Subject: Problem 4 of Midterm
From: Rajmohan Rajaraman (rraj@ccs.neu.edu)
Date: Sat Nov 10 2001 - 16:21:43 EST
In the sample solution to Problem 4 of the midterm, I had claimed --
without proof -- that the arrival process into queue 2 is Poisson,
because the departure process out of queue 1 is Poisson. In class,
Rui Wang had asked why this was true, and I was unable to provide a
proof. I have gone over the claim since then and have been able to
show that it is true. The issue turned out to be much more subtle
than what I intended when I formulated the problem. I have prepared a
note on this problem, which is available from the course home page at:
http://www.ccs.neu.edu/home/rraj/Courses/3510/F01/mt_addendum.ps
Please print out the document and go over the argument. While it is
somewhat intricate, I hope it is instructive and reveals some of
complexities that arise when analyzing networks of nodes -- even a
network, as simple as one consisting of 2 nodes!
Now with regard to the use of the problem in the midterm, I realize
now that it was inappropriate to include that problem, in its present
form, with all its nuances and intricacies. The wording of the
problem was also questionable -- since students were confused as to
whether the service times for a packet in the two queues were the
same. I apologize for this oversight.
In order to address the above issue, I have decided to give full
credit to all students for Problem 4. This may not necessarily be the
fairest solution, but the best possible under the current
circumstances.
Please come by my office any time next week with your midterm, or
bring your midterm to the following class, to get credit. Best,
Rajmohan.
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