Realistic cellular automaton model for synchronized two-lane traffic [Elektronische Ressource] : simulation, validation, and applications / von Andreas Pottmeier

Andreas Pottmeier

Sujets

• Handel

Informations

• Publié par: universitat_duisburg-essen
• Publié le: 01 janvier 2008
• Nombre de lectures: 15
• Langue: English
• Poids de l'ouvrage: 5 Mo

Extrait

Realistic Cellular Automaton Model for
Synchronized Two-Lane Traffic
Simulation, Validation, and Applications
Vom Fachbereich Physik
der Universitat Duisburg-Essen¨
zur Erlangung des akademischen Grades
eines Doktors der Naturwissenschaften
genehmigte Dissertation
von
Andreas Pottmeier
aus
Krefeld
Referent: Prof. Dr. Michael Schreckenberg
Korreferent: Prof. Dr. Dietrich E. Wolf
Tag der mundlichen Prufung: 18. Dezember 2007¨ ¨Contents
Abstract iii
1 Preface 1
1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2 Measuring Traffic Observables 5
2.1 Measurement Observables . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.2 Experimentally Observed Traffic States . . . . . . . . . . . . . . . . . . . . 10
2.2.1 Free-Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.2.2 Wide Moving Jams and Stop-and-Go Traffic . . . . . . . . . . . . . 12
2.2.3 Synchronized Flow and Pinch Effect . . . . . . . . . . . . . . . . . . 13
2.2.4 Multi-Lane Characteristics . . . . . . . . . . . . . . . . . . . . . . . 15
3 Modeling Vehicular Traffic 19
3.1 Simple Stochastic CA Models . . . . . . . . . . . . . . . . . . . . . . . . . . 19
3.1.1 The Cellular Automaton Model by Nagel and Schreckenberg . . . . 20
3.1.2 The VDR Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
3.1.3 The BL Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
4 Model Validation 27
4.1 Aggregated Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
4.1.1 Local Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
4.1.2 Global Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . 29
4.1.3 Traffic Patterns . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
4.2 Single-Vehicle Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
5 The Model by Lee et al. 33
5.1 Definition of the Single-Lane Model. . . . . . . . . . . . . . . . . . . . . . . 34
5.1.1 Basic Features . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
5.1.2 System Initialization . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
5.2 Comparison with Empirical Single-Vehicle Data . . . . . . . . . . . . . . . . 41
5.2.1 Time-Headway Distribution . . . . . . . . . . . . . . . . . . . . . . . 42
5.2.2 Correlation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
5.2.3 Gap Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
5.2.4 Optimal-Velocity Function. . . . . . . . . . . . . . . . . . . . . . . . 46
5.3 Life-Time of Synchronized Traffic . . . . . . . . . . . . . . . . . . . . . . . . 47
5.4 Model Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
5.4.1 Attitude . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
5.4.2 Reduction of the Attitude . . . . . . . . . . . . . . . . . . . . . . . . 53
5.4.3 Randomization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
iContents
5.4.4 Influence of the Additional Safety Gap . . . . . . . . . . . . . . . . . 58
5.4.5 Investigation of t . . . . . . . . . . . . . . . . . . . . . . . . . . . 60safe
5.5 Accidents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
5.5.1 Accidents’ Reasons . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
5.5.2 Accident Frequency . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
5.5.3 Concept of Proof . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
5.6 Accident Avoidance and Modified Models . . . . . . . . . . . . . . . . . . . 70
5.6.1 Simplified Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
5.6.2 Safe Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
5.7 Open Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
5.8 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
6 Multi-lane Traffic: Extension of the Model by Lee et al. 83
6.1 Two-Lane Traffic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
6.1.1 Lane Changing Rules . . . . . . . . . . . . . . . . . . . . . . . . . . 85
6.1.2 Basic Features and Model Validation . . . . . . . . . . . . . . . . . . 88
6.2 Introduction of Trucks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
6.3 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
7 Defects 103
7.1 Modeling of On-Ramps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
7.1.1 Single-Lane System. . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
7.1.2 Life-Time of Synchronized Traffic at an On-ramp . . . . . . . . . . . 110
7.1.3 Insertion Velocity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
7.1.4 Insertion Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
7.1.5 Time Scales and the Connection to Ramp Metering Algorithms . . . 115
7.1.6 Two-Lane System . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
7.1.7 (De-)Coupled Lanes . . . . . . . . . . . . . . . . . . . . . . . . . . . 120
7.2 Localized Defects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122
7.2.1 Velocity Defect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122
7.2.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
7.3 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
A Testing Accident Behaviour 127
A.1 Basic Definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127
A.2 Calculating the Set of Safe States . . . . . . . . . . . . . . . . . . . . . . . . 127
A.3 Introducing State Classes . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128
A.4 Specializing to the Model by Lee et al. . . . . . . . . . . . . . . . . . . . . . 130
A.5 Results. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133
Bibliography 135
Summary and Outlook 147
Zusammenfassung und Ausblick 151
Danksagung 155
iiAbstract
An objective of current traffic-research is the realistic description of vehicular traffic by
means of traffic modeling. Since no present traffic model is capable to reproduce all
empirical characteristics, the development of such a model is of main interest. Thus, this
thesis presents a realistic cellular automaton model for multi-lane traffic and validates it
by means of empirical single-vehicle data. In contrast to present approaches a limited
deceleration capability is assigned to the vehicles. Moreover, the velocity of the vehicles
is determined on the basis of the local neighborhood. Therefore, the drivers are divided
into optimistic or pessimistic drivers. The former may underestimate their safety distance
if their neighborhood admits it. The latter always keep a safe distance. This results in
a convincing reproduction of the microscopic and macroscopic features of synchronized
traffic. The anticipation of the leader’s velocity is thereby essential for the reproduction
of synchronized traffic.
This thesis is divided into three main parts. The first one validates the single-lane model
by Lee et al. by means of empirical data. This approach builds the basis for the further
developmentsofthisthesis. Then,thefundamentalcharacteristicsaresummarized. Thisis
followedbynewresultsconcerningthecomparisonwithempiricalfindingsthatconfirmthe
good reproduction of the reality. The analyses also show the important and fundamental
property of synchronized traffic: its density dependent life-time. Nevertheless, accidents
appear in the stationary state. Thus, the model approach has to be modified so that it is
capable to model multi-lane traffic.
The adapted model is enhanced in the next part by a realistic lane change algorithm. A
multi-lane model is formulated that reproduces the empirical data even better than the
single-laneapproach. Moreover,specifictwo-lanecharacteristicslikethedensitydependent
lane change frequency are reproduced as well as the coupling of the lanes. Moreover, if
the velocity difference between the two lanes is too high, the lanes may decouple, i.e.,
different traffic states emerge on the two lanes. This is a direct consequence of the limited
deceleration capability of the vehicles.
Inthelastpartofthethesisthetwo-lanemodelisappliedtoopensystemswithbottlenecks
like an on-ramp and a speed-limit. The empirically observed complex structures of the
synchronized traffic are reproduced here in great detail. Thus, the approach discussed in
this thesis exceeds the present in the degree of realism. Because of the reliability of the
presented model it is supposed to be implemented to simulate the whole network of North
Rhine-Westphalia.
iiiAbstract
iv1 Preface
1.1 Introduction
For many road users traffic congestions are a daily recurring experience and they spent
much time on the road standing in a traffic jam although much effort is made to avoid
such situations.
In particular, two factors worsen the situation: On the one hand, the amount of vehicular
traffic still rises. Especially, the number of trucks increses permanently. On the other
hand, the extension of the network is seldom possible although the maximum capacity of
many pa