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The article presents a mathematical study of a hydrodynamic model of traffic flow on a circular highway. The concepts discussed in the study include fluid dynamics, the number of vehicles per unit length of the roadway, and the fundamental diagram or fundamental curve. Details on the mathematical notations, equilibrium set, and priority rule of the study are provided.

How to alleviate the damages of cascading failures triggered by the overload of edges/nodes is common in complex networks. To describe the whole cascading failures process from edges overloading to nodes malfunctioning and the dynamic spanning clustering with the evolvement of traffic flow, we propose a capacity assignment model by introducing an equilibrium assignment rule of flow in artificially created scale-free traffic networks. Additionally, the capacity update rule of node is given in this paper. We show that a single failed edge may undergo the cascading failures of nodes, and a small failure has the potential to trigger a global cascade. It is suggested that enhancing the capacity of node is particularly important for the design of any complex network to defense the cascading failures. Meanwhile, it has very important theoretical significance and practical application worthiness in the development of effective methods to alleviate the damage of one or some failed edges/nodes. [ABSTRACT FROM AUTHOR]

Capacity has traditionally been defined deterministically, and has been assumed to occur immediately before breakdown. Recent studies, however, have shown that the value of capacity, i.e., maximum throughput, is probabilistic, and does not always occur immediately before the breakdown. Four different types of flows (i.e., maximum prebreakdown flow, breakdown flow, maximum queue discharge flow, and average queue discharge flow) referred to as “capacity flows” in this paper, are considered to examine how they differ by day of the week and time of the day, and whether they are significantly different by type of freeway segment. Speed and volume data were obtained, which were initially collected by remote traffic microwave sensors at the US-202 southbound near Philadelphia, from May to August 2004. The four types of flows described above were collected and distinguished by time period, day of the week, and segment type. In conclusion, the mean capacity flows were different during different times of the day, but were the same each day of the week. In comparing segment types, capacity flows per lane are generally not equal between merging, diverging, weaving, and lane drop segments. [ABSTRACT FROM AUTHOR]

Online traffic flow modeling is of increasing importance due to intelligent transport systems and technologies. The flow-density relation plays an important role in traffic flow modeling and provides a basic way to illustrate traffic flow behavior under different traffic flow and traffic density conditions. Until now the research effort has focused mainly on the shape of the relation. The time series of the relation has not been identified clearly, even though the time series of the relation reflects the upstream/downstream traffic conditions and should be considered in the traffic flow modeling. In this paper, the dynamic flow-density relation is identified based on the classification of traffic states and is quantified employing fuzzy logic. The quantified dynamic flow-density relation builds the basis for online application of a macroscopic traffic flow model. The new approach to online modeling of traffic flow applying the dynamic flow-density relation alleviates parameter calibration problems stemming from the static flow-density relation. [ABSTRACT FROM AUTHOR]

Stability analysis of a single-lane microscopic car-following model is studied analytically from the perspective of delayed reactions of human drivers. In the literature, the delayed reactions of the drivers are modeled with discrete delays, which assume that drivers make their control decisions based on the stimuli they receive from a point of time in the history. We improve this model by introducing a distribution of delays, which assumes that the control actions are based on information distributed over an interval of time in history. Such an assumption is more realistic, as it takes into consideration the memory capabilities of the drivers and the inevitable heterogeneity of their delay times. We calculate exact stability regions in the parameter space of some realistic delay distributions. Case studies are provided demonstrating the application of the results. [ABSTRACT FROM AUTHOR]

Weaving areas are one of the major highway facilities that have long been investigated by researchers. Their capacities are currently estimated based on the density 27 pc/km/ln. There is no specific reason why this method can produce accurate estimates. In addition, no data collection has been performed to validate them. This study develops a generalized capacity estimation model for weaving areas, which is applicable to the entire range of configurations of weaving areas, and compares the resulting capacity estimates to field estimates. The proposed methodology is based on gap acceptance theory and linear programming techniques. Speed and flow data over several days were obtained and analyzed to extract the capacity of three study sites along the QE Expressway, Toronto. It was found that, for the three study sites, the proposed methodology provides capacity estimates that are closer to the field-observed capacity values than the Highway Capacity Manual (2000) estimates. [ABSTRACT FROM AUTHOR]

Chapter 16 of the Highway Capacity Manual 2000 (HCM 2000) includes models and procedures for calculating capacity and delay at signalized intersections. However, the procedures do not provide estimation of the optimal cycle length which would result in the minimal intersection delay. A quick estimation method for determining the cycle length is described in Appendix A, Chap. 10 of the HCM 2000 for planning level applications. In this method, a simple equation is used to estimate the cycle length if it is not available. However, the estimated cycle length may not be the optimal cycle length from the point of view of achieving minimum intersection delay. To develop a new cycle length model, the Webster’s minimum delay cycle length model is first considered. However, based on our study, Webster’s minimum delay cycle length model overestimates the optimal cycle length compared to the results from the HCM 2000 delay calculation method, especially under high traffic volume conditions. After investigating three new models developed during this study, an exponential-type cycle length model is recommended. Based on a series of CORSIM simulation runs, the cycle length predicted by this model provides better results than the current quick estimation method of the HCM 2000. [ABSTRACT FROM AUTHOR]

Any application of intelligent transportation systems (ITS) to freeway operations and control relies on understanding behavior of freeway bottlenecks. By improving our understanding of the formation and dissipation of queues at active freeway bottlenecks (points characterized by the presence of queued traffic immediately upstream and unqueued traffic immediately downstream) we can improve the techniques used to manage freeway traffic—one of the hallmarks of ITS. It is shown freeway bottlenecks' activations can be diagnosed definitively using archived inductive loop detector data (measured at 20- 30-sec intervals) from two sites in Toronto, Canada. Once the bottlenecks' locations and times of activation were determined, potential signals of their activations were explored. It is shown that certain potential signals were evident immediately before upstream queue formation, and that these were reproducible from day to day (over three or four days examined) at the sites studied. As a result, it is suggested that these signals be used for systematic investigation of bottleneck behavior in either real time or in retrospect, on a more widespread basis as part of a real-time ITS control system. [ABSTRACT FROM AUTHOR]

Virtually all proposed systems for highway automation have at least one mode in common-steady-state car following. The nature of this mode is extremely important, as it can determine the upper limit of flow capacity of an automated highway. This limit is explored for a linear headway controller, and a fundamental relation between the effective vehicle response time and the permissible traffic stream density is obtained. The required intervehicular spacing with a linear headway controller is shown to be proportional to the effective vehicle time constant for small-signal inputs; thus, one can achieve small spacings and high flow rates by reducing this parameter to I see or less. However, the vehicle is then highly responsive to small changes in lead-vehicle speed- possibly resulting in both passenger discomfort and poor fuel economy. These shortcomings can be avoided by using a linear velocity controller for automatic car following. [ABSTRACT FROM AUTHOR]