The convergence of diagonalization algorithms for asymmetric network equilibrium problems

We provide a sufficient condition for the convergence of diagonalization algorithms for equilibrium traffic assignment problems with asymmetric Jacobian matrix B(v) of the link user cost mapping s(v) of the flow v. When

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, where D(v^*) > 0 is the diagonal of B(v^*) and v^* is the equilibrium flow, we demonstrate a local convergence theorem for nonlinear cost functions. The implication of this result for practical applications of the model are outlined.     

Train movement simulation by element increment method

The article presents an element increment method that is developed by current time increment method of train traction calculation. A railway route was divided, breaking it down into elements of different lengths. A whole train movement simulation curve (v–t curve and v–S curve) was formed by splitting the joints of each of the elements' individual simulation curves. During this process, the train velocity variance was calculated by time increment method with assistance of polynomial fitting technology. Additionally, a step‐by‐step method with iteration was used to combine each element and makes the whole simulation curve continuous. Meanwhile, the energy‐saving issue was also taken into account to optimize the simulation curve. This article gives more details about the modeling by providing an example of a railway route based on moving block control. The element increment method is a more effective way to calculate train traction of high‐speed railway, and it is an alternative method to train movement simulation for aiding macroscopic railway transportation planning. Copyright © 2017 John Wiley & Sons, Ltd.     

The dynamics of traffic assignment and traffic control: A theoretical study

The paper considers traffic assignment, with traffic controls, in an increasingly dynamic way. First, a natural way of introducing the responsive policy, P_o, into steady state traffic assignment is presented. Then it is shown that natural stability results follow within a dynamical version of this static equilibrium model (still with a constant demand). We are able to obtain similar stability results when queues are explicitly allowed for, provided demand is constant. Finally we allow demand to vary with time; we consider the dynamic assignment problem with signal-settings now fixed. Here we assume that vehicles are very short and that deterministic queueing theory applies, and show that the time-dependent queueing delay at the bottleneck at the end of a link is a monotone function of the time-dependent input profile to the bottleneck. We have been unable to obtain results when dynamic demand and responsive signal control are combined.     

Finding the k reliable shortest paths under travel time uncertainty

This paper investigates the problem of finding the K reliable shortest paths (KRSP) in stochastic networks under travel time uncertainty. The KRSP problem extends the classical K loopless shortest paths problem to the stochastic networks by explicitly considering travel time reliability. In this study, a deviation path approach is established for finding K α-reliable paths in stochastic networks. A deviation path algorithm is proposed to exactly solve the KRSP problem in large-scale networks. The A^* technique is introduced to further improve the KRSP finding performance. A case study using real traffic information is performed to validate the proposed algorithm. The results indicate that the proposed algorithm can determine KRSP under various travel time reliability values within reasonable computational times. The introduced A^* technique can significantly improve KRSP finding performance.     

Analyzing fluctuations in car-following

Many car-following models predict a stable car-following behavior with a very small fluctuation around an equilibrium value g¹ of the net headway g with zero speed-difference Δv between the following and the lead vehicle. However, it is well-known and additionally demonstrated by data in this paper, that the fluctuations are much larger than these models predict. Typically, the fluctuation in speed difference is around ±2 m/s, while the fluctuation in the net time headway T = g/v can be as big as one or even two seconds, which is as large as the mean time headway itself. By analyzing data from loop detectors as well as data from vehicle trajectories, evidence is provided that this randomness is not due to driver heterogeneity, but can be attributed to an internal stochasticity of the driver itself. A final model-based analysis supports the hypothesis, that the preferred headway of the driver is the parameter that is not kept constant but fluctuates strongly, thus causing the even macroscopically observable randomness in traffic flow.     

A dynamic traffic assignment model for the assessment of moving bottlenecks

Moving bottlenecks in highway traffic are defined as a situation in which a slow-moving vehicle, be it a truck hauling heavy equipment or an oversized vehicle, or a long convey, disrupts the continuous flow of the general traffic. The effect of moving bottlenecks on traffic flow is an important factor in the evaluation of network performance. This effect, though, cannot be assessed properly by existing transportation tools, especially when the bottleneck travels relatively long distances in the network.This paper develops a dynamic traffic assignment (DTA) model that can evaluate the effects of moving bottlenecks on network performance in terms of both travel times and traveling paths. The model assumes that the characteristics of the moving bottleneck, such as traveling path, physical dimensions, and desired speed, are predefined and, therefore, suitable for planned conveys.The DTA model is based on a mesoscopic simulation network-loading procedure with unique features that allow assessing the special dynamic characteristics of a moving bottleneck. By permitting traffic density and speed to vary along a link, the simulation can capture the queue caused by the moving bottleneck while preserving the causality principles of traffic dynamics.     

A pedestrian flow model considering the impact of local density: Voronoi diagram based heuristics approach

Local density, which is an indicator for comfortable moving of a pedestrian, is rarely considered in traditional force based and heuristics based pedestrian flow models. However, comfortable moving is surely a demand of pedestrian in normal situations. Recently, Voronoi diagram had been successfully adopted to obtain the local density of a pedestrian in empirical studies. In this paper, Voronoi diagram is introduced into the heuristics based pedestrian flow model. It provides not only local density but also other information for determining moving velocity and direction. Those information include personal space, safe distance, neighbors, and three elementary characteristics directions. Several typical scenarios are set up to verify the proposed model. The simulation results show that the velocity-density relations and capacities of bottleneck are consistent with the empirical data, and many self-organization phenomena, i.e., arching phenomenon and lane formation, are also reproduced. The pedestrians are likely to be homogeneously distributed when they are sensitive to local density, otherwise pedestrians are non-uniformly distributed and the stop-and-go waves are likely to be reproduced. Such results indicate that the Voronoi diagram is a promising tool in modeling pedestrian dynamics.     

Comparison of pedestrian trip generation models

Using Poisson regression and negative binomial regression, this paper presents an empirical comparison of four different regression models for the estimation of pedestrian demand at the regional level and finds the most appropriate model with reference to the National Household Travel Survey (NHTS) 2001 data for the Baltimore (USA) region. The results show that Poisson regression seems to be more appropriate for pedestrian trip generation modeling in terms of χ² ratio test, Pseudo R², and Akaike's information criterion (AIC). However, R² based on deviance residuals and estimated log‐likelihood value at convergence confirmed the empirical studies that negative binomial regression is more appropriate for the over‐dispersed dependent variable than Poisson regression. Copyright © 2011 John Wiley & Sons, Ltd.     

Bottleneck congestion: Differentiating the coarse charge

The traditional bottleneck model for road congestion promotes the implementation of a triangular, and time varying, charge as the optimal solution for the road congestion externality. However, cognitive and technological barriers put a practical limit to the degree of differentiation real world implementations can handle. The traditional approach to accommodate for this concern has been a step toll, with the single step coarse charge as its simplest case.In this paper we study how efficiency of the coarse charge can be improved by differentiating its level and timing across groups of travellers. We use the traditional bottleneck model to analyse how the coarse charge can be differentiated over two groups of travellers assuming inelastic peak-hour demand.The results of our analysis indicate that differentiating the coarse charge across two groups of travellers considerably improves its efficiency without increasing cognitive effort and decision making costs for the individual traveller. A numeric illustration reveals a welfare gain of 69% of the first-best charge, up from 53% for the generic coarse charge. This increase is similar to what is obtained by moving from the coarse charge to a generic two step toll. Once different groups have been defined, one could in fact achieve the same gains by temporal separation of drivers, for example by use of licence plate numbers.The presented charging regime has a considerable degree of flexibility with respect to the share of travellers to attribute to each scheme, which further adds to its merits in practical applicability.     

Passing Bays for Slow Moving Vehicles on Rural Two‐lane Roads

Abstract

Slow‐moving vehicles, including agricultural vehicles, on arterial highways can cause serious delays to other traffic as well as posing an extra safety risk. This paper elaborates on a small‐scale solution for these problems: the passing bay. It investigates the impacts of a passing bay on the total delay for other motorized vehicles, the number of passing manoeuvres and hindered vehicles, and the mean delay per hindered vehicle. The latter is also considered to be an indicator for traffic safety. The calculations are performed for two characteristic trips with a slow‐moving vehicle. The passing bay is an effective solution to reducing delays on arterial highways when two‐way hourly volumes exceed 600–1000 vehicles. The effects depend on the trip length and speed of the slow‐moving vehicle, and on the passing sight distance limitations of the road. A distance of 2–4?km between the passing bays seems an acceptable compromise between the reduction of delay for other motorized vehicles and the extra discomfort and delay for drivers of slow‐moving vehicles. This result also shows that passing bays are not effective in regions where slow‐moving vehicles mainly make trips shorter than this distance.     

Behavior of the cell transmission model and effectiveness of ramp metering

The paper characterizes the behavior of the cell transmission model of a freeway, divided into N sections or cells, each with one on-ramp and one off-ramp. The state of the dynamical system is the N-dimensional vector n of vehicle densities in the N sections. A feasible stationary demand pattern induces a unique equilibrium flow in each section. However, there is an infinite set—in fact a continuum—of equilibrium states, including a unique uncongested equilibrium n^u in which free flow speed prevails in all sections, and a unique most congested equilibrium n^con. In every other equilibrium n^e one or more sections are congested, and n^u  n^e  n^con. Every equilibrium is stable and every trajectory converges to some equilibrium state.Two implications for ramp metering are explored. First, if the demand exceeds capacity and the ramps are not metered, every trajectory converges to the most congested equilibrium. Moreover, there is a ramp metering strategy that increases discharge flows and reduces total travel time compared with the no-metering strategy. Second, even when the demand is feasible but the freeway is initially congested, there is a ramp metering strategy that moves the system to the uncongested equilibrium and reduces total travel time. The two conclusions show that congestion invariably indicates wastefulness of freeway resources that ramp metering can eliminate.     

A queueing system for airport buses

The use of remote terminals to relieve airport congestion leads rather naturally to queueing systems with batch arrivals occuring at fixed time intervals to a multiple server service facility. In this paper arrival point steady-state solutions to the D^[X]/M/c queueing system are presented. Solution of the steady-state equation WP = W and Neuts' method of solving the GI^[X]/M/c system are used to obtain steady-state system size densities. Results obtained using the two methods are compared with each other as well as with simulation results.     

Time-dependent Hyperstar algorithm for robust vehicle navigation

The vehicle navigation problem studied in Bell (2009) is revisited and a time-dependent reverse Hyperstar algorithm is presented. This minimises the expected time of arrival at the destination, and all intermediate nodes, where expectation is based on a pessimistic (or risk-averse) view of unknown link delays. This may also be regarded as a hyperpath version of the Chabini and Lan (2002) algorithm, which itself is a time-dependent A^* algorithm. Links are assigned undelayed travel times and maximum delays, both of which are potentially functions of the time of arrival at the respective link. Probabilities for link use are sought that minimise the driver’s maximum exposure to delay on the approach to each node, leading to the determination of a pessimistic expected time of arrival at the destination and all intermediate nodes. Since the context considered is vehicle navigation, the probability of link use measures link attractiveness, so a link with a zero probability of use is unattractive while a link with a probability of use equal to one will have no attractive alternatives. A solution algorithm is presented and proven to solve the problem provided the node potentials are feasible and a FIFO condition applies to undelayed link travel times. The paper concludes with a numerical example.     

Capacity-constrained traffic forecasting model

Projecting future traffic is an important stage in any traffic and transportation planning study. Accurate traffic forecasting is vital for transportation planning, highway safety evaluation, traffic operations analysis, and geometric and pavement design among others. In view of its importance, this paper introduces a regression-based traffic forecasting methodology for a one dimensional capacity-constrained highway. Five different prediction functions are tested; the best was selected according to the accuracy of projections against historical traffic data. The three-parameter logistic function produced more accurate projections compared to other functions tested when highway capacity constraints were taken into consideration. The R ² values at various test locations ranged from 88% to 98%, indicating good prediction capability. Using the Fisher's information matrix approach, the t-statistic test showed all parameters in the logistic function were highly statistically significant. To evaluate reliability of projections, predictive intervals were calculated at a 95% level of confidence. Predictions using the logistic function were also compared to those predicted using the compound growth rate and linear regression methods. The results show that the proposed methodology generates much more reasonable projections than current practices.     

An augmented Lagrangian origin‐based algorithm for link‐capacitated traffic assignment problem

The origin‐based algorithm is embedded into the augmented Lagrangian method for the link‐capacitated traffic assignment problem. In order to solve the “nonexistence” problem due to the second partial derivatives of the augmented Lagrangian function at some specific points, the approximate expressions of the second partial derivatives are amended in the origin‐based algorithm. The graph of last common nodes is developed on the basis of the restricted single‐origin network. A method is proposed for finding n–1 last common nodes of the restricted single‐origin network, resulting in computational complexity of O(n²) in finding last common nodes. Numerical analysis on the Sioux Falls network and Chicago Sketch network demonstrated the effectiveness and characteristics of the proposed algorithm. Copyright © 2014 John Wiley & Sons, Ltd.     

Feedback control speed harmonization algorithm: Methodology and preliminary testing

The capacity drop phenomenon, which reduces the maximum bottleneck discharge rate following the onset of congestion, is a critical restriction in transportation networks that produces additional traffic congestion. Consequently, preventing or reducing the occurrence of the capacity drop not only mitigates traffic congestion, but can also produce environmental and traffic safety benefits. In addressing this problem, the paper develops a novel bang-bang feedback control speed harmonization (SH) or Variable Speed Limit (VSL) algorithm, that attempts to prevent or delay the breakdown of a bottleneck and thus reduce traffic congestion. The novelty of the system lies in the fact that it is both proactive and reactive in responding to the dynamic stochastic nature of traffic. The system is proactive because it uses a calibrated fundamental diagram to initially identify the optimum throughput to maintain within the SH zone. Furthermore, the system is reactive (dynamic) because it monitors the traffic stream directly upstream of the bottleneck to adjustment the metering rate to capture the dynamic and stochastic nature of traffic. The steady-state traffic states in the vicinity of a lane-drop bottleneck before and after applying the SH algorithm is analyzed to demonstrate the effectiveness of the algorithm in alleviating the capacity drop. We demonstrate theoretically that the SH algorithm is effective in enhancing the bottleneck discharge rate. A microscopic simulation of the network using the INTEGRATION software further demonstrates the benefits of the algorithm in increasing the bottleneck discharge rate, decreasing vehicle delay, and reducing vehicle fuel consumption and CO₂ emission levels. Specifically, compared with the base case without the SH algorithm, the advisory speed limit increases the bottleneck discharge rate by approximately 7%, reduces the overall system delay by approximately 20%, and reduces the system-wide fuel consumption and CO₂ emission levels by 5%.     

The use of demand correlation in the modeling of air carrier departure delays as first‐order autoregressive random processes

A method for modeling air carrier departure delays at commercial‐service airports as autoregressive random processes is presented. This method employs the correlation of a priori demand data to significantly reduce prediction error in the optimal least‐squares estimator for additive white noise. The reduction factor of the prediction error is demonstrated to be on the order of 10² over that of the unbiased estimator. Copyright © 2011 John Wiley & Sons, Ltd.     

Parameters of moving sidewalks for airport terminal pier fingers

A moving sidewalk system installed at an airport pier finger is analyzed. The optimal length of the moving sidewalk and the optimal spacing between the access points which minimize the total cost of the system are obtained using methods of calculus, for a number of cases based on the different proportions of arriving, departing and transferring passengers and for two different types of moving sidewalks: elevated, at‐grade.

The optimal length of the moving sidewalk is shown to be linearly related to the length of the concourse, and to the total passenger demand. The effect due to preticketed transferees is insignificant.

The optimal spacing between access points is shown to be proportional to the square‐root of either the cost of an access escalator or the cost of inconvenience to a passenger due to an intermediate gap, depending on the moving sidewalk system under consideration. It also changes with the percentage of preticketed transferees.     

Assessing the cost and CO2e impacts of rerouteing UK import containers

Among the most important trade-related issues currently confronting the UK are the environmental implications of very large volumes of containerised freight being handled at a small number of ports while there appears to be significant potential for using other ports and water-rail intermodal connections. Six UK ports are selected for the analysis: Hull/Immingham, Liverpool, Felixstowe, Southampton, Dover and Bristol. Through an origin-destination analysis, the cost and CO₂e impacts of UK port trade patterns are compared using the actual situation against three proposed Scenarios: (1) the re-direction of containers by a combined expansion of Hull and Immingham; Liverpool; and Bristol, (2) moving containers by rail facilitated via expanded capacity at Southampton, and (3) moving containers by rail through expanded capacity at Felixstowe. The research found that transporting containers from Felixstowe and Southampton to the northern regions by rail has the lowest CO₂e impact, and is the most feasible option, although constraints exist in terms of infrastructure provision, water depth and rail network capacity.     

The independence of volume-capacity ratio of private toll roads in general networks

In a general traffic network under some widely used assumptions, this paper proves that the level of service, represented by the volume-capacity (v/c) ratio, offered by a profit-maximizing private firm on a private toll road is independent of another competitor’s choice of capacity and toll rate for another private toll road. The v/c ratio will be the same as the one provided by a centralized welfare-maximizing traffic authority. Moreover, the ratio remains the same even in a regulated market where the authority imposes a cap for the generalized travel cost on the private toll road.