilized. [Copyright &y& Elsevier]

In a traffic-aware route search (TARS), the user provides start and target locations and sets of search terms. The goal is to find the fastest route from the start location to the target via geographic entities (points of interest) that correspond to the search terms, while taking into account variations in the travel speed due to changes in traffic conditions, and the possibility that some visited entities will not satisfy the search requirements. A TARS query may include temporal constraints and order constraints that restrict the order by which entities are visited. Since TARS generalizes the Traveling-Salesperson Problem, it is an NP-hard problem. Thus, it is unlikely to find a polynomial-time algorithm for evaluating TARS queries. Hence, we present in this paper three heuristics to answer TARS queries-a local greedy approach, a global greedy approach and an algorithm that computes a linear approximation to the travel speeds, formulates the problem as a Mixed Integer Linear Programming (MILP) problem and uses a solver to find a solution. We provide an experimental evaluation based on actual traffic data and show that using a MILP solver to find a solution is effective and can be done within a limited running time in many real-life scenarios. The local-greedy approach is the least effective in finding a fast route, however, it has the best running time and it is the most scalable. [ABSTRACT FROM AUTHOR]

Highlights: [•] The on-and-off (OAO) signal model and its continuum approximation are compared. [•] The continuum signal model has a number of computational and modeling advantages. [•] Convergence of the OAO model to the continuum model with diminishing signal cycle is analyzed. [•] Approximation errors of the continuum model are given for non-infinitesimal signal cycles. [•] These results depend on the presence of queue spillback and the fundamental diagram assumed. [Copyright &y& Elsevier]

Highlights: [•] Develop a sampling-based method to characterize temporal and spatial correlation structure in path finding problem. [•] Propose a Lagrangian substitution approach to handle non-anticipativity constraint associated with a priori path. [•] Develop solution algorithms to improve solution quality and find approximate optimal solutions. [ABSTRACT FROM AUTHOR]

Highlights: [•] We use geographically weighted regression to estimate speed correlations across links. [•] We combine continuous speed measurements and GPS data. [•] RP data are drawn from a real-life peak-avoidance experiment. [•] We estimate departure time choice models using door-to-door travel times. [•] The value of time may be biased if imprecise measures of travel time are used. [ABSTRACT FROM AUTHOR]

Highlights: [•] A route guidance strategy based on determination of traffic conditions. [•] Taking easily obtained inflow and outflow of a link and road capacity as input. [•] Being capable of providing stable splitting rates. [•] Being capable of approximating user optimal equilibrium in different conditions. [Copyright &y& Elsevier]

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

Abstract: We present a traffic model that extends the linear car-following model as well as the min-plus traffic model (a model based on the min-plus algebra). A discrete-time car-dynamics describing the traffic on a 1-lane road without passing is interpreted as a dynamic programming equation of a stochastic optimal control problem of a Markov chain. This variational formulation permits to characterize the stability of the car-dynamics and to determine the stationary regimes when they exist. The model is based on a piecewise linear approximation of the fundamental traffic diagram. [Copyright &y& Elsevier]

Abstract: The multiobjective shortest path problem arises in many transportation and logistics applications, either as a stand-alone network routing problem or a subroutine of a more complex multiobjective network optimization problem. It has been addressed by different solution strategies, including labeling methods, ranking methods, constraint methods, and parametric methods. Increasing attention has been paid to parametric methods in recent years, partially because of its simple algorithmic logic and its flexibility of being used in different user-preference decision-making environments. The core idea of a parametric algorithm is scalarization, by which a multiobjective shortest path problem can be tackled by repeatedly solving a single-objective subproblem. However, existing parametric algorithms suffer two notorious deficiencies, which considerably limit its further applications: first, typical subroutines for the single-objective subproblem in general cannot capture nonextreme Pareto-optimal paths; second, parametric algorithms for biobjective problems cannot be directly extended to solving multiobjective problems. This paper provides some algorithmic improvements that can partially overcome these deficiencies. In particular, the contribution of this work is twofold: first, in the biobjective parametric solution framework, we propose an approximate label-setting algorithm for the parameterized, constrained single-objective subproblem, which is capable of identifying all extreme paths and a large percentage (i.e., 85–100%) of nonextreme paths; second, we suggest a general projection scheme that can decompose a multiobjective problem into a number of biobjective problems. The approximate parametric algorithm runs in polynomial time. The algorithmic design and solution performance of the algorithm for multiobjective shortest path problems are illustrated, and numerically evaluated and compared with a benchmark algorithm in terms of solution completeness and efficiency. [Copyright &y& Elsevier]

Abstract: This paper studies a multiple-server queueing model under the assumptions of renewal arrival processes and limited buffer size. An approximation for the loss probability and the asymptotic behavior are studied under the heavy traffic conditions. We present an asymptotic analysis of the loss probability when both the arrival rate and number of servers approach infinity. In illustrative examples, the loss probabilities are estimated with heavy traffic under three common distributions of inter-arrival times: exponential, deterministic and Erlang-r distributions, respectively. [Copyright &y& Elsevier]

Sensor systems as critical components of a transportation network provide a variety of real-time traffic surveillance information for traffic management and control. The deployment of sensors significantly affects their overall surveillance effectiveness. This paper proposes a reliable sensor location model to optimize surveillance effectiveness when sensors are subject to site-dependent probabilistic failures, and a general effectiveness measure is proposed to encompass most existing measures needed for engineering practice (e.g., flow volume coverage, vehicle-mile coverage, and squared error reduction). The problem is first formulated into a compact mixed-integer program, and we develop a variety of solution algorithms (including a custom-designed Lagrangian relaxation algorithm) and analyze their properties. We also propose alternative formulations including a continuum approximation model for single corridor problems and reliable fixed-charge sensor location models. Numerical case studies are conducted to test the performance of the proposed algorithms and draw managerial insights on how different parameter settings (e.g., failure probability and spatial heterogeneity) affect overall surveillance effectiveness and the optimal sensor deployment. [ABSTRACT FROM AUTHOR]

Abstract: The knowledge of path marginal cost (PMC) is central to system-optimal dynamic traffic assignment (SO-DTA) problems. In this paper, we propose a method to approximate PMC in general networks when traffic dynamics are modeled by either the point-queue or the kinematic wave traffic flow model. This study examines in detail the flow interactions between downstream and upstream bottleneck links, and shows that the changes in cumulative flows on all the network links caused by an arbitrary flow perturbation can be computed. This offers a way to approximate PMC, which is incorporated in the solution of the least marginal cost problem, a central component of the path-based SO-DTA problem. The approximation scheme allows us to solve path-based SO-DTA problems for general networks with and without queue spillback and/or departure time choices. Numerical examples are provided to demonstrate the effectiveness of the proposed method, and the results show that the SO state produces considerably lower total network cost, shorter congestion duration, and smaller travel delay on bottleneck links than those of produced by the user-optimal state, particularly when the departure time choice is considered. [Copyright &y& Elsevier]

In this paper, we study a traffic intersection with vehicle-actuated traffic signal control. Traffic lights stay green until all lanes within a group are emptied. Assuming general renewal arrival processes, we derive exact limiting distributions of the delays under heavy traffic (HT) conditions. Furthermore, we derive the light traffic (LT) limit of the mean delays for intersections with Poisson arrivals, and develop a heuristic adaptation of this limit to capture the LT behavior for other interarrival-time distributions. We combine the LT and HT results to develop closed-form approximations for the mean delays of vehicles in each lane. These closed-form approximations are quite accurate, very insightful, and simple to implement. [ABSTRACT FROM AUTHOR]

Abstract: The noise generation parameter for an individual road vehicle is introduced. It can be determined from the measurement of the pass-by maximum level. Along with the traffic flow and vehicle speed, it can be used for approximation of the long term A-weighted time average sound level. [Copyright &y& Elsevier]

Abstract: Railway conflict detection and resolution is the daily task faced by dispatchers and consists of adjusting train schedules whenever disturbances make the timetable infeasible. The main objective pursued by dispatchers in this task is the minimization of train delays, while train operating companies are also interested in other indicators of passenger dissatisfaction. The two objectives are conflicting whenever train delay reduction requires cancellation of some connected services, causing extra waiting times to transferring passengers. In fact, the infrastructure company and the train operating companies discuss on which connection to keep or drop in order to reach a compromise solution. This paper considers the bi-objective problem of minimizing train delays and missed connections in order to provide a set of feasible non-dominated schedules to support this decisional process. We use a detailed alternative graph model to ensure schedule feasibility and develop two heuristic algorithms to compute the Pareto front of non-dominated schedules. Our computational study, based on a complex and densely occupied Dutch railway network, shows that good coordination of connected train services is important to achieve real-time efficiency of railway services since the management of connections may heavily affect train punctuality. The two algorithms approximate accurately the Pareto front in a limited computation time. [Copyright &y& Elsevier]

Abstract: This letter conducts the outage analysis for an amplify-and-forward (AF) based two-way relaying by jointly considering outage events at the two senders with asymmetric traffics. Unlike the current research activities, our goal is to explore the impact of traffic asymmetry on the system outage probability. We first derive the exact expressions of outage probability for the AF scenario over Rayleigh fading channels. To gain more insight, approximated expressions are developed at high signal-to-noise ratio (SNR) region. After that we interestingly find that the asymmetry of system traffics has significant impact on the system outage probability and the outage probability in the system is determined only by the one-way channel or related simultaneously to the two-way links, depending on the level of asymmetry between the two senders’ information rates. Simulation experiments are done. The simulation results verify our propositions and validate the accuracy of our derived expressions. [Copyright &y& Elsevier]

Abstract: The paper presents an idealised dynamical model of day-to-day or within-day re-routeing using splitting rates at nodes, or node-exit flows, rather than route-flows. It is shown that under certain conditions the dynamical model gives rise to a sequence of link flow vectors which converges to a set of approximate Wardrop equilibria. A special dynamical signal green-time re-allocation model is added; the combination is also shown (in outline) to converge to the set of approximate consistent equilibria under certain conditions. Finally the paper uses model network results to illustrate a method of designing fixed time signal timings to meet different scenarios. [Copyright &y& Elsevier]

Abstract: A continuum model that describes a disordered, heterogeneous traffic stream is presented. Such systems are widely prevalent in developing countries where classical traffic models cannot be readily applied. The characteristics of such systems are unique since drivers of smaller vehicles exploit their maneuverability to move ahead through lateral gaps at lower speeds. At higher speeds, larger vehicles press their advantage of greater motive power. The traffic stream at the microscopic level is disordered and defines a porous medium. Each vehicle is considered to move through a series of pores defined by other vehicles. A speed-density relationship that explicitly considers the pore space distribution is presented. This captures the considerable dynamics between vehicle classes that are overlooked when all classes are converted to a reference class (usually Passenger Car Equivalents) as is traditionally done. Using a finite difference approximation scheme, traffic evolution for a two-class traffic stream is shown. [Copyright &y& Elsevier]

Abstract: Traffic matrix (TM) is a key input of traffic engineering and network management. However, it is significantly difficult to attain TM directly, and so TM estimation is so far an interesting topic. Though many methods of TM estimation are proposed, TM is generally unavailable in the large-scale IP backbone networks and is difficult to be estimated accurately. This paper proposes a novel method of TM estimation in large-scale IP backbone networks, which is based on the generalized regression neural network (GRNN), called GRNN TM estimation (GRNNTME) method. Firstly, building on top of GRNN, we present a multi-input and multi-output model of large-scale TM estimation. Because of the powerful capability of learning and generalizing of GRNN, the output of our model can sufficiently capture the spatio-temporal correlations of TM. This ensures that the estimation of TM can accurately be attained. And then GRNNTME uses the procedure of data posttreating further to make the output of our model closer to real value. Finally, we use the real data from the Abilene Network to validate GRNNTME. Simulation results show that GRNNTME can perform well the accurate and fast estimation of TM, track its dynamics, and holds the stronger robustness and lower estimation errors. [Copyright &y& Elsevier]

Abstract: Multifractal detrended cross-correlation analysis (MF-DXA) has been developed to detect the long-range power-law cross-correlation of considered signals in the presence of non-stationarity. However, crossovers arising from extrinsic periodic trends make the scaling behavior difficult to analyze. We introduce a Fourier filtering method to eliminate the trend effects and systematically investigate the multifractal cross-correlation of simulated and real traffic signals. The crossover locations are found approximately corresponding to the periods of underlying trend. Traffic velocity on one road and flows on adjacent roads show strong cross-correlation. They also present weak multifractality after periodic trends are removed. The traffic velocity and flow are cross-correlated in opposite directions which is accordant to their actual evolution. [Copyright &y& Elsevier]

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]

The Street Routing Problem (SRP) is a special case of the well-known Vehicle Routing Problem (VRP). The goal is to service a large number of customers in the city zone. New heuristics for solving a complex SRP is evaluated based on real data. This paper presents several approximations to the length of SRP using the mixed transportation mode and compares them with the published approximations used for VRP or Travelling Salesman Problems (TSP). The system was tested in five real world instances ranging from 12 000 to 29 000 customers. [ABSTRACT FROM AUTHOR]

The coarsest approximation of the structure of a complex network, such as the Internet, is a simple undirected unweighted graph. This approximation, however, loses too much detail. In reality, objects represented by vertices and edges in such a graph possess some nontrivial internal structure that varies across and differentiates among distinct types of links or nodes. In this work, we abstract such additional information as network annotations. We introduce a network topology modeling framework that treats annotations as an extended correlation profile of a network. Assuming we have this profile measured for a given network, we present an algorithm to rescale it in order to construct networks of varying size that still reproduce the original measured annotation Using this methodology, we accurately capture the network properties essential for realistic simulations of network applications and protocols, or any other simulations involving complex network topologies, including modeling and simulation of network evolution. We apply our approach to the Autonomous System (AS) topology of the Internet annotated with business relationships between ASs. This topology captures the large-scale structure of the Internet. In depth understanding of this structure and tools to model it are cornerstones of research on future Internet architectures and designs. We find that our techniques are able to accurately capture the structure of annotation correlations within this topology, thus reproducing a number of its important properties in synthetically-generated random graphs. [ABSTRACT FROM AUTHOR]

Daganzo’s criticisms of second-order fluid approximations of traffic flow [C. Daganzo, Transpn. Res. B. 29, 277 (1995)] and Aw and Rascle’s proposal how to overcome them [A. Aw, M. Rascle, SIAM J. Appl. Math. 60, 916 (2000)] have stimulated an intensive scientific activity in the field of traffic modeling. Here, we will revisit their arguments and the interpretations behind them. We will start by analyzing the linear stability of traffic models, which is a widely established approach to study the ability of traffic models to describe emergent traffic jams. Besides deriving a collection of useful formulas for stability analyses, the main attention is put on the characteristic speeds, which are related to the group velocities of the linearized model equations. Most macroscopic traffic models with a dynamic velocity equation appear to predict two characteristic speeds, one of which is faster than the average velocity. This has been claimed to constitute a theoretical inconsistency. We will carefully discuss arguments for and against this view. In particular, we will shed some new light on the problem by comparing Payne’s macroscopic traffic model with the Aw-Rascle model and macroscopic with microscopic traffic models. [ABSTRACT FROM AUTHOR]

We find a simple, partially altruistic mechanism that can increase global gain for a community of selfish agents. The mechanism is implied in the phenomena found in the minority game. We apply the mechanism to a two-road traffic system to maximise traffic flow. [ABSTRACT FROM AUTHOR]

This study performs a theoretical analysis of instability in a departure time choice problem. Stability of equilibrium is an important factor for reliability of travel time. If equilibrium is not stable, travel time changes over a period of days even if demand and network performance are stable. This study examines the stability of a dynamic user equilibrium problem by using the departure time choice problem. The mechanism of day-to-day changes in a traveller's behaviour is determined first, and then a function that indicates dissimilarity to equilibrium is defined. The day-to-day changes in the dissimilarity function are mathematically examined using approximations. A numerical test is also carried out to verify the result. Results of these analyses show that there can be a case where the system does not converge to equilibrium. It is also indicated that this instability should be caused by the non-monotonicity of the schedule cost. [ABSTRACT FROM AUTHOR]

Practical large-scale nonlinear control systems require an intensive and time-consuming effort for the fine-tuning of their control parameters in order to achieve a satisfactory performance. In most cases, the fine-tuning process may take years and. is performed by experienced personnel. The purpose of this paper is to introduce and analyze a systematic approach for the automatic fine-tuning of the control parameters of practical large-scale nonlinear control systems and investigate its efficiency when applied to the recently developed urban traffic control strategy traffic-responsive urban control. The proposed approach is based on a concept similar to the Simultaneous Perturbation Stochastic Approximation (SPSA) algorithm. The difference between the SPSA algorithm and the proposed approach is that, SPSA employs an approximation of the gradient of an appropriate objective function using only the most recent fine-tuning experiments, while in the proposed approach the approximation of the gradient is performed by using a linear-in-the-parameters approximator that incorporates information of a user-specified time-window of the past experiments. Mathematical analysis of the proposed approach establishes its convergence properties and that SPSA can be regarded as a special case of the proposed approach. Simulation results using the traffic network of the city of Chania, Greece—a typical urban traffic network containing all possible varieties of complex junction staging—demonstrate the efficiency of the proposed approach. [ABSTRACT FROM AUTHOR]

We discuss the problems of spatio-temporal reasoning in the context of hierarchical information maps and approximate reasoning networks (AR networks). Hierarchical information maps are used for representations of domain knowledge about objects, their parts, and their dynamical changes. AR networks are patterns constructed over sensory measurements and they are discovered from hierarchical information maps and experimental data. They make it possible to approximate domain knowledge, i.e., complex spatio-temporal concepts and reasonings represented in hierarchical information maps. Experiments with classifiers based on AR schemes using a road traffic simulator are also briefly presented. [ABSTRACT FROM AUTHOR]