This document summarizes an assignment on modeling traffic flow using optimal speed models. It discusses three types of traffic models, with a focus on microscopic models that model individual vehicle behavior. Optimal speed models assume each driver aims to travel at a safe speed based on the distance to the vehicle ahead. The assignment covers the theoretical basis of optimal speed models, their ability to describe traffic properties like congestion formation, and applications such as analyzing rear-end collisions and suppressing traffic jams.

1. MASTER OF ENGINEERINGCLASS ASSIGNMENT
Civil Engineering Department
Bayero University Kano
SPS/16/MCE/00080
CourseLecturer
Prof. H.M.Alhassan
MAY,2017

2. INTRODUCTION:
•Traffic flow model are models
concerned with analytical formulation
of traffic phenomenon, mechanisms
and extension of these formulations to
realize greater understanding in
traffic.
•There are three(3) types of traffic
models, these are: macroscopic,
mesoscopic and microscopic traffic
flow models.

3. MICROSCOPIC TRAFFIC MODEL
• A microscopic model describes the car
following behaviour as well as lane
changing behaviour of each vehicle in
traffic.
• Several theories have been proposed to
model car following behaviour which can
be divided into three classes based on
behavioural assumptions namely: safe
distance models, stimulus response models
and optimal speed models.

4. OPTIMALSPEED MODEL
•In car following model, the followers
acceleration tends to zero in the
absence of leader.
•To remedy this, another model was
introduced based on the assumption
that each driver has a safe speed
which depends on distance headway
of the leader. This modeling approach
is called OPTIMAL SPEED.

5. THEORETICAL BASIS
• OSM is a traffic flow model proposed by
Bando et al.
• The governing equation is as follows
 dx i/dt = vi
 dvi/dt = a [V(xi+1-xi)-vi]
Positions Xi and velocities Vi of cars, the
parameter “a” is the sensitivity denoting
speed of response.

6. •This OS model describes the following
features
A car will keep the maximum speed
with enough the distance to the next
car.
A car tries to run with optimal
velocity determined by the distance
to the next car.

7. APPLICATION
• Optimal velocity models are also used to:
Describe many properties of traffic flows
Evolution of traffic congestion
Formation of stop and go waves
Analysis of rear end collision
Application to intelligent transport
system, especially how to suppress the
emergence of traffic congestion.

8. APPLICATION
• Optimal velocity models are also used to:
Describe many properties of traffic flows
Evolution of traffic congestion
Formation of stop and go waves
Analysis of rear end collision
Application to intelligent transport
system, especially how to suppress the
emergence of traffic congestion.

9. CONCLUSION
• The microscopic car-following model is a
favorite type of traffic flow theory to
describe the individual behaviour of
drivers. The most well known car-following
model the optimal velocity (OV) model,
which has successfully revealed the
dynamical evolution process of traffic
congestion in a simple way. Thereafter,
inspired by the OV model, some new car-
following models were successively put
forward to describe the nature of traffic
more realistically.

10. REFERENCE
• Bando, M.,K. Hasebe, A. Nakayama, A. Shibata and Y.
Sugiyama (1994). Structure Stability of Congestion on Traffic
Dynamics. Japan J. Indust. Appl. Math., 11(2), 203-223
• Bando, M.,K. Hasebe, A. Nakayama, A. Shibata and Y.
Sugiyama (1995). Dynamical Model of Traffic Congestion and
Numerical Simulation. Physical Reviews E, 51(2), 1035-1042
• M. Bando, K. Hasebe, K. Nakanishi, A. Nakayama, Phys. Rev.
E 58 (1998) 5429
• May, A.D., 1990. Traffic Flow Fundamentals. Prentice-Hall,
New York, USA.
• Zhu, W., Liu, Y., 2008. A total generalized optimal velocity
model and its numerical tests. Journal of Shanghai Jiaotong
University (Science), 13(2):166-170.[doi:10. 1007/s12204-008-
0166-9]