IEOR 161
University of California, Berkeley
Spring 2010
Homework 8
Due date:
April 9 (in discussion session), 2010.
The following are taken from “Introduction to Probability Models” by Sheldon Ross (
9th Edi
tion
).
1. 4.18, 4.20, 4.23
Note: These problems involve computing the stationary distribution of a Markov chain using
the alance equations; we will cover this on Tuesday in class (or you can read ahead). The
simulation problems you have been doing have basically involved computing the stationary
distribution using simulation (as opposed to solving the balance equations).
2. A tandem queue can be described as follows: there are 2 servers in series. Customers arrive
at server 1, receive service one at a time and move to server 2 once service at station 1 is
complete. Customers leave the system after completing service at station 2. If a server is
busy, customers wait in a buﬀer (assume it is inﬁnite). Assume that arrivals occur according
to a Poisson Process of rate
λ
= 1 and that the service rates at servers 1 and 2 are
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 Spring '08
 Lim
 Operations Research, Probability theory, Markov chain, Sheldon Ross, tth event time

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