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IEOR 4106: Introduction to Operations Research: Stochastic Models
Spring 2009, Professor Whitt
Homework Assignment 6: Tuesday, March 3
Due on Tuesday, March 10.
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 '08
 Whitt
 Operations Research

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