This document provides a review of optimal speed traffic models. It begins with introductions to traffic modeling approaches including microscopic and macroscopic models. Microscopic models describe individual vehicle dynamics while macroscopic models use aggregated quantities like density and flow. The optimal velocity model is then defined as a car-following model where vehicles accelerate/decelerate to match an optimal speed based on headway. Properties, applications, and limitations of the optimal velocity model are discussed. Research on extensions like the full velocity difference model is also summarized. The document concludes with recommendations for further studying simulation problems to improve understanding of jam formation and congestion dynamics.

1. PRESENTATION
R E V IE W O F O P T IM A L S P E E D T R A F F IC
M O D E L
Y U N U S A H A M I S U G A B A S AWA
( S P S / 1 6 / M E C / 0 0 0 6 6 )
M . E N G I N C I V I L E N G I N E E R I N G A S S I G N M E N T,
S U B M I T T E D
T O
P R O F, H . M . A L H A S S A N
C IV IL E N G IN E E R IG D E PA RT M E N T
B AY E R O U N IV E R S IT Y K A N O ,
N IG E R IA

2. GENERAL INTRODUCTION.
Recently, traffic problems have attracted
considerable attention, due to the fact that
traffic behavior is important in our lives.
When car density increases, traffic jams
appear. A variety of approaches have been
applied to describe the collective properties
of traffic flow: car-following models,
cellular automaton models, gas kinetic
models, and hydrodynamic models.

3. GENERAL INTRODUCTION CONT.
The traffic flow models are classified into the
deterministic and stochastic models. Nagel and
Schreckenberg have introduced a stochastic
cellular automaton model. It has been shown
that the start-stop waves (traffic jams) appear
in the congested traffic region as observed in
real freeway traffic. Bando et al. have proposed
the deterministic optimal velocity model in
which a car accelerates or decelerates according
to the dynamic equation of car motion with the
optimal velocity function.

4. INTRODUCTION AND HISTORY OF MODELS
MICROSCOPIC TRAFFIC MODELS
Microscopic traffic flow models describe
dynamics of traffic flow at the level of each
individual vehicle. They have existed since the
1960s with the typical car-following models.
• Car-following models describe the processes
in which drivers follow each other in the traffic
stream. The car-following process is of the
main processes in all microscopic models as
well as in modern traffic flow.

5. MICROSCOPIC TRAFFIC MODELS
• Microscopic traffic flow models describe
dynamics of traffic flow at the level of each
individual vehicle. They have existed since the
1960s with the typical car-following models.
• Car-following models describe the processes
in which drivers follow each other in the
traffic stream. The car-following process is of
the main processes in all microscopic models
as well as in modern traffic flow.

6. CAR FOLLOWING MODELS,
Is one of the most useful tools for
traffic dynamics, have been developed
more than six decades. There are two
main objectives in the car process:
(ⅰ) Reducing the speed difference and
(ⅱ) Maintain an appropriate spacing
between the following vehicle and the
leading vehicle.

7. CAR FOLLOWING MODELS,

8. DEFINATION OF OPTIMAL SPEED MODEL
Optimal speed limit can be defined as process or
situation where by a moving vehicle attain and
maintain maximum legally permitted design pavement
speed limit on a freeway or maintain a maximum
legally permitted speed limit of a moving vehicle over
a period of time on an free way (Flow stream) without
accelerating further of the permitted speed limit.
Optimum speed limit varies across the globe because
each country base on their nature of their road set an
optimum speed limit by their legislative also enforced
by either police or road related agencies. Example
10mph in 1861 by UK, Switzerland 120km/hr in 1994,
Australia 100km/hr in 1996 etc.

9. OPTIMAL VELOCITY MODEL
The Optimal Velocity Model (OVM) is a time-
continuous model whose acceleration function is of
the form am ic (s,v), i.e., the speed difference
exogenous variable is missing. The acceleration
equation is given by
=
𝑣𝑜𝑝𝑡 𝑠 − 𝑣
𝑡
𝑜𝑝𝑡𝑖𝑚𝑎𝑙 𝑣𝑒𝑙𝑜𝑐𝑡𝑦 𝑀𝑜𝑑𝑒𝑙 (1)
This equation describes the adaption of the actual
speed v=v α to the optimal velocity v opt(s)on a time
scale given by the adaptation time τ. Comparing the
acceleration equation with the steady-state condition
it becomes evident that the optimal velocity (OV)
function 14vopt(s)is equivalent to the microscopic
fundamental diagram ve(s). It should obey the
plausibility conditions.

10. PROPERTIES OF OPTIMAL SPEED
MODEL.
1•On a quantitative level, the OVM results are
unrealistic.
2• On a qualitative level, the simulation outcome has a
strong dependency on the fine tuning of the model
parameters, i.e., the OVM is not robust.
3 • These deficiencies are mainly due to the fact that
the OVM acceleration function does not contain
the speed difference as exogenous variable.
4 • the simulated driver reaction depends only on the
gap but is the same whether the leading vehicle is
slower or faster than the subject vehicle. This
corresponds to an extremely shortsighted
driving style.

11. FULL VELOCITY DIFFERENCE MODEL
in 2006, Zhi peng and yui- cai conducted a detailed
analysis of FVDM As in the OVM, the steady-state
equilibrium is directly given by the optimal velocity
Function v opt. When assuming suitable values for the
speed difference sensitivity γ of the order of, the
FVDM remains accident-free for speed adaptation
times of the order of several seconds. It turns out that
model is able to realistically simulate the cruising
phase, in contrast to the original model , and produces
realistic accelerations, in contrast to the OVM.

12. MICROSCOPIC TRAFFIC MODEL
Microscopic models typically refer to
simulation models that include
randomized characteristics and
behaviors of an array of drivers and
vehicles as they traverse a network.
The performance of these models is
typically averaged over several “runs”
to account for the randomized driver
and vehicle characteristics.

13. (Bando et al., 1995). The optimal velocity
model has not the ability to explain only
individual behavior of a vehicle, but also
its connectivity to some mac-roscopic
values such as traffic flow and density
(Nugrahani, 2013). As mentioned, there
are two major approaches to describe
the traffic flow problem.

14. MACROSCOPIC TRAFFIC FLOW
Macroscopic Traffic models make use of
the picture of traffic flow as a physical
flow of a fluid. They describe the traffic
dynamics in terms of aggre-gated
macroscopic quantities such as the
traffic density, traffic flow or the average
velocity as a function of space and time
cor-responding to partial differential
equations. By way of contrast,
microscopic traffic models describe the
motion of each indi-vidual vehicle. They
model the action, such as accelerations,
decelerations and lane changes of each
driver as a response to the surrounding
traffic.

15. MACROSCOPIC TRAFFIC FLOW FIG
(Kesting et al., 2008) (Fig. 1).
Fig. 1Illustration of different traffic modeling
approaches

16. GREENSHIELD’S MODEL
The Greenshield’s model represents how
the behavior of one parameter of traffic
flow changes with respect to another.
The most simple relation between speed
and density is proposed by green shield
and scalled the fundamental relation or
fundamen-tal diagram later (van
Wageningen, 2014; Jabeena, 2013).

17. MICROSCOPIC TRAFFIC MODEL
CON’T
Unlike macroscopic models, traffic demand
values are generally inputs and typically do not
result from path choice within the model,
therefore, there may not be a predetermined
throughput. As a result, assigned traffic
volumes at specific locations such as midblock
or a turn movement may not match the input
demand due to constraints on the network
metering flow. For example, queues will build in
a microscopic model and only vehicles that can
make it through a bottleneck in a given time
period will be observed.

18. ADVANTAGE OF OPTIMAL SPEED MODEL.
It reduce fuel consumption
It reduce accident rate
It makes driving safer
It helps in maintaining the design life span of the
pavement.
It reduces pollution.
It increase traffic flow speed and its stability
It prevent over speeding

19. DISADVANTAGE OF OPTIMUM SPEED MODEL
* It wastes time for commercial drivers that
are used to
* travel with high speed.
* It cause s over speeding
* It increase accident
* It causes road dilapidation .

20. LIMITATION AND CHARACTERISTIC OF
OPTIMUM SPEED LIMIT
LIMITATION OF OPTIMUM SPEED MODEL
The OVM does not have a time delay in its model
expression, which makes it convenient for theoretical
analysis.
The optimal speed function assumes that there is a one-
to-one correspondence between the spatial headway
and the optimal driving speed in steady traffic state.

21. CHARACTERISTIC OF OPTIMUM SPEED LIMIT
1. Synthesize existing knowledge about speed and factors that
either influence speed or are an outcome of speed such as Safety,
Environmental Impacts, Road User Costs
2. To analyze speed data to determine the vehicle operating speed
impacts from different vehicle classifications, temporal factors,
environmental factors, and road factors. Such as Road
Engineering, Regulatory and Enforcement Environment, Driver
Attitude and Behaviour, Weather Factors, Temporal Factors,
Vehicle Classification,

22. 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, especially how to
suppress the emergence of traffic congestion.

23. RESEARCH ON OPTIMAL SPEED MODELS
Some of the researches on the optimal speed models are
as follows;
Optimal speed advisory for connecting vehicles in arterial
road and the impact on mixed traffic by Nianfeng Wan,
ArdalanVahidi, Andre Luckow.
Effect of optimal estimation of flux difference information
on the lattice traffic flow model by Shu-hongYang,Chun-
guiLi∗,Xin-laiTang,ChuanTian.
Traffic simulation models calibration using speed–density
relationship: An automated procedure based on genetic
algorithm by SandroChiapponea, OrazioGiuffrèa, Anna
Granàa,∗, RaffaeleMauroc, Antonino SferlazzabQ1.
Speed management in rural two-way roads: speed limit
definition through expert-based system. Nuno Gregórioa,*,
Ana BastosSilvaa, Alvaro Secoa.
Evidence for speed flow relationships Nicholas Taylor (TRL,
ntaylor@trl.co.uk) Nathan Bourne (TRL) Simon Notley (TRL)
George Skrobanski (English Highways Agency).

24. CONCLUTION
It can be concluded that, it is
difficult to accurately predict
the behavior of drivers during
jam formation and congestion.
And also it is very difficult to
predict optimal speed function
such situation,

25. RECOMMENDATIONS
Based on the above observation, it is
recommended that study should continue
to be carried out so as to cover simulation
problem with intension to have result that
will show in future. It is also
recommended to African Countries’s
researchers to go deep in to the world of
optimal speed traffic model research with
intention to come up with a lot of
solutions to traffic problems.

26. REFERENCES.
M. Bando, K(1995). Hasebe, A. Nakayama, A. Shibata, and Y.
Sugiyama, “Dynamical Modelof Traffic Congestion and
Numerical Simulation”, Phys. Rev. E 51, 1035-1042 (1995).[2] M.
Bando, K. Hasebe, A. Nakayama, A. Shibata, and Y. Sugiyama,
“Structure Stability of Congestion in Traffic Dynamics”, Japan
Journal of Industrial and Applied Mathemat-ics 11, 203-223
(1994).[3] M. Bando, K. Hasebe, K. Nakanishi, A. Nakayama, A.
Shibata, and Y. Sugiyama,Aghabayk, K., Sarvi, M., Young, W.
(2015) A State-of the-Art Review of Car-Following Models with
Particular Considerations of Heavy Vehicles. Transport Reviews.
35(1), pp. 82-105.

27. THANK You