A stochastic model for highway traffic

Rural two-lane highways are the most common road type both in Poland and globally. In terms of kilometres, their length is by far greater than that of motorways and expressways. They are roads of one carriageway for each direction, which makes the overtaking of slower vehicles possible only when there is a gap in the stream of traffic moving from the opposite direction. Motorways and express roads are dual carriageways that are expected to support high speed travel mainly over long distances. Express roads have somewhat lower technical parameters and a lower speed limit than motorways. Two-lane highways are used for both short- and long-distance travel. The paper presents selected studies conducted in Poland in 2016–2018 on rural two-lane highways and focuses on the context of the need for their reliability. The research was carried out on selected short and longer road sections located in various surroundings, grouped in terms of curvature change rate CCR, longitudinal slopes and cross-sections (width of lanes and shoulders). The studies of traffic volumes, travel time and travel speed, as well as traffic density, will be used to analyze traffic performance and identify measures of travel time reliability. The analyzed roads were characterized by good technical parameters and significant variability of traffic volume throughout the day, week and year. Some roads experience congestion, i.e., situations in which traffic volume Q is close to or above respective road capacity C. In order to determine the form of the suitable reliability measures, it will be important to determine the extent to which a road’s geometric and traffic characteristics impact travel speed and time. The paper presents well-known reliability measures for dual carriageways and proposes new measures, along with an evaluation of their usefulness in the assessment of the functioning of two-lane highways.

For the electric hydrostatic pump unit (EPU), which is a crucial component in the electro hydraulic servo pump control system (EHSPCS), nonlinear flow modelling is a key challenge to achieve high performance operation, especially in position control. For the nonlinear flow of EPUs, simple linearization combined with compensation has become a popular control method recently. However, the control performance is constrained by the reliance on deviation correction. This paper proposes utilizing the Gauss Newton iterative method to investigate the nonlinear flow modeling in the EPU, aiming to obtain the mapping relationship between the load flow and operating parameters in the EPU, thereby directly improving the control performance. A nonlinear flow model is built by utilizing the Gauss Newton iterative method based on test data obtained from various operating conditions, and the mapping relationship is presented accordingly. Experimental studies show that compared to well-established methods, this model exhibits high accuracy and practicality in improving the control performance, particularly in position control of the EPU.

An important method to study the seepage characteristics of rock fractures is using nonlinear flow models. However, existing nonlinear flow models are unable to describe the flow law of water-soil particles mixture through the rough fractures of soft rock because the rheological properties of the fluid are rarely considered. In this study, a novel nonlinear flow model (WST model) for water-soil particles mixture through rough fracture of silty mudstone under low water head was proposed based on local viscous pressure drops and local pressure drops. To verify the accuracy of the model, saturated seepage experiments were carried out on five silty mudstone samples with a rough fracture under low water head. The results demonstrate that compared with the MT model (a nonlinear flow model for fluid flowing though rough rock fracture at a low velocity), the WST model is preferable to fit experimental data, showing better precision in describing nonlinear flow through rough fracture of silty mudstone under low water head conditions. Furthermore, the WST model is particularly applicable when the average height of the surface of all fracture units relative to the datum plane is less than 0.62 mm and the Reynolds number is less than 620. In addition, the disordered movement of soil particles under the combined action of inertia and water head is the main reason for the nonlinear flow of water–solid particles mixture in the silty mudstone fracture.

As traffic volumes increase in many jurisdictions in both urban and rural areas, the demand on the highway network also increases. Specifically, as rural traffic volumes rise in Texas, the pressure on the state's network of two-lane highways rises accordingly. High proportions of heavy vehicles compound the problem and contribute to a decrease in safety as impatient drivers attempt to pass slower vehicles in no-passing zones or to pass trucks, despite diminished sight distance beyond such vehicles. Previous research in Texas demonstrated that periodic passing lanes can improve operations on two-lane highways with low to moderate volumes; these Super 2 highways can provide many benefits of a four-lane alignment at lower cost. The current Texas Roadway Design Manual contains these guidelines for highways with average daily traffic (ADT) lower than 5,000 vehicles per day. A current project expands on that research to develop design guidelines for passing lanes on two-lane highways with higher volumes. The project investigates the effects of volume, terrain, and heavy vehicles on traffic flow. This paper discusses findings from field observations of existing Super 2 highway corridors in Texas and computer modeling of traffic conditions on a simulated Super 2 corridor. Results indicate that passing lanes do provide added benefit at higher traffic volumes by reducing delay and percent time spent following. The incremental benefit of adding passing lanes or adding length to lanes diminished, and the effects of ADT on operations were more substantial than the effects of terrain or truck percentage for the study corridor.

Energy flow calculation is a fundamental problem of the integrated power and gas system (IPGS) operation and planning. However, the nonlinear gas flow model introduces major challenges to the energy flow calculation. In this paper, we propose a tractably convex optimization model to solve the energy flow problem in IPGSs. It is demonstrated that the proposed optimization model has the same optimal solution as the original nonlinear steady energy flow model. Also, piecewise linearization is adopted to tightly linearize the nonlinear objective function of the model, which transforms the formulated convex optimization into a linear program one. Thus, the computation complexity of the proposed energy flow model is significantly reduced as compared with the existing methods. In addition, the proposed model can be extended to probabilistic energy flow estimation. Extensive case studies are conducted to validate the effectiveness of the proposed energy flow model using three IPGSs.

This report summarizes our work to develop advanced forward and inverse solvers and uncertainty quantification capabilities for a nonlinear 3D full Stokes continental-scale ice sheet flow model. The components include: (1) forward solver: a new state-of-the-art parallel adaptive scalable high-order-accurate mass-conservative Newton-based 3D nonlinear full Stokes ice sheet flow simulator; (2) inverse solver: a new adjoint-based inexact Newton method for solution of deterministic inverse problems governed by the above 3D nonlinear full Stokes ice flow model; and (3) uncertainty quantification: a novel Hessian-based Bayesian method for quantifying uncertainties in the inverse ice sheet flow solution and propagating them forward into predictions of quantities of interest such as ice mass flux to the ocean.

The problem of modelling the complex behaviour of freeway flow leads to a nonlinear macroscopic model. Unfortunately, high dimensional non-linear characteristics could not be performed easily. The paper´s purpose is to introduce a new, general modelling formalism for freeway traffic flow modelling, respectively control. Linear Parameter Varying (LPV) systems represent a numerically tractable class of complex non-linear systems. The main idea is to derive some arbitrary, time dependent parameters by capturing the nonlinearities in the system. Even if the transformation of the full nonlinear model to affine and quasi Linear Parameter Varying (qLPV) system is not unique, an appropriate qLPV model is presented and a computationally low demanding form is given. More, the paper investigates the problem of selecting the adequate scheduling variables, endogenous parameters and some linear approximations giving a novel way to describe freeway traffic systems. An important aspect of the model selection is the feasibili ty of the resulted system throughout the controller and observer design. The paper describes the problem of quadratic stabilizability and detectability for LPV flow models. The Linear Matrix Inequality (LMI) conditions are developed to verify these important properties. Finally, a numeric example suggests the application of the LPV structure for a general freeway section with on- and off-ramps. The comparison of the simulation response of the non-linear and the derived nominal LPV model has also been investigated.

In this paper, the multivariate Bernstein polynomials defined on a simplex are viewed as sampling operators, and a generalization by allowing the sampling operators to take place at scattered sites is studied. Both stochastic and deterministic aspects are applied in the study. On the stochastic aspect, a Chebyshev type estimate for the sampling operators is established. On the deterministic aspect, combining the theory of uniform distribution and the discrepancy method, the rate of approximating continuous function and L p convergence for these operators are studied, respectively.

The existing many fuzzy traffic controllers could not be applied to the traffic congestion situation because they have been developed and applied for a non-congestion traffic flow. In this paper, therefore, we propose a traffic light controlling FLC that is able to cope with traffic congestion appropriately. In order to consider such situation as missing the green signal because of spillback of upper crossroad, it uses as an input variable a degree of traffic congestion of upper roads, which vehicles on a crossroad are to proceed to. It uses the first-order Sugeno fuzzy model for modeling nonlinear traffic flow. In experiment, we compared and analyzed the fixed traffic signal controller and the proposed FLC. As a result of experiment, the proposed FLC showed more enhanced performance than the fixed traffic signal controller.

Safety–collision transition induced by lane changing in traffic flow

The two basic problems facing the Trans-Canada Highway through Rogers Pass, namely the winter problem of adequate vehicle storage areas during avalanche control and the summer problem of maintaining an acceptable level of service by ensuring adequate passing opportunities, may be linked through a common denominator — passing lanes. This paper presents the findings of a recently completed study of the Trans-Canada Highway through Mount Revelstoke and Glacier National Park. The study method is based on the fact that traffic flow characteristics, highway conditions, and operational requirements vary considerably from season to season. Thus, the analysis was broken into two parts, namely a separate analysis of winter and summer conditions. A traffic simulation model was used to determine those locations that could serve as potential sites for passing lanes during summer. The traffic simulation model developed for the passing lane analysis utilized files that describe road geometry, summer traffic flow and composition, and vehicle performance. A separate simulation model was developed to determine vehicle storage requirements of ponding areas during avalanche control. The model developed for winter traffic characteristics also provided the basis for a flexible traffic management strategy. Cross-section elements were developed to accommodate an auxiliary lane to be used as a passing lane in summer and as a parking lane to increase the capacity of ponding areas during avalanche control in winter. Design requirements called for triple stacking of vehicles in ponding areas during avalanche control. To accommodate design year traffic volumes at an acceptable level of service during the summer months, 12 passing lanes totalling 23 km in length were recommended. Six ponding areas, totalling 4 km in length, are coincident with four of the passing lane locations. The paper concludes with a general discussion on the benefits of linking traffic simulation with geometric design to demonstrate how the design life of rural two-lane highways can be extended by the use of low-cost operational improvements such as passing lanes. Key words: highway planning and engineering, two-lane highways traffic management during avalanche stabilization, passing lanes, cross-section elements, Trans-Canada Highway.

[1] Sparse geologic dictionaries provide a novel approach for subsurface flow model representation and calibration. Learning sparse dictionaries from prior training data sets is an effective approach to describe complex geologic connectivity patterns in subsurface imaging applications. However, the computational cost of sparse learning algorithms becomes prohibitive for large models. Performing the sparse dictionary learning process on smaller image patches (segments) provides a simple approach to address this problem in image processing applications. However, in underdetermined subsurface flow model calibration inverse problems, reconstruction of a segmented image can introduce significant structural distortion and discontinuity at the boundaries of the segments. This paper proposes an alternative sparse learning approach where the sparse dictionaries are learned from low-rank representations of the large-scale training data set in spectral domains (e.g., frequency domain). The objective is to develop a computationally efficient dictionary learning approach that emphasizes large-scale spatial connectivity patterns. This is achieved by removing the strong spatial correlations in the training data, thereby eliminating a large number of insignificant components from the sparse learning computation. In addition to improving the computational complexity, sparse learning from low-rank training data sets suppresses the small-scale details from entering the reconstruction of large-scale connectivity patterns, thereby providing a regularization effect in solving the resulting ill-posed inverse problems. We apply the proposed approach to travel-time tomography inversion and nonlinear subsurface flow model calibration inverse problems to demonstrate its effectiveness and practicality.

The complexity and computational burden of nonlinear power flow (PF) models have motivated the introduction of various approximations. While these approximations provide tractability and reduced computational burden in PF, for optimal power flow (OPF) and control purpose, the accuracy of these models becomes a major concern in the presence of high renewable energy penetration/increased demand in distribution feeders. This paper compares and analyzes, for the first time to our knowledge, the performance of commonly used PF models in OPF formulations for single-phase and unbalanced three-phase distribution systems. Simulations performed on the phase-coupled and phase-decoupled versions of the IEEE 123-node and a reduced model extracted from the IEEE 8500-node feeder with varying levels of negative and positive net loads show that, ignoring mutual coupling impedances, as in the phase-decoupled PF models, is the largest source of error on the voltage profiles. Also, the performance of the linear PF models is acceptable only for a small range around the nominal operating point; hence, they can lead to large errors if used in OPF/control framework that seeks solutions on wider operating range.

A theoretical investigation of the rolling motion of triform configurations at high angles of attack is presented. A nonlinear aerodynamic flow model, derived from strip and slender body theories, is used to predict the aerodynamic roll coefficients of triform tailed missiles at high angles of attack. The flow model predictions are compared to the estimates of a panel-based code and a computational fluid dynamics code at two Mach numbers.

A non-linear fluid suspension model for blood flow