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

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）

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

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

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.

u-k models k kj k0 qm u0 uf

q-u models u uf k0 u0 kj qm q

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

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?

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

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?

Greenberg Feasible Region Underwood Greenshields Northwestern

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