A review on optimal Speed Traffic Flow model, M. Eng. Class Assignment- Advanced Traffic Engineering

1. BAYERO UNIVERSITY
KANO
Review of Optimal Speed TRAFFIC
Traffic FLOW MODEL
M.Eng. Class Assignment
Presented By
Isa Abdulkadir
Lecturer: Prof. H.M. AL Hassan
19th May, 2017

2. Introduction
A traffic model is a mathematical representation that is
used to describe and estimate the behaviour of traffic
flow
Some Key Challenges to Traffic Volume
Economic development
Social Development
The UK Eddington study states that the
monetary cost due to road congestion will reach
£22 billion (at 2002 prices) per annum for all
road users by 2025, in which 13 per cent of road
traffic will be subjected to stop-and-go travel
conditions.

3. Continuous construction of new roads will not be a
sustainable solution to traffic congestion due to the
increasingly constrained financial, physical, and
environmental conditions. Consequently, governments,
businesses, and research teams around the world want to
explore alternative ways to effectively utilise and
manage existing road infrastructure. In fact, adding new
infrastructure may induce more demand for travel and
hence is not an effective option. Therefore, a sustainable
solution for mitigating congestion calls for the effective
management of the existing infrastructure through
appropriate control methods. Optimization modelling of
Speed traffic flow is sustainable solution for congestion
of highways.

4. Optimal Speed model
Optimal Speed (OS) model is a traffic flow model
proposed by Bando et al (1995). The governing
equation is as follows,
dxi/dt = vi dvi/dt = a [V(xi+1-xi)-vi],
with positions xi and speeds vi of cars. The
parameter "a" is sensitivity denoting the speed of
the response. This model involves the phase
transition from the uniform flow phase to the traffic
jam

5. Model
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 Speed
determined by the distance to the next car.

6. Optimal Speed models in another approach
generally based on the difference between the
driver’s desired Speed and the current Speed of
the vehicle as a stimulus for the driver’s actions.
One of the first models learning on an analysis
of the trajectories of vehicles is Newell (1961)
has proposed the model.

7. With V (Sn (t)) is the optimal Speed under the
headway Sn (t). This model has directly given
the speed of nth car by the optimal Speed
function. Based on this model, (Bando et al.,
1995; Nugrahani, 2013) introduce an Optimal
Speed Model (OSM), is given by

8. Where κ is the sensitivity. Helbing and Tilch
(1998) given the function of OSM model as
follows
Where L is the length of vehicle, and V1, V2, C1,
C2 parameters calibrated.

9. Application
Several studies has shown that proper
implementation of Optimum Speed Traffic
Model can contribute to the improvement
of the efficiency of free way operations by
reducing accident rate, real time traffic
congestion and travel cost etc.

10. Current State of Research
Many studies and researches were carried out on driver's behavior in different
situations like a case when he meets a static obstacle or when he meets a
dynamic obstacle. Several studies are made on modeling driver behavior in
another following car and such studies are often referred to as car following
theories of vehicular traffic.
As researchers understood the importance of car-following, research has also
sought to develop vehicle-based technologies that can control it in order to
improve safety and increase capacity. The concept of automated highways
where vehicles follow one another under specified rules has been around for
quite some time. More recent efforts by vehicle manufacturers to develop
adaptive cruise control (ACC) and cooperative adaptive cruise control (CACC)
mechanisms for use in passenger vehicles have the potential not only to
significantly increase safety, but also to result in significant changes in traffic
flow and car-following. Studies have shown that ACC may reduce congestion
even at a market penetration of 20 % of vehicles in the traffic stream.

11. Conclusion
The microscopic car-following model is a favorite type
of traffic flow theory to describe the individual behavior
of drivers. In this work we presented the most car-
following model well known the optimal Speed (OS)
model, which has successfully revealed the dynamical
evolution process of traffic congestion in a simple way.
Thereafter, inspired by the OS model, some new car-
following models were successively put forward to
describe the nature of traffic more realistically.
Incorporating a new optimal Speed function or
introducing multiple information of headway or Speed
difference, or acceleration difference extended some,
whereas others considered the individual anticipation
behavior.

12. Recommendation
• Researchers should develop strong car-following
model, which avoid the collision and interpreted the
traffic flow in a real manner.
• Apart from the real nature of the CF models, an
additional concern for traffic safety in driver errors.
These consist of errors in perception, judgment,
distraction and delay in reaction time. Errors in real
data have a stochastic nature. Any research that can
model human errors would be significantly valuable
in determine optimal speed on a highway
• The main disadvantage of this model is that its gives
unrealistically large Accelerations in some
circumstances as such correction factors should be
researched.

13. Reference:
• Foundamental Relations Of Traffic Flow. 1st ed. INDIA: NPTEL, 2007. Print. [Accessed
14thApril, 17]
• Hadiuzzaman, Md. et al. "Evaluating Performance Of A Proactive Optimal Variable Speed
Limit Control Using Different Objective Functions". Procedia - Social and Behavioral
Sciences 96 (2013): 2895-2906. Web. 14 Apr. 2017.
• Hosseinlou, Mansour Hadji, Salman Aghidi Kheyrabadi, and Abbas Zolfaghari. "Determining
Optimal Speed Limits In Traffic Networks". IATSS Research 39.1 (2015): 36-41. Web. 14 Apr.
2017.
• "Modeling Vehicle Interactions And The Movement Of Groups Of Vehicles". N.p., 2017.
Web. 19 Apr. 2017.
• Owen, Larry E, and Yunlong Zhang. A Multi-Regime Microscopic Traffic Simulation
Approach. 1st ed. Print. [19 Apr. 19, 17]
• Castanheira, Micael, and Gerard Roland. "The Optimal Speed Of Transition: A General
Equilibrium Analysis". International Economic Review 41.1 (2000): 219-240. Web.
• "THE DEVELOPMENT OF A NATURALISTIC CAR FOLLOWING MODEL FOR
ASSESSING MANAGED MOTORWAY SYSTEMS’ SAFETY EFFECTS". N.p., 2017. Web.
19 Apr. 2017.
• "Modelling And Optimisation Of Dynamic Motorway Traffic". N.p., 2017. Web. 20 Apr.
2017.
• "Optimal Velocity Model". Traffic.phys.cs.is.nagoya-u.ac.jp. N.p., 2017. Web. 26 Apr. 2017.