A Concise Introduction to Traffic Engineering: Theoretical Fundamentals and Case Studies

208 Pages·2021·7.032 MB·English

by  Marco Guerrieri, Raffaele Mauro

Springer Tracts in Civil Engineering
Marco Guerrieri
Raffaele Mauro
A Concise
Introduction
to Traffic
Engineering
Theoretical Fundamentals and Case
Studies
Springer Tracts in Civil Engineering
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Marco Guerrieri Raffaele Mauro
(cid:129)
A Concise Introduction
fi
to Traf c Engineering
Theoretical Fundamentals and Case Studies
123
MarcoGuerrieri Raffaele Mauro
DICAM DICAM
University of Trento University of Trento
Trento, Italy Trento, Italy
ISSN 2366-259X ISSN 2366-2603 (electronic)
SpringerTracts inCivil Engineering
ISBN978-3-030-60722-7 ISBN978-3-030-60723-4 (eBook)
https://doi.org/10.1007/978-3-030-60723-4
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Preface
This book contains a selection offundamentals topics of traffic engineering useful
for highways facilities design and control.
The treatment is basic, but it does not neglect to illustrate the most recent and
crucial theoretical aspects which are at the root of several Highway Engineering
applications, like, for instance, the essential aspects of highways traffic stream
reliability calculation and automated highway systems control.
In order for these topics to be better understood, varied illustrative examples of
applicationsareprovidedingreatdetail.Wehaveactuallysoughttouseanintuitive
and discursive, rather than formal and abstract style throughout the book.
Shortly, the contents are as follows:
(cid:129) Chapter 1 provides the definition of macroscopic traffic variables and the
deduction of the fundamental traffic flow relationship;
(cid:129) Chapter 2 offers an intuitive definition of transport demand, capacity and flow.
The main macroscopic flow models, levels of service and traffic hysteresis
phenomena are also dealt with;
(cid:129) Chapter3gives anintroduction totheflowcontinuityequation, dynamictraffic
flow models and kinematic and shock waves. Since these topics are usually
difficult for beginners, the mathematical treatment is highly detailed;
(cid:129) Chapter 4 describes some of the main microscopic models (linear and nonlin-
ear).Thesedynamictrafficmodelsinvolvestudyinglocalinstability,asymptotic
instability and flow breakdown. Moreover, a genealogy of the main traffic
models (macroscopic, mesoscopic and microscopic) is reviewed in a synthetic
way;
(cid:129) Chapter 5 deals with the fundamentals of random and traffic processes and
provides a very accurate description of probability models for arrival, speed,
headwayandvehiculardensityprocesses.Alsothemaincounting,headwayand
speed probability distributions are shown;
(cid:129) Chapter 6 presents an advanced method for estimating flow reliability on
highwaysanddescribesthecurrentsystemsofhighwaytrafficmanagementand
control. In this chapter, a rigorous capacity definition is offered. The basic
v
vi Preface
characteristics of the Automated Highway System are also introduced. Finally,
theHSMmethodtoestimate theannual crash frequencyexpectedonhighways
and the COPERT method to calculate the polluting emissions are both
illustrated;
(cid:129) Chapter 7 presents the gap acceptance theory, in that it is of great applicative
interest in studying road intersections. Therefore, some models for estimating
the critical gap and the follow-up time for at-grade unsignalized intersections
and roundabouts are described;
(cid:129) Chapter 8 deals with the models for studying queues in road transport systems
underaunitaryapproach.Theyaretheprobabilisticmodelsforstationarystate,
the deterministic solutions in congestion, and the heuristic solutions for sta-
tionary and non-stationary states. The treatment of these models is unusual but
can be directly applied to practical cases;
(cid:129) Chapter9dealswithunsignalizedintersectionsandmethodsfordeterminingthe
measures of effectiveness (MOE): waiting times and delays. To this regard, the
TRLmethodforestimatingcapacity,queues,delaysatthree-armintersectionsis
exemplified;
(cid:129) Chapter10covers signalizedintersections.TheHCM modelforthecalculation
and functional analysis of such intersections is illustrated in detail.
AndreaPompigna,Ph.D.inTransportationEngineering,istheauthorofChap.8.
We are deeply grateful to Andrea Pompigna also for his invaluable help in dis-
cussing critically the topics with us, as well as revising the whole book in a
systematic way.
Finally, we wish to thank Autostrade del Brennero S.p.A. (Trento) for sup-
portingourrecentresearchontrafficflowtheoryandcontrolatDICAM,University
of Trento.
Palermo, Italy Marco Guerrieri
Palma Campania (Naples), Italy Raffaele Mauro
July 2020
Contents
1 MacroscopicVariablesandFundamentalRelationshipsofTraffic
Flow Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 Interrupted and Uninterrupted Traffic Flows . . . . . . . . . . . . . . . 1
1.2 Inference of Macroscopic Flow Variables. . . . . . . . . . . . . . . . . 2
1.2.1 Traffic Variables Referred to the Time Domain . . . . . . 4
1.2.2 Traffic Flow, Traffic Volume and Capacity . . . . . . . . . 8
1.2.3 Peak Hour Factor. . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
1.2.4 Estimating of Design Hourly Volume DHV. . . . . . . . . 11
1.2.5 Traffic Variables Referred to the Space Domain. . . . . . 13
1.2.6 Fundamental Flow Relationship . . . . . . . . . . . . . . . . . 16
1.2.7 Traffic Flow Stationarity. . . . . . . . . . . . . . . . . . . . . . . 18
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
2 Macroscopic Traffic Flow Models . . . . . . . . . . . . . . . . . . . . . . . . . . 23
2.1 Transportation Demand, Capacity and Flow . . . . . . . . . . . . . . . 23
2.2 Relationship Between Macroscopic Traffic Flow Variables . . . . 26
2.3 Properties of the Mathematic Traffic Flow Models and
Operational Flow Conditions. . . . . . . . . . . . . . . . . . . . . . . . . . 27
2.3.1 Single-Regime Models . . . . . . . . . . . . . . . . . . . . . . . . 29
2.3.2 Levels of Service . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
2.3.3 Other Characterizations of the Operational Traffic
Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
2.4 Experimental Definition of a Traffic Flow Model . . . . . . . . . . . 35
2.5 Deterministic Multi-regime Traffic Flow Models. . . . . . . . . . . . 36
2.6 Physical Interpretation of the Capacity. . . . . . . . . . . . . . . . . . . 36
2.7 Hysteresis in Traffic Flows . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
2.8 Kerner’s Three-Phase Traffic Theory . . . . . . . . . . . . . . . . . . . . 38
2.9 Case Study: Service Levels According to Greenshields’
Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
vii
viii Contents
2.10 Case Study: Calibration of Greenshields’ Flow Model . . . . . . . 41
2.11 Case Study: Calibration of May’s Flow Model. . . . . . . . . . . . . 44
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
3 Continuity Flow Equation, Kinematic Waves and Shock Waves. . . 49
3.1 Fluid Dynamic Analogy for the Traffic Flow . . . . . . . . . . . . . . 49
3.1.1 Deduction of the Continuity Equation . . . . . . . . . . . . . 51
3.1.2 Boundary and Initial Conditions . . . . . . . . . . . . . . . . . 52
3.1.3 Kinematic Waves . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
3.1.4 Perturbations of the Traffic Flow and Speed. . . . . . . . . 57
3.2 The LWR Model and Shock Waves. . . . . . . . . . . . . . . . . . . . . 58
3.2.1 Case Study: Queue Formation and Dissipation Due
to Presence of a Heavy Vehicle on a Two-Lane
Undivided Highway . . . . . . . . . . . . . . . . . . . . . . . . . . 62
3.2.2 Case Study: Estimation of the Effects of an Accident
on the Flow in a Two-Lane Dual Carriageway
Highway . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
4 Microscopic Models and Traffic Instability. . . . . . . . . . . . . . . . . . . 65
4.1 Microscopic Models: Car-Following Theory. . . . . . . . . . . . . . . 65
4.2 Linear Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
4.3 Impulsive Variations of Vehicle Speeds: Traffic Instability
and Stop (‘phantom Traffic Jams’). . . . . . . . . . . . . . . . . . . . . . 67
4.3.1 Local Instability and Asymptotic Instability . . . . . . . . . 72
4.4 Non-linear Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
4.5 Derivation of Macroscopic Models from the Microscopic
Non-linear Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
4.6 Traffic Model Genealogy. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
5 Fundamentals of Random and Traffic Processes. . . . . . . . . . . . . . . 77
5.1 Traffic Processes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
5.2 Counting Probability Distributions. . . . . . . . . . . . . . . . . . . . . . 84
5.2.1 General Criterion for Selecting the Appropriate
Counting Probability Distribution . . . . . . . . . . . . . . . . 86
5.3 Probability Distribution for Time Headways. . . . . . . . . . . . . . . 94
5.4 Speed Processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
6 Traffic Management and Control Systems . . . . . . . . . . . . . . . . . . . 103
6.1 Preliminary Considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
6.2 Flow Reliability on Highways . . . . . . . . . . . . . . . . . . . . . . . . . 104
6.2.1 Case Study: Assessment of the Reliability Laws
from Traffic Surveys. . . . . . . . . . . . . . . . . . . . . . . . . . 106
Contents ix
6.3 The Ramp-Metering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108
6.3.1 System Analysis for an Isolated On-Ramp. . . . . . . . . . 109
6.3.2 System Analysis for On-Ramps and Off-Ramps . . . . . . 111
6.4 Hard Shoulder Running System. . . . . . . . . . . . . . . . . . . . . . . . 113
6.4.1 Capacity Estimation of Highways with HSR
System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
6.4.2 Case Study: Traffic Flow Parameters Estimation
After HSR System Activation . . . . . . . . . . . . . . . . . . . 114
6.5 Variable Speed Limits (VSL) . . . . . . . . . . . . . . . . . . . . . . . . . 116
6.6 Automated Highway System (AHS). . . . . . . . . . . . . . . . . . . . . 118
6.6.1 Estimation of the Increase in Lane Capacity. . . . . . . . . 119
6.7 C-ITS, C-Roads and Smart-Roads . . . . . . . . . . . . . . . . . . . . . . 120
6.7.1 C-ITS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120
6.7.2 C-Road Platform . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
6.7.3 Smart-Roads . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122
6.8 Crash Frequency Estimation: The HSM Method. . . . . . . . . . . . 123
6.9 Models for Estimating Traffic Pollutant Emissions . . . . . . . . . . 125
6.9.1 The Macroscopic Model COPERT . . . . . . . . . . . . . . . 125
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128
7 Interference Between Traffic Flows: The Gap Acceptance
Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131
7.1 Estimation of the Critical Gap and Follow-Up Time . . . . . . . . . 133
7.1.1 Estimation of the Average Critical Gap: Ashworth’s
Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134
7.1.2 Estimation of the Average Critical Gap: Miller’s
Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134
7.2 Characteristic Values of the Critical Gap and the Follow-Up
Time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135
7.2.1 T and T for Unsignalized Intersections . . . . . . . . . . . 135
c f
7.2.2 T and T for Roundabouts . . . . . . . . . . . . . . . . . . . . . 136
c f
7.3 TheTheoreticalCapacityofTrafficStreamsinanUnsignalized
At-Grade Intersection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139
8 Queue Formation: General Models. . . . . . . . . . . . . . . . . . . . . . . . . 141
8.1 Queuing Systems: Variables and Basic Relationships . . . . . . . . 142
8.1.1 Little’s Law . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146
8.2 Operating Conditions and Models for Waiting Systems. . . . . . . 146
8.3 Probabilistic Models for Steady-State. . . . . . . . . . . . . . . . . . . . 147
8.4 Deterministic Solutions in Congestion . . . . . . . . . . . . . . . . . . . 152
8.5 Heuristic Solutions for Steady and Non-steady States . . . . . . . . 155
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161