IEOR 4106: Introduction to Operations Research: Stochastic Models
Spring 2011, Professor Whitt
Homework Assignment 6: Tuesday, March 1
Due on Tuesday, March 8.
Chapter 6: ContinuousTime Markov Chains
Read Sections 6.16.5 in Ross. Do the following exercises at the end of Chapter 6.
You are asked to turn in the problems without answers in the back, but you should do all
the problems.
2. (Answer in back)
Remarks: The object here is to construct a continuoustime Markov chain (CTMC) model.
There are two key steps: (1) defining the state space and (2) specifying the local transition
structure. When we define the state space, we can define the CTMC stochastic process taking
values in that state space. The state space is discrete, and so can be identified with a subset
of the integers, but here it is better to use pairs of integers. The question in applications is:
What are the states?
The “local” transition structure of a CTMC can be defined in two ways. First, following
Section 6.2 of Ross, we can specify the transition matrix
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 Spring '11
 WhitWard
 Operations Research, Markov chain, continuoustime markov, transition rate, CTMC

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