Today
Classification of States
Limiting probabilities
Doubly Stochastic
Absorbing Chains
2
Period of Markov Chain
d(j), the period of a state j is the largest
positive integer d such that every n with Pjjn>0
is an integer multiple of d
d(j) is the greates

OR/MATH 442:
Stochastic Operations Research
Lecture 5
Today
Classification of States
Limiting probabilities
Doubly Stochastic
Absorbing Chains
2
Period of Markov Chain
d(j), the period of a state j is the largest
positive integer d such that every n with

OR/MATH 442 Stochastic Operations Research
Assignment # 3 Due October 10, 2014
When answering assignment questions, be sure to show all of your work. Points will be awarded for each
step of the process. The assignment is due before the beginning of class.

OR/MATH 442:
Stochastic Operations Research
Write down 3 words or phases you would use
to describe the term Stochastic.
OR/MATH 442: Stochastic OR
Today:
Course expectations
Introductions
Background on Stochastic Processes
Break
Review of Probability
Note

OR/MATH 442:
Stochastic Operations Research
Lecture 10
Today
Infinite Server Queues
Queueing Networks
2
Infinite Server Queues
A system in which customer never has to wait
for service
Examples:
A companys life in the industry
A student in a college

OR/MATH 442:
Stochastic Operations Research
Lecture 4
Today
What is a stochastic process?
What is a Markov chain?
Transition probabilities of Markov chain
n-step Transition Probabilities
Chapman-Kolmogorov Equations
Classification of States
2
Stocha

OR/MATH 442:
Stochastic Operations Research
Lecture 8
Today
Continuous Time Markov Process
Birth and Death Process
M/M/1 Queues
2
Markov Process
Future depends on current state of the
process rather than probabilistically restarting
Definition: A Markov p

OR/MATH 442:
Stochastic Operations Research
Lecture 7
Today
Review Exponential and Poisson Distributions
Poisson Processes
2
Review
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