Shockwave Analysis on Motorways and Possibility of Damping by Autonomous Vehicles

Motamedidehkordi, Nassim; Benz, Thomas; Margreiter, Martin

doi:10.1007/978-3-319-20855-8_4

Cited by 5 publications

(3 citation statements)

References 7 publications

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“…2), which have been made and/or reviewed, for example, in [19,[58][59][60][61][62][63], are invalid for the real word. Therefore, simulation approaches of [19,[58][59][60][61][62][63] lead to incorrect conclusions about the impact of ACC vehicles as well as of automatic driving on real traffic flow.…”

Section: Effect Of Automatic Driving On Traffic Flowmentioning

confidence: 97%

Failure of classical traffic flow theories: a critical review

Kerner

2015

Elektrotech. Inftech.

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We explain that the fundamental empirical basis for automatic driving, reliable control and optimization of traffic and transportation networks is the set of empirical features of traffic breakdown at a road bottleneck. We show why generally accepted traffic and transportation theories and models are not consistent with this empirical fundament of traffic science. In particular, these classical traffic theories are as follows: (i) the Lighthill-Whitham-Richards (LWR) theory and traffic flow models in the framework of the LWR theory (for example, Daganzo's cell transmission model) that explain traffic breakdown through a fundamental diagram of traffic flow, (ii) General Motors (GM) class of traffic-flow models that explain traffic breakdown through traffic flow instability due to a driver reaction time (for example, the following well-known models belong to the GM model class: Gipps's model, Payne's model, Newell's optimal velocity (OV) model, Wiedemann's model (VISSIM traffic simulation tool), Bando et al. OV model, Treiber's Intelligent Driver Model, Krauß model (SUMO tool), the Aw-Rascle model), (iii) the classical understanding of stochastic highway capacity, and (iv) Wardrop's principles for dynamic control, assignment, and optimization of traffic and transportation networks.In turn, this can explain why dynamics network optimization and control approaches based on these classical traffic flow theories failed by their applications in the real world. We discuss why rather that the assumption about the existence of stochastic highway capacity, at any time instant there should be the infinite number of highway capacities within a range of the flow rate between a minimum capacity and a maximum capacity as assumed in three-phase theory introduced by the author. Because the assumption about the infinite number of highway capacities is consistent with the set of the fundamental empirical features of traffic breakdown at highway bottlenecks, this can be considered a theoretical fundament for the development of reliable automatic driving, control and optimization of vehicular traffic and transportation networks. We discuss briefly some features of the three-phase theory explaining the empirical fundament of transportation science.

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Section: Effect Of Automatic Driving On Traffic Flowmentioning

confidence: 97%

Failure of classical traffic flow theories: a critical review

Kerner

2015

Elektrotech. Inftech.

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“…Consequently the following data type would be able to model the dynamic behavior for the area of observation on a road or highway as a composition of shockwave's elements, i.e., flow, density, region's index and density range with multiple regions depicted in Figure 2. The function n_crossing:((sw → num) → real) accepts two variables of data types sw and num, respectively, and returns the number of vehicles crossed to or from the boundary of the region with index n (according to Equations (17) and (18) The function sw_list:((sw)list → (real)list) accepts an element of data type (sw)list and multiplies each element of the list with time (the required time length of the shockwave to be considered for the analysis) and then returns the new list of real values. This represents the space regions in the time-space diagram or a shockwave over a time length according to the shockwave analysis [13].…”

Section: B Formalization Of Shockwavementioning

confidence: 99%

“…As time progresses, this shockwave moves in the direction of the traffic flow, by creating new shockwaves that replace the earlier shockwaves, depending on the average values of these parameters in the respective regions. The analysis based on these foundations, called shockwave analysis [13], provides the rate of formation or dissipation of the congestion [18] and thus the identification of the congested areas by calculating the queue size/number of vehicles. The work in this paper identifies the mathematical foundations of transportation systems that are required to conduct such analysis within the sound core of a higher-order-logic theorem prover.…”

Section: Introductionmentioning

confidence: 99%

Toward the Formalization of Macroscopic Models of Traffic Flow Using Higher-Order-Logic Theorem Proving

et al. 2020

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Next-generation transportation will be integrated, interconnected and highly autonomous. One key challenge in traffic management is ensuring safety while maintaining the required level of service quality. In such future mobility systems, rigorous formalization and validation will thus become critical to ensure that the transportation network operates as intended, traffic properties are reliably maintained, and services resume in a timely manner after potential disruptions. Formal methods have recently gained considerable attention as a modeling and verification paradigm capable of addressing many challenges associated with next-generation transportation systems. In this regard, we propose to use higher-orderlogic theorem proving for formally analyzing transportation systems. As a first step towards this direction, we present a logical framework for the formal analysis of macroscopic models of traffic flow. Leveraging upon the high expressiveness of the underlying logic, we formally model the continuous components of macroscopic models while capturing their real behavior. In particular, we present a formalization of some foundation concepts of macroscopic models, namely density, flow rate, mean speed, relative occupancy, and shockwave using the higher-order-logic theorem prover HOL Light. This choice is primarily motivated by the fact that the macroscopic models deal with the traffic flow dynamics and thus play a vital role in planning strategies in allocating resources for implementing optimized and balanced transportation systems. For illustration, we perform the formal input-output and shockwave analysis of a German freeway. The case study demonstrated the practicability of this formal approach due to the high expressiveness of the underlying logic. The proposed research is first step towards formalizing the foundational mathematical theories and core concepts of traffic flow theory. This accomplishment will open new ways to plan and model various components of the transportation systems such as highway links, ramp metering, merging behavior and eventually address the problem of routing vehicles in a network of automated vehicles. INDEX TERMS Input-output analysis, macroscopic model, shockwave analysis, theorem proving, transportation modeling, validation methods.

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Introduction—The Reason for Paradigm Shift in Transportation Science

Kerner

2017

Breakdown in Traffic Networks

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Shockwave Analysis on Motorways and Possibility of Damping by Autonomous Vehicles

Cited by 5 publications

References 7 publications

Failure of classical traffic flow theories: a critical review

Failure of classical traffic flow theories: a critical review

Toward the Formalization of Macroscopic Models of Traffic Flow Using Higher-Order-Logic Theorem Proving

Introduction—The Reason for Paradigm Shift in Transportation Science

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