PBW 654

Applied Statistics - I

Urban Operations Research

Fall 2015

Hossam Abdelgawad, PhD, P.Eng.

Assistant Professor, Public Works Dept.

Faculty of Engineering, Cairo University

Teaching Staff…

Instructor Hossam Abdelgawad Assistant Professor

Office: 3rd Floor, Architectural Building

Email: hossam.abdelgawad@alumni.utoronto.ca

Office hours:

Mondays and Tuesdays by appointment

2

Course Mechanics… Lectures

Monday 12:00pm-3:00pm (3rd Floor, Arch Building, Dr. Hossam’s Office)

Evaluation

Problem Sets and Midterm 40%

Final Exam: 60%

Software

MS-Excel©

Programming

Text

Lecture Notes

Richard Larson and Amedeo Odoni, Urban Operations Research, 1981, Prentice Hall, (available at: http://web.mit.edu/urban_or_book/www/book/)

Course Material

Lectures, tutorials, problem sets, solutions, and (some) readings will be posted on a website / drop box link / email

3

Acknowledgment… MIT

Prof. Amer Shalaby – UofT

Prof. Mohamed Wahba – UBC

4

Course Management…

Lectures, tutorials, problem sets, solutions, and (some) readings will be posted on a website / drop box link

5

Course Information…

Covers quantitative methods and

techniques for the analysis and modelling of

urban transportation and service systems

Emphasizes probabilistic and optimization

methods for designing efficient operations

for various transportation systems

6

Course Outline… Unit I

Probabilistic Modelling and Poisson

Processes

What do you mean “it’s Random”?

Poisson Processes

Poisson Processes and Random Incidence

Functions of Random Variables

Unit II

Queuing Systems

Steady State and Little’s Law

M/M/1, M/M/m, M/M/∞, M/G/1

Deterministic Queuing

Unit III

Network Modelling and Facility

Location

Shortest Path Problem

Chinese Postman Problem, Travelling

Salesman Problem

Facility Location

Unit IV

Mathematical Programming and

Simulation Modelling

Linear and Integer Programming

Network Programming

Simulation Modelling

7

Background and History Urban OR is not new

1736, the Seven Bridges of Königsberg is a historically notable problem in mathematics

1937, Merrill Flood of Columbia University stimulated serious interest in the “traveling salesman problem” (see Chapter 6) through his efforts to route school buses more efficiently

8

Scope

This course deals with the application of OR (Operations Research) methods and techniques to the analysis and modelling of urban service systems

Urban Service Systems

Transportation systems Bus, subway, highway, sidewalk, etc.

Logistically-oriented service systems Bunched Up Buses

Door to door pickup and delivery services (mail delivery, garbage collection, school bus routing)

Emergency services (police, fire, ambulances)

Street maintenance services (snowplowing, street sweeping)

Services at fixed locations (libraries, clinics, community centres)

9

Analysis and Modelling

Analysis and modelling are essential for the

deployment of

(i) new services or

(ii) enhancements of existing services.

Effective deployment requires (typically):

Operational planning (aka functional design)

Design the details of the service

Operational control

Determine the rules/strategies/etc. to control operations

10

Analysis and Modelling

The “Systems Approach” is usually implemented to carry out operational planning and control

Define the problem

Identify objectives

Identify alternative options to achieve the objectives

Model each option and analyze the consequences

Compare the options and select the best

Examples

Buying a new laptop?

Building a new subway line?

11

The Big Picture…

OR/MS Methods

Linear/Integer Programming

Network Programming

Project Scheduling

Inventory Models

Queuing Models

Simulation

Goal Programming

Dynamic Programming

Forecasting

Transport Operations

Strategic Network Design

Vehicle Routing

Transit Vehicle Scheduling

Transit Crew Scheduling

Transit Real-Time Control Operations

Traffic Flow Modelling

Traffic Lights Operations

Runway and Air Traffic Operations

Airline Crew Scheduling

…

12

OR Methods of this course

Probabilistic modelling

most urban services face uncertainties related to time of occurrence, type, location, and quantity of demands.

required to analyze non-deterministic behavior of the systems

Queuing theory

required to analyze congestion effects caused by the interaction between demand and supply of service

Network (or Graph) theory

required in the overall analysis of transportation networks and related routing problems, network design problems and location problems

Linear Programming

Used to find optimal solutions to a wide variety of problems

Simulation

may be necessary when analytical techniques fail 13

Approach… Develop understanding of transport operations

Demonstrate how to develop, solve and interpret

the results of probabilistic models applied to transport operations

Develop decision and policy making aids for large-scale, complex transportation systems

14

Main Topics… Random Variables and Probability Distributions

Pedestrian Crossing Problem,

Little’s Laws for Queuing Systems,

Birth-and-Death phenomenon of queuing

processes,

Facility Location Problems,

Routing and Network Analysis,

Mathematical Programming and Simulation

Modelling

15

Course

Overview

16

Probability Modelling (Unit I)

Types of Random Variables

Discrete Random Variables

Continuous Random Variables

Relationships between Random Variables

Independent

Mutual Exclusive

Often used Probability Distributions

Probability Mass Functions for Discrete RV

Probability Density Functions for Continous RV

17

Poisson Processes (Unit I)

Postulates of the Poisson Process

Properties of the Poisson Process

Random Incidence Process

Pedestrian Crossing Problem

18

Queueing Process and Queueing

System… (Unit II)

Source

of users/

customers

C C C C C C

Queue

C

C

C

C

C

C

C

Servers

Size of

user source

Arrivals

process

Queue discipline and

Queue capacity

Service process Number of servers

Arrival point

at the system

Departure point

from the system

Queueing System

19

What is a queuing system?

“Steady state” measures and Little’s Laws

Birth-and-Death Queuing Systems

Various Queueing System Configurations

M/M/1

M/M/m

M/G/1

Queuing systems with finite queue capacity -- “turning customers away”

Queuing systems with priorities

Deterministic Queuing Systems

Queueing Process and Queueing

System… (Unit II)

20

Chicago

Dallas

Cleveland Kansas City

Atlanta Los Angeles

Boston

Network Modelling and Facility

Location (Unit III)

21

Network Modelling and Facility

Location (Unit III)

Shortest Path Problem

Chinese Postman Problem

Travel Salesman Problem

Facility Location

22

Time - Space Network

Representation

Cleveland

Chicago

Kansas City

Atlanta

Dallas

Los Angeles

Boston

Mon Tue Thu Wed Mon Fri Sun Sat

23

0

....

.................

....

.....

..

)....(

22221

222222221

111212111

2211

i

mnmnmm

nn

nn

nn

x

bxaxaxa

bxaxaxa

bxaxaxa

ts

xcxcxcMIN

Mathematical Programming –

Linear Programming (Unit IV)

24

Big Picture and Simulation

Modelling

Probabilistic Modelling

and Poisson Processes

Network Modelling

and Facility Location

Queueing Systems

Mathematical Programming

Simulation Modelling

25