Chapter 1
Probability Review
INEN 4570 STOCHASTIC
PROCESSES
Dr. Nedim Vardar
1
Probability - What is it?
Definition:
Likelihood or chance that a particular event will occur
A numerical value that measures the uncertainty that a
particular event will occ

Chapter 5
Inventory Theory
INEN 4570 STOCHASTIC
PROCESSES
Dr. Nedim Vardar
1
5.Stochastic Inventory Theory
5.1 Single Period Stochastic Inventory Model
Newsvendor model
5.2 Multi-Period Stochastic Inventory Models
2
Safety Stock Calculations
Expected D

SYSTEM RECORD OF INSPECTION AND TESTING
This form is to be completed by the system inspection and testing contractor at the time of a system test.
It shall be permitted to modify this form as needed to provide a more complete and/or clear record.
Insert N

INTER AMERICAN UNIVERSITY OF PUERTO RICO
BAYAMON CAMPUS
SCHOOL OF ENGINEERING
INDUSTRIAL ENGINEERING DEPARTMENT
INEN 4570 STOCHASTIC PROCESSES
Oriented Elective
Catalog Description:
Application of basic concepts and techniques related to random processes

Stochastic processes
M. Veeraraghavan; Feb. 10, 2004
A stochastic process (SP) is a family of random variables cfw_ X ( t ) t T defined on a given probability space, indexed by the time variable t , where t varies over an index set T . [1]
Just as a rand

Chapter 4
Queueing Theory
INEN 4570 STOCHASTIC
PROCESSES
Dr. Nedim Vardar
1
Queueing Systems
Basic Structure
Input
Source
Queue
Service
Mechanism
A queue is a waiting line of customers requiring service from
one or more servers.
1. Customers need not be p

INTER AMERICAN UNIVERSITY-SCHOOL OF ENGINEERING
INEN 4570 STOCHASTIC PROCESSES
HOMEWORK #3 (Due date: November 05, 2014)
1) An engineering company employs three types of engineers: junior engineers, senior engineers, and
partners. During a given year, the

ABSORBING MARKOV CHAINS - EXAMPLES
1. A study using Markov chains to estimate a patients prognosis for improving under various
treatment plans gives the following transition matrix as an example. Estimate the probability that
a well person will eventually

INTER AMERICAN UNIVERSITY
Department of Industrial Engineering
INEN 4570 STOCHASTIC PROCESSES
HOMEWORK 2 (To be submitted on October 01, 2014)
1. A survey of American car buyers indicates that if a person buys a Ford, there is a XY%
chance that their next

INTER AMERICAN UNIVERSITY
Department of Industrial Engineering
INEN 4570 STOCHASTIC PROCESSES
STEADY-STATE MARKOV CHAINS
EXAMPLES
Example 1: Professor X either walks to school, or he rides his bicycle. If he
walks to school one day, then the next day, he

INTER AMERICAN UNIVERSITY
Department of Industrial Engineering
INEN 4570 STOCHASTIC PROCESSES
HOMEWORK 1 (Due date: September 24, 2014)
1. A survey of American TV buyers indicates that if a person buys a Samsung TV, there is an
XY% chance that their next

Chapter 3
Markov Chains
INEN 4570 STOCHASTIC
PROCESSES
Dr. Nedim Vardar
1
Definitions:
The state of a Markov chain at time t is the value of Xt.
For example, if Xt = 6, we say the process is in state 6 at
time t.
The state space of a Markov chain, S, i

Chapter 2
STOCHASTIC PROCESSES
INEN 4570 STOCHASTIC
PROCESSES
Dr. Nedim Vardar
1
1. INTRODUCTION
Definition: A stochastic process is a family of random
variables.
Random variables are characteristics or outcomes that vary
from observation to observation.

Chapter 3
Markov Chains-Examples
INEN 4570 STOCHASTIC
PROCESSES
Dr. Nedim Vardar
1
Example-1:
In analyzing switching by Business Class customers between
airlines the following data has been obtained by British Airways
(BA):
If the last flight by a Busine

Solutions Markov Chains l
16.41) Given the following one-step transition matrices of a Markov chain,
determine the classes of the Markov chain and whether they are
recurrent.
. 0 9
C)
O
"U
II
o o -*
_ > o
o O Owlw
o O Owlw
All states communicate, all stat