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E-grāmata: Introduction to Network Traffic Flow Theory: Principles, Concepts, Models, and Methods

(The Institute of Transportation Studies, University of California, Irvine, California, USA)
  • Formāts: EPUB+DRM
  • Izdošanas datums: 13-Apr-2021
  • Izdevniecība: Elsevier Science Publishing Co Inc
  • Valoda: eng
  • ISBN-13: 9780128158418
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Introduction to Network Traffic Flow Theory: Principles, Concepts, Models, and MethodsPalielināt
  • Formāts: EPUB+DRM
  • Izdošanas datums: 13-Apr-2021
  • Izdevniecība: Elsevier Science Publishing Co Inc
  • Valoda: eng
  • ISBN-13: 9780128158418
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Introduction to Network Traffic Flow Theory: Modeling, Analysis, Simulation, and Empirics provides a comprehensive introduction to modern theories for modeling, mathematical analysis and traffic simulations in road networks. The book breaks ground, addressing traffic flow theory in a network setting and providing researchers and transportation professionals with a better understanding of how network traffic flows behave, how congestion builds and dissipates, and how to develop strategies to alleviate network traffic congestion. The book also shows how network traffic flow theory is key to understanding traffic estimation, control, management and planning.

Users wills find this to be a great resource on both theory and applications across a wide swath of subjects, including road networks and reduced traffic congestion.

  • Covers the most theoretically and practically relevant network traffic flow theories
  • Provides a systematic introduction to traditional and recently developed models, including cell transmission, link transmission, link queue, point queue, macroscopic and microscopic models, junction models and network stationary states
  • Applies modern network traffic flow theory to real-world applications in modeling, analysis, estimation, control, management and planning
Preface xiii
Acknowledgments xvii
Acronyms xix
Notations xxi
I Basics
1 Introduction
1.1 Transportation system analysis
3(2)
1.2 Traffic flow theory
5(3)
1.3 Principles, concepts, models, and methods in traffic flow theory
8(1)
1.4 A brief overview of the book
9(4)
Notes
11(1)
Problems
12(1)
2 Definitions of variables
2.1 Three traffic scenarios and space-time diagrams
13(2)
2.2 The three-dimensional representation of traffic flow and primary variables
15(3)
2.3 More derived variables in three coordinates
18(4)
2.3.1 In the flow coordinates
18(1)
2.3.2 In the trajectory coordinates
19(1)
2.3.3 In the schedule coordinates
20(1)
2.3.4 Higher-order derivatives of the primary variables
21(1)
2.3.5 Relationships among the secondary variables
21(1)
2.4 Detection
22(5)
2.4.1 Edie's formulas
22(2)
2.4.2 Detectors
24(3)
2.5 Multi-commodity traffic on a multilane road
27(6)
2.5.1 Multi-commodity traffic
27(1)
2.5.2 Lane-changing traffic
28(1)
Notes
29(2)
Problems
31(2)
3 Basic principles
3.1 Conservation laws
33(4)
3.1.1 In the flow coordinates
34(1)
3.1.2 In other coordinates
35(1)
3.1.3 Conservation laws in other traffic systems
35(2)
3.2 Collision-free condition and other first-order constraints
37(2)
3.2.1 Constraints on density and jpacing
37(1)
3.2.2 Constraints on speed and pace
37(1)
3.2.3 Constraints on flow-rate and headway
38(1)
3.2.4 Clearance and time gap
38(1)
3.3 Fundamental diagram
39(13)
3.3.1 Derivation and observation
39(1)
3.3.2 General fundamental diagrams
40(3)
3.3.3 The Greenshields fundamental diagram
43(1)
3.3.4 The triangular fundamental diagram
43(3)
3.3.5 Fundamental diagrams in other secondary variables
46(2)
3.3.6 Non-concave flow-density relations and non-decreasing speed-density relations
48(1)
3.3.7 Fundamental diagrams of inhomogeneous roads and lane-changing traffic
49(1)
3.3.8 Multi-commodity fundamental diagrams
50(1)
3.3.9 Network fundamental diagram
51(1)
3.4 Bounded acceleration and higher-order constraints
52(5)
Notes
53(2)
Problems
55(2)
4 Basic concepts
4.1 Steady states
57(1)
4.2 The simple lead-vehicle problem
58(2)
4.3 Stationary states
60(3)
4.3.1 Definition
60(1)
4.3.2 Equilibrium stationary state in a lane-drop/sag/tunnel zone
61(1)
4.3.3 Considering bounded acceleration
62(1)
4.4 Bottlenecks on a road
63(3)
4.4.1 Capacity reduction
64(1)
4.4.2 More on lane-drop bottlenecks
64(1)
4.4.3 Capacity drop
65(1)
4.5 First-in-first-out (FIFO)
66(3)
4.5.1 FIFO multilane traffic
67(1)
4.5.2 Non-FIFO traffic
68(1)
4.6 First-in-first-out and unifiable equilibrium states
69(7)
Notes
70(1)
Problems
71(5)
II First-Order Models
5 The Lighthill-Whitham-Richards (LWR) model
5.1 Model derivation
76(3)
5.1.1 With the Greenshields fundamental diagram
76(1)
5.1.2 Equivalent formulations in other coordinates
77(1)
5.1.3 Initial and boundary conditions
77(2)
5.2 Extensions
79(3)
5.3 The initial value problem with the triangular fundamental diagram and linear transport equation
82(3)
5.3.1 Under-critical initial conditions
82(1)
5.3.2 Over-critical initial conditions
83(1)
5.3.3 Mixed under- and over-critical initial conditions
84(1)
5.4 General fundamental diagram and characteristic wave
85(2)
5.4.1 Steady solutions
85(1)
5.4.2 Nearly steady solutions and characteristic wave
85(2)
5.5 Solutions to the Riemann problem, shock and rarefaction waves, and entropy condition
87(5)
5.5.1 Shockwave
88(1)
5.5.2 Rarefaction wave
89(1)
5.5.3 Entropy condition
90(1)
5.5.4 Riemann solutions with the triangular fundamental diagram
91(1)
5.6 Stationary states and boundary fluxes in Riemann solutions
92(2)
5.7 Inhomogeneous LWR model
94(5)
5.7.1 Location-dependent speed limits
94(3)
5.7.2 Location-dependent number of lanes
97(2)
5.8 An example with a moving bottleneck
99(6)
Notes
101(1)
Problems
102(3)
6 The Cell Transmission Model (CTM)
6.1 Numerical methods for solving the LWR model
105(4)
6.1.1 Finite difference methods
107(1)
6.1.2 The Godunov method
108(1)
6.2 The Cell Transmission Model
109(7)
6.2.1 Demand and supply
109(3)
6.2.2 Boundary flux function
112(1)
6.2.3 Boundary conditions
113(1)
6.2.4 The CTM
113(3)
6.2.5 Numerical accuracy and computational cost
116(1)
6.3 Stationary states on a link
116(1)
6.4 Numerical solutions to the Riemann problem
117(3)
6.4.1 Shock wave
118(1)
6.4.2 Rarefaction wave
118(2)
6.5 Generalized CTM for link traffic
120(3)
6.5.1 Inhomogeneous roads
120(1)
6.5.2 Multi-commodity models
121(2)
6.6 Junction models
123(10)
6.6.1 Diverge models
125(1)
6.6.2 Merge models
126(1)
6.6.3 General junction models
127(1)
Notes
127(3)
Problems
130(3)
7 Newell's simplified kinematic wave model
7.1 The Hamilton-Jacobi equations and the Hopf-Lax formula for the LWR model
133(8)
7.1.1 The four Hamilton-Jacobi equations equivalent to the LWR model
134(1)
7.1.2 The variational principle
134(2)
7.1.3 The Hopf-Lax formula
136(3)
7.1.4 The Riemann problem
139(2)
7.2 Newell's simplified kinematic wave model
141(6)
7.2.1 Derivation
143(1)
7.2.2 Properties
144(2)
7.2.3 Newell's model in the trajectory coordinates
146(1)
7.3 Queueing dynamics on a road segment
147(4)
Notes
148(1)
Problems
149(2)
8 The Link Transmission Model (LTM)
8.1 Basic variables
151(1)
8.2 New link variables: link demand, supply, queue, and vacancy
152(4)
8.3 Continuous Link Transmission Model
156(1)
8.4 Discrete Link Transmission Model
157(2)
8.5 Homogeneous signalized road networks
159(2)
8.6 Stationary states on a link
161(4)
8.6.1 Definition
161(1)
8.6.2 Simple boundary value problem for a road segment
161(2)
Notes
163(1)
Problems
163(2)
9 Newell's simplified car-following model
9.1 Derivation
165(3)
9.2 Properties
168(3)
9.2.1 First-order principles
168(1)
9.2.2 Equivalent formulations
169(2)
9.3 Applications
171(7)
9.3.1 Simple accelerating problem (queue discharge problem)
171(1)
9.3.2 Simple braking problem
172(1)
Notes
173(1)
Problems
173(5)
III Queueing Models
10 The link queue model
10.1 Link density, demand, and supply
178(1)
10.1.1 Basic relations
178(1)
10.1.2 Definitions of link demand and supply
179(1)
10.2 Link queue model
179(2)
10.2.1 Continuous version
180(1)
10.2.2 Discrete version
180(1)
10.3 Well-defined and collision-free conditions
181(1)
10.4 Simple boundary value problem
182(3)
10.4.1 Stationary states
182(2)
10.4.2 Dynamic solution of a simple boundary value problem
184(1)
10.5 Applications and extensions
185(6)
10.5.1 Network fundamental diagram on a signalized ring road
185(1)
10.5.2 Modified demand function and the queue discharge problem
185(2)
Notes
187(1)
Problems
188(3)
11 Point queue model
11.1 Derivation
191(3)
11.1.1 Point queue as a limit of a road segment
191(2)
11.1.2 Definitions of queue and vacancy sizes and internal demand and supply
193(1)
11.2 Equivalent formulations
194(2)
11.2.1 Continuous versions
194(1)
11.2.2 Discrete versions
195(1)
11.3 Properties
196(4)
11.3.1 Queueing times
196(1)
11.3.2 Integral version
197(2)
11.3.3 With a constant external supply
199(1)
11.4 Departure time choice at a single bottleneck
200(9)
11.4.1 Costs
200(2)
11.4.2 User equilibrium
202(2)
Notes
204(1)
Problems
205(4)
12 The bathtub model
12.1 A unified space dimension
209(2)
12.1.1 Traditional transportation system analysis
209(1)
12.1.2 A new paradigm
210(1)
12.2 Definitions of network-wide trip variables
211(12)
12.2.1 Travel demand
211(4)
12.2.2 Active trips
215(3)
12.2.3 Averages speed and completion rates
218(4)
12.2.4 A network queue
222(1)
12.3 Three conservation equations
223(4)
12.3.1 Conservation in total number of trips
223(1)
12.3.2 Conservation in the trip-miles-traveled
223(1)
12.3.3 Conservation in the relative number of trips
224(2)
12.3.4 Relationship among the three conservation laws
226(1)
12.4 Three simplification assumptions
227(9)
12.4.1 The bathtub assumption
227(5)
12.4.2 Network fundamental diagram
232(2)
12.4.3 Time-independent negative exponential distribution of trip distances
234(2)
12.5 Bathtub models
236(2)
12.5.1 Derivation
236(1)
12.5.2 Vickrey's bathtub model
237(1)
12.6 Numerical methods
238(5)
12.6.1 A numerical method for solving the integral form
238(1)
12.6.2 A numerical method for solving the differential form
238(1)
12.6.3 A numerical example
239(1)
Notes
239(3)
Problems
242(1)
Bibliography 243(10)
Index 253
Wenlong Jin is an Associate Professor in the Institute of Transportation Studies, at the University of California, Irvine, focusing on the study of drivers' individual choice behaviours (trajectories) and collective queueing processes (cumulative flows). His research interests include modeling and analysing dynamic and stationary traffic patterns at bottlenecks in road networks, using junction models, cell transmission models, link transmission models, capacity drop models, and network stationary models. He has published more than 40 journal articles, including in Elseviers Transportation Research Part B: Methodological (for which he serves on the Editorial Advisory Board), and Transportation Research Part C: Emerging Technologies.
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