IE 5202 • Final • Operations Research II

Absorbing Markov Chains

Matrix Structure

Inverse of a Matrix

Expected Number of State Visits

Example

Expected Time Until Absoption

Example

Absorption Probabilities

Example

Counting Processes

Assumptions of Poisson Processes

Example 1

Memoryless Property

Example 2

Minimum of Exponential Random Variables

Example 3

Thinning

Example 4

Superposition

Example 5

Non-homogenous Poisson Processes

Example 6

From Discrete to Continuous

Example 1

Example 2

Example 3

Steady State Distribution

Q Matrix

Example 4

Example 5

Example 6

A subproblem of CTMC

Random Rates, Finite Chain

Example 1

Random Rates, Infinite Chain

Example 2

Equal Rates, Infinite Chain, Single Server

Example 3

Equal Rates, Finite Chain, Single Server

Example 4

Equal Rates, Finite Chain, Multiple Servers

Example 5

Kendall's Notation

Terminology

M/M/1 Queue

Example 1

M/M/s Queue

Example 2

M/M/1/K Queue

Example 3

M/M/s/K Queue

Example 4

Absorption Probabilities in DTMCs 1

Absorption Probabilities in DTMCs 2

Exponential Distribution and Poisson Processes 1

Exponential Distribution and Poisson Processes 2

Exponential Distribution and Poisson Processes 3

Exponential Distribution and Poisson Processes 4

Exponential Distribution and Poisson Processes 5

Continuous Time Markov Chains 1

Continuous Time Markov Chains 2

Birth and Death 1

Birth and Death 2

Birth and Death 3

Birth and Death 4

Queueing Theory 1

Queueing Theory 2

Queueing Theory 3

Queueing Theory 4

Queueing Theory 5

Queueing Theory 6

Queueing Theory 7

Queueing Theory 8