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This paper is devoted to the mathematical modeling of traffic flow in a large automobile network. A statistical model of traffic flow proposed by the authors and designed for full-scale modeling of the operation of large-scale transport systems on long time intervals is used. A model has been constructed for one of the sides of the Moscow Ring Road and experiments have been carried out for two ways of jamming on the highway. The functionality of the naive entry control model has been tested in both types of the experiments. It has been shown that even the simplest method of limiting the incoming flow is efficient in terms of highway travel time losses. [ABSTRACT FROM AUTHOR]

In this paper, we propose enhanced fundamental diagrams based on different water film depths by considering the effects of hydroplaning using a physical method. Various factors are calculated to describe the total safe distance headway of main vehicle components. These factors include the driver reaction times, reaction distances, vehicle braking times, and vehicle braking distances corresponding to different water film depths. An excellent match is found between the computed braking distance, the braking time calculated using the proposed numerical model, and the results published in other papers. These calculations are performed to estimate the distance headway and quantitatively analyse the relationships between the speed, density, and water film depth. By using three road-specific parameters estimated by our proposed model, namely, the free-flow speed, jam density, and capacity flow, a link transmission model is developed to analyse the dynamic impact of the water film depth. [ABSTRACT FROM AUTHOR]

To form ergonomic driving conditions in the "driver–vehicle–road environment" system, it is proposed to use a mathematical model of automatic control theory, in which special features of traffic control are determined by the transition process described by transfer functions of the vehicle and the driver. The proposed model makes it possible to simulate vehicle speed control processes in accordance with road conditions whose impact on the driver is estimated by the complex characteristic: maximum entropy of the traffic environment. [ABSTRACT FROM AUTHOR]

Urban traffic congestion is a common problem that affects many cities around the world. In this paper, an actual urban traffic simulation model (AUTM) for traffic congestion predicting and avoiding is proposed, which includes three key components: the map and transfer (MT) conversion method, the optimized spatial evolution rules, and a congestion-avoidance routing algorithm. Three key techniques are combined in our proposed model: (1) The MT conversion method is proposed to get actual urban cellular spaces, which apply the optimized spatial evolution rules to simulate the vehicular dynamics better. (2) AUTM is proposed for simulating traffic congestion and predicting the effect of adding overpasses and roadblocks. (3) The congestion-avoidance routing algorithm is proposed for vehicles to dynamically update their routes toward their destinations, which can achieve traffic optimization in urban simulations. This paper presents the results of applying this novel model to a large-scale real-world case in different urban traffic congestion situations. Extensive experimental simulations in various actual cities have been carried out. Our results in the extreme case are encouraging: The prediction accuracy of traffic congestions is almost 89%, and the variance of prediction road density is less than 0.15. [ABSTRACT FROM AUTHOR]

We consider a two-node tandem queueing network in which the upstream queue is M/G/1 and each job reuses its upstream service requirement when moving to the downstream queue. Both servers employ the first-in-first-out policy. We investigate the amount of work in the second queue at certain embedded arrival time points, namely when the upstream queue has just emptied. We focus on the case of infinite-variance service times and obtain a heavy traffic process limit for the embedded Markov chain. [ABSTRACT FROM AUTHOR]

Taking advantage of peer-to-peer transmission underlying cellular networks, device-to-device (D2D) communications offer various benefits such as coverage extension, traffic offloading, and improved energy efficiency. In this paper, we focus on a promising scenario where a D2D local area network is formed to relay packets for an out-of-coverage source device. A one-sided auction model is formulated from a unique perspective in which the source device decides the allocation of its packets among the helpers and charges reserve payments to the helpers according to their bids. The winning helpers only collect rewards from the source's deposit at the base station when the assigned packets are successfully relayed. In this model, we further take into account the budget constraints of the helpers to capture the helpers' resource limits and the risks that the helpers are willing to take. Based on this model, we propose three auction mechanisms targeting economic properties such as individual rationality, efficiency, and truthfulness. An enhanced Martello & Toth algorithm is first developed for the VCG-based auction to determine packet allocation that optimizes the source's quality of service. The probabilistic entrance auction mechanism uses sequential second price auction to achieve a low computational cost. The randomized mechanism involves a randomization over the above two mechanisms to satisfy certain requirement for social welfare while minimizing the computational time. We also conduct extensive simulations to examine the performance of the proposed mechanisms. [ABSTRACT FROM AUTHOR]

Differing from the traditional traffic, connected vehicles enable information sharing between vehicles at vicinity to facilitate cooperative path planning, which may positively affect the congestion propagation process. In this paper, we propose to modeling and simulating traffic congestion propagation in such new situation where the path planning is driven by a temporal or spatial preference with aims at investigating the effects of various factors on traffic congestion, e.g. traffic light, mobility pattern, traffic density and communication radius. Simulations show that the traffic congestion is indeed affected by the concerned factors; however, the traffic congestion fails to be mitigated persistently as the communication radius increases beyond a certain threshold. The result is helpful for understanding the traffic congestion propagation in connected vehicles. [ABSTRACT FROM AUTHOR]

In recent years, the topic of car-following has experimented an increased importance in traffic engineering and safety research. This has become a very interesting topic because of the development of driverless cars (Google driverless cars, ). Driving models which describe the interaction between adjacent vehicles in the same lane have a big interest in simulation modeling, such as the Quick-Thinking-Driver model. A non-linear version of it can be given using the logistic map, and then chaos appears. We show that an infinite-dimensional version of the linear model presents a chaotic behaviour using the same approach as for studying chaos of death models of cell growth. [ABSTRACT FROM AUTHOR]

Using a model of traffic flow dynamics as an example, we study the phenomenon of self-organization in large systems under the influence of a random force. [ABSTRACT FROM AUTHOR]

We present a microscopic model for the dynamics of a transportation flow based on cellular automata with improved lane changing rules. With this model, we study the influence of crossing transportation flows on the throughput of a multilane highway. For a two-lane highway with an exit, we obtain space-time density diagrams for different distributions of exiting cars along the lanes. Our results indicate how important traffic control is for the throughput of automobile roads. [ABSTRACT FROM AUTHOR]

Severe weather conditions and inherent uncertainties in various components of railway traffic systems can lead to equipment breakdown and reduced capacity on tracks and stations. This paper formulates a two-stage fuzzy optimization model to obtain a robust rescheduling plan under irregular traffic conditions, and a scenario-based representation is adapted to characterize fuzzy recovery time durations on a double-track railway line. The model aims to minimize the expected total delay time in the rescheduled train schedule with respect to the original timetable. Two decomposed sub-models are further developed corresponding to the trains in different directions, and then GAMS optimization software is used to obtain the robust rescheduling plan. The numerical experiments demonstrate the effectiveness of the proposed approaches. [ABSTRACT FROM AUTHOR]

There has been a debate in the transportation research community over the validity of a class of traffic flow models. These models have the peculiar property that one of its characteristic speeds is faster than that of vehicular traffic. This note attempts to provide an overview of the diverging views on how to interpret this property, and specific comments on the interpretation of Helbing and Johansson [ On the controversy around Daganzo’s requiem for and Aw-Rascle’s resurrection of second-order traffic flow models, Eur. Phys. J. B (2009), DOI: 10.1140/epjb/e2009-00182-7]. We showed that having faster-than-traffic characteristics does produce counterintuitive predictions, and they cannot be explained away by a linear stability analysis. As such, the existence of such characteristics must be justified by the physics of traffic, and verified through empirical observations. [ABSTRACT FROM AUTHOR]

Driven many-particle systems with nonlinear interactions are known to often display multi-stability, i.e. depending on the respective initial condition, there may be different outcomes. Here, we study this phenomenon for traffic models, some of which show stable and linearly unstable density regimes, but areas of metastability in between. In these areas, perturbations larger than a certain critical amplitude will cause a lasting breakdown of traffic, while smaller ones will fade away. While there are common methods to study linear instability, non-linear instability had to be studied numerically in the past. Here, we present an analytical study for the optimal velocity model with a stepwise specification of the optimal velocity function and a simple kind of perturbation. Despite various approximations, the analytical results are shown to reproduce numerical results very well. [ABSTRACT FROM AUTHOR]

This contribution compares several different approaches allowing one to derive macroscopic traffic equation directly from microscopic car-following models. While it is shown that some conventional approaches lead to theoretical problems, it is proposed to use an approach reminding of smoothed particle hydrodynamics to avoid gradient expansions. The derivation circumvents approximations and, therefore, demonstrates the large range of validity of macroscopic traffic equations, without the need of averaging over many vehicles. It also gives an expression for the “traffic pressure”, which generalizes previously used formulas. Furthermore, the method avoids theoretical inconsistencies of macroscopic traffic models, which have been criticized in the past by Daganzo and others. [ABSTRACT FROM AUTHOR]

Traffic is highly influenced by network structure and human behaviour. Small changes in the human behaviour can lead to huge changes in the load of a traffic network. Current transportation models do not, and most of them cannot, research such random behaviour but always calculate a steady state. In our multi-agent transport simulation, we frequently observe seemingly random “network breakdowns”, huge traffic jams that spread over a big part of the network, making a normal traffic flow impossible. This paper describes the investigations that were performed on the results of our large-scale multi-agent transport simulations in an attempt to contribute to the better understanding of the dynamic processes in such simulations and, hopefully, better understanding and modelling of the real-world. [ABSTRACT FROM AUTHOR]

By comparing microscopic traffic flow models with a different number of phases in the context of a simple scenario, the similarities as well as the differences of the various traffic flow models can be discussed. It turns out that there is a certain range of traffic flow conditions, where it is difficult to discern the space-time patterns produced by the different models. However, there are some other regions in the parameter space, where clear differences can be detected. Although the results obtained here cannot directly transformed into a real test with real-world data, they may help to finally define realistic scenarios which would result in a clear decision about which model describes reality best. [ABSTRACT FROM AUTHOR]

Mathematical models of control of traffic in the Internet are considered. Analysis is made on approaches, models, interpretation methods, and questions arising in problems of congestion control on the basis of the interaction of TCP/AQM protocols. [ABSTRACT FROM AUTHOR]

Sensors are used to monitor traffic in networks. For example, in transportation networks, they may be used to measure traffic volumes on given arcs and paths of the network. This paper refers to anactivesensor when it reads identifications of vehicles, including their routes in the network, that the vehicles actively provide when they use the network. On the other hand, the conventional inductance loop detectors arepassivesensors that mostlycountvehicles at points in a network to obtain traffic volumes (e.g., vehicles per hour) on a lane or road of the network.This paper introduces a new set of network location problems that determine where to locate active sensors in order to monitor or manage particular classes of identified traffic streams. In particular, it focuses on the development of two generic locational decision models for active sensors, which seek to answer these questions: (1) “How many and where should such sensors be located to obtain sufficient information on flow volumes on specified paths?”, and (2) “Given that the traffic management planners have already located count detectors on some network arcs, how many and where should active sensors be located to get the maximum information on flow volumes on specified paths?”The problem is formulated and analyzed for three different scenarios depending on whether there are already count detectors on arcs and if so, whether all the arcs or a fraction of them have them. Location of an active sensor results in a set of linear equations in path flow variables, whose solution provide the path flows. The general problem, which is related to the set-covering problem, is shown to be NP-Hard, but special cases are devised, where an arc may carry only two routes, that are shown to be polynomially solvable. New graph theoretic models and theorems are obtained for the latter cases, including the introduction of thegeneralized edge-covering by nodesproblem on thepath intersection graphfor these special cases. An exact algorithm for the special cases and an approximate one for the general case are presented. [ABSTRACT FROM AUTHOR]

A mathematical model for the distributed traffic control algorithm used in modern data transfer networks is designed and distributions of the important characteristics of the algorithm are derived. Numerical examples are given. [ABSTRACT FROM AUTHOR]