Introduction How IT &Business Process Fit Together What is modeling? What is Simulation? Modeling & Simulation in Business Process Management The Seven-Step Model-Building Process Transportation An overview on transportation modeling Transport model scope & structure Car Traffic Jam Problem Aim of Transportation Model Types of Traffic Models Microscopic Traffic model & Simulation Cellular Automaton model Conclusion Solving Transportation Problem by Software Application Class Example

1. Modeling BusinessModeling Business
ManagementManagement
SystemsSystems
TransportationTransportation
By:By: Sherin Haroun El RashiedSherin Haroun El Rashied

2. Presentation OutlinePresentation Outline

3. IntroductionIntroduction

4. How IT &Business Process FitHow IT &Business Process Fit
TogetherTogether

5.  A simulation is an imitation of the operation of a real-world process or system.
 The act of simulating something first requires that a model be developed; this model
represents the key characteristics, behaviors and functions of the selected physical
or abstract system or process.
What is Simulation?What is Simulation?

6.  It accelerates change from old to new system.
 It minimizes the risk of change.
 It allows experts to analyze, improve and control the key factors of any business.
 It provides a mechanism of robust validation under realistic conditions
Simulation is a tool for managing change.Simulation is a tool for managing change.
What is Simulation?What is Simulation?

7. Models are:
A means of understanding the problems involved in building something;
An aid to communication between those involved in the project and the user.
A component of the methods used in development activities such as the analysis of the
requirements for an artefact and the design of the artefact.
Modeling is a tool that represents the simulationModeling is a tool that represents the simulation
What is Modeling?What is Modeling?

8. Models for simulation can be simple or complex. Some
modeling and simulation tools allow you to create
detailed models of business processes with a high
degree of fidelity to actual processes.
Modeling & Simulation in BusinessModeling & Simulation in Business
Process ManagementProcess Management

9. The Benefits of Using Modeling &The Benefits of Using Modeling &
SimulationSimulation

10. TransportationTransportation

11.  Transport models are a systematic representation of the complex real-world transport and
land use system as it exists. They are powerful tools for assessing the impact of transport
infrastructure options and for identifying how the transport system is likely to perform in
future, which is essential for the development of an effective urban planning practice.
 Transport models use mathematical relationships to represent the numerous complex
decisions people make about travel so that future demand can be predicted, and to replicate
observed travel patterns at various levels of geography.
 At the most fundamental level, transport models comprise:
An Overview on TransportationAn Overview on Transportation
ModelingModeling

12.  The scope of the transport model is defined by following policy issues:
Establishing a suitable model scope and structure for transport modeling and analysis
is not a simple process. A number of modeling approaches exist, ranging from the
option of using no formal transport models to the most complex microsimulation
models.
Establishing a suitable model scope and structure for transport modeling and analysis
is not a simple process. A number of modeling approaches exist, ranging from the
option of using no formal transport models to the most complex microsimulation
models.
Transport Model ScopeTransport Model Scope

13. A database
The inputs
to the
modeling
process,
A travel
demand
model
A freight
model
A transport
supply
model
An
assignment
module
The required
outputs,
Other
information
1. Consolidating the modeling task
2. Data collection
3. Model estimation
4. Options development
5. Options modeling
6. Sensitivity analysis
7. Economic appraisal
8. Modeling report
Transport Model StructureTransport Model Structure

14. 1. What will our community look like in the future?
 How many people? (population forecasts)
 What will they do? (economic forecasts)
 Where will they do it? (land use pattern)
2. What are the travel patterns in the future?
 How many trips? (trip generation)
 Where will the trips go? (trip distribution)
 What modes will they use? (mode split)
 What routes will they take? (traffic assignment)
 What will be the effects of this travel? (impact analysis)
How Do Models Fit in The TransportHow Do Models Fit in The Transport
Planning ProcessPlanning Process

15. Car Traffic JamCar Traffic Jam
ProblemProblem

16. To Study The Impact of The Chosen Model
on The Traffic Flow Problems.
Aim of Transportation ModelAim of Transportation Model

17. Microscopic traffic flow
models (Car-Following Model)
simulate single vehicle-driver
units, based on driver’s
behavior.
Macroscopic traffic flow
model study the characteristics
of traffic flow like average
velocity, density, flow and
mean speed of a traffic stream.
Mesoscopic models (model: Gas-
Kinetic Traffic Flow Model)
combine the properties of both
microscopic and macroscopic
models.
Microscopic
Macroscopic
Mesoscopic
Types of Traffic ModelTypes of Traffic Model

18. Traffic jam!?Traffic jam!?

19.  There are three behaviors:
 In order to achieve accuracy in modeling the traffic, many factors must be
considered. This leads to a simulation model with high degree of parameters (50
parameters model is common).
External Factors
Microscopic Traffic ModelMicroscopic Traffic Model

20. Fundamental Diagram:
The fundamental diagram describes the connection between density and flow
rate on the road.
When the density is low, that is, vehicles are far from each other, the flow
increases linearly with increasing density.
When the density reaches certain value, vehicles start to interact with each other,
drivers become cautious and lower their velocities to maintain a safe distance to the
vehicle ahead. The lowering of velocities causes the flow to decrease.
As the density still increases, vehicle velocities get lower and finally a point is
reached when traffic is completely jammed and the flow rate drops to zero.
In the theory of traffic flow, it is supposed that the average flow rate (Q(ρ)) is
related to the density (ρ) and the average velocity of vehicles (V (ρ)) as Q(ρ) = ρ V(ρ).
(Q = flow, ρ = density, V = velocity)
Transportation Ideal RuleTransportation Ideal Rule

21.  Cellular automaton model is one of the microscopic traffic models. In this model, a roadway is
made up of cells like the points in a lattice or like the checker board and time is also discredited.
Vesicles move from on cell to another. The first research using Cellular Automaton model for
traffics simulation was conducted by Nagel and Schreckenberg (1992). They simulate the single-
lane highway traffic flow by a stochastic CA model. The basic rule of the traffic flow is that each
vehicle move v sites at each time. The velocity will add 1 if there is no cars v space ahead and
slow down to𝑖−1 if there is another vehicle𝑖 spaces ahead. The velocity will slow down
randomly with the probability𝑖. There are some CA models have been quiet used, like Nagel-
Schreckenberg model (1992) and BJH model (Benjamin, Johnson and Hui 1996).
 In the CA model, the street is divided into cells at a typical space which is the space occupied by
vehicles in a dense jam. The space is depended by car length and distance to the preceding car.
Each cell can be occupied at most one car or empty. There exist a maximum speed𝑖𝑖𝑖𝑖 and the
velocity of each car can take the value between𝑖=0,1,2,…,𝑖𝑖𝑖𝑖.
 The simplest traffic CA model is developed by Wolfram (1986, 1994) and Biham et al (1992). The
model is described as the asymmetric simple exclusion model on one dimensional roadway. The
formula is as following:
𝑥𝑥(𝑥+1)=𝑥𝑥(𝑥)+ 𝑥𝑥𝑥(1,𝑥𝑥+1(𝑥)−𝑥𝑥(𝑥)−1)
Cellular Automaton ModelCellular Automaton Model

22.  According to rule 184, the evolution of a particular cell depends on its two immediate neighbors, i.e.
the cells in front of and behind it.
 Black or “1” indicates that the cell is occupied by a “vehicle” and white or “0” indicates “empty
spaces”.
 In this diagram, “vehicles” are moving to the right. If the “vehicle” has an “empty space” in front of it,
it will move one unit to the right. Otherwise, it will remain in its original cell.
Cellular Automaton ModelCellular Automaton Model

23. The Four Movement Steps which lead to a realistic behavior, has been introduced in 1992 by Nagel
und Schreckenberg.
Step 1. All the vehicles whose velocity has not reached the maximum 𝑖𝑖𝑖𝑖 will accelerate by one
unit.
Step 2. Assume a car has m empty cells in front of it. If the velocity of the car (𝑖) is bigger than m,
then the velocity becomes tom. If the velocity of the car (𝑖) is smaller than m, then the velocity
changes to 𝑖. (𝑖→𝑖𝑖𝑖[𝑖,𝑖])
Cellular Automaton ModelCellular Automaton Model

24.  Step 3. The velocity of the car may reduce by one unit with the probability𝑖.
 Step 4. After3 steps, the new position of the vehicle can be determined by the current velocity
and current position. (𝑖𝑖 →𝑖𝑖+𝑖𝑖)′
The mathematical formula can be as shown:
𝑖𝑖+1=𝑖𝑖𝑖{0,𝑖𝑖𝑖(𝑖𝑖𝑖𝑖,𝑖𝑖−1,𝑖𝑖+1)−𝑖𝑖(𝑖)} 𝑖𝑖(𝑖+1)=𝑖𝑖(𝑖)+ 𝑖𝑖𝑖{0,𝑖𝑖𝑖(𝑖𝑖𝑖𝑖,𝑖𝑖+1(𝑖)−𝑖𝑖(𝑖)−1,𝑖𝑖(𝑖)
−𝑖𝑖(𝑖−1)−1+1)−𝑖𝑖(𝑖)}
𝑥𝑥(𝑥) : the Boolean random variable. 𝑥𝑥(𝑥)=1 with the probability p, 𝑥𝑥(𝑥)=0 with the probability 1-p.
Cellular Automaton ModelCellular Automaton Model

25. The one-lane highway traffic model is based on the former Cellular Automaton model. There exists one
highway which is a close boundary system. The highway is divided in equal size cells. Each cell can either
occupy one vehicle or is empty. Each vehicle can be described by position and velocity. 𝑖𝑖 is the position of
i th vehicle and 𝑖𝑖 is the velocity of 𝑖 th vehicle. Before each movement, we first define the gap between
successive vehicles. 𝑖𝑖𝑖𝑖 is the gap space between i th vehicle and 𝑖-1 𝑖 vehicle. There are four steps inℎ
the model.
Rules and Algorithm
Simulation of Traditional CellularSimulation of Traditional Cellular
Automaton ModelAutomaton Model

26.  The traditional CA model has a close
boundary for each time step the cars leaving
the system will entry the road immediately.
 In the new model, we set the following rules:
 For each time step, a car will come to
the road with a probability λ.
 If the cars can not enter the road, they
will line up in the entrance.
 The length of queuing is L.
 The cars reach the end of the road will
leave.
Algorithm for improved one-lane model
Modeling and Simulation of Single-lane HighwayModeling and Simulation of Single-lane Highway
Traffic with Open Boundary and Queuing SystemTraffic with Open Boundary and Queuing System

27. Cellular automaton approach has the following advantages:
1. CA model is easy to understand and to implement in computer.
2. CA model is able to reproduce the complex traffic phenomenon and reflect the
characteristics of traffic flow. The simulation shows the change of cellular in
every time steps.
- Microscopic Level: Observer can get each vehicle’s speed at each time,
displacement and distance of each car.
- Macroscopic Level: Average speed, density and flow of traffic flow.
1. CA model is able to simulate both one-lane roadway and multi-lane
roadway, distinguish small vehicles and big vehicles by setting.
Advantages of Cellular AutomatonAdvantages of Cellular Automaton
ModelModel

28.  From the simulation we had, the phantom jam can be explained.
 With the increase in the number of vehicles on the road, vehicle density
increases. The smaller the spacing between vehicles, the higher the
interaction.
 When density is low, the vehicles’ movement are free. When the vehicle is
moving forward, the relationship between position and time is linear and
vehicle keeps constant speed.
 When the density increases, the degree of free movement reduces and traffic
blocking is generated in roadway. The relationship between position and time
is non-linear.
 Traffic movement and congestion appear alternately, similar to the peaks and
troughs of the wave propagation.
ConclusionConclusion

29. SolvingSolving
TransportationTransportation
Problem byProblem by
SoftwareSoftware
ApplicationApplication

30. Solving Transportation Problem bySolving Transportation Problem by
Software Application (Isbak)Software Application (Isbak)

32. Probability distributions / Discrete / Poisson
Example:
Calculate the hourly flow rate in a road section is 120 vph. Use Poisson distribution to model this vehicle
arrival
Solution:
The flow rate is given as (µ) = 120 vph = 120/60 = 2 vehicle per minute. Hence, the probability of zero
vehicles arriving in one minute p(0) can be computed as follows:
Example#1 on Transportation ProblemExample#1 on Transportation Problem

33. The above calculations can be repeated for all the cases as tabulated in
Table
Example#1 on Transportation ProblemExample#1 on Transportation Problem

34. Probability values of vehicle arrivals
computed using Poisson distribution
Cumulative probability values of vehicle
arrivals computed using Poisson
distribution
Example#1 on Transportation ProblemExample#1 on Transportation Problem

35. Spreadsheets Distribution - PoissonSpreadsheets Distribution - Poisson

36. Solving Vehicle Routing Problems Using ExcelSolving Vehicle Routing Problems Using Excel

37. Calculate the hourly flow rate in a road section is 180 vph.
Use Poisson distribution to model this vehicle arrival
Class ExampleClass Example

38.  Operations Research AP P LI CATI O N S AN D A LGOR I T HMS
 Modeling and simulation of highway traffic using a cellular automaton approach,
Examensarbete i matematik, 30 hp - Handledare och examinator: Ingemar Kaj
December 2011 – Department
 Traffic Simulation, Josh Gilkerson - Wei Li - David Owen
 Greenshields, B.D. (1933).The Photographic Method of studying Traffic Behavior,
Proceedings of the 13th Annual Meeting of the Highway Research Board.
 Greenshields, B.D. (1935). A study of highway capacity, Proceedings Highway
Research, Record, Washington Volume 14, pp. 448-477.
 Lighthill, M.H., Whitham, G.B.,(1955). On kinematic waves II: A theory of traffic flow
on long, crowded roads. Proceedings of The Royal Society of London Ser. A 229, 317-
345.
 http://www.open.edu/openlearn/science-maths-technology/computing-and-
ict/models-and-modelling/content-section-2.1
 https://en.wikipedia.org/wiki/Simulation
ReferencesReferences