1. Traffic Stream Models Basics Field Data Models Trivariate relationship
Bivariate relationships
Field Data
Field locations
Field observations
Models
Single- and multi-regime models
Family of models
12/26/05
Traffic stream models

2. Glossary Traffic stream models 交通流模型 Free-flow regime 自由流段
Transitional-flow regime 过渡流段
Congested-flow regime 阻塞流段
Lane drop 道路变窄
Single-regime model 单个模型（单枝模型）
Multiregime model 分段模型（多枝模型）

3. Basics Trivariate relationship Triple data: (qi, ki, ui)
Three dimension curve Next page…
Qualitatively description, see Textbook p.285
Quantitatively description Models
Basic equation – trivariate relationship
Traffic stream models – bivariate relationships

4. Greenshields’models Developed by Greenshields in 1935
The typical models which are still frequently used now
How to develop the models? 18 13
104 7
Lack of data 39 12 51

5. Model development Statistics least square method Model forms
Boundary conditions: k=0, u=uf; k=kj, u=0
Optimum condition: k=k0, u=u0, q→qmax
Three types of models: u-k, q-u, q-k
u-k models: used for theoretical work
q-u models: used for capacity analysis
q-k models: considered to be basic equation, used for shock wave analysis, etc.

6. u-k models k kj k0 qm u0 uf

7. q-u models u uf k0 u0 kj qm q

8. q-k models q u0 uw qm uf A
wAB B k0 kj

9. Field data Importance of field location
To obtain complete theoretical curves, the data collection must be taken at the right location during a selected time period
An example of a freeway, see Fig.10-2, p.288
How to conclude the results?......p.290
Field observations
Highspeed freeway data (Los Angeles, 1976)
Freeway data (55mph speed limit, Chicago,1967)
Tunnel data (New York, 1967)
Arterial street data (United Kingdom, 1987)
What are the meaningful results of these data sets?

10. Strengths and weakness?
Models
Single-regime models
Greenshields
Greenberg
Underwood
Northwestern
Multiregime models
Edie
Deficiencies?
Strengths and weakness?

11. Family of models What the relationships between them?
Generalized car-following model
Car-following models --- microscopic
Traffic stream models --- macroscopic
What the relationships between them?

12. Greenberg
Feasible
Region
Underwood
Greenshields
Northwestern

14. u u k0 u0 k kj kj qm q k0 qm q u0 uf u q u0 qm uf k k0 kj k