Assignment #3 for Computer Simulation (Spring 1999)
Situation:
It has been determined that a high-speed network switch can be modeled as an
M/D/1/k queue. That is, packet arrivals are Poisson and their service time
is deterministic. Since this is a high-speed switch, memory used for
buffering is expensive. You are are on the design team for the switch and are
responsible for the buffer design. Too much buffering and the switch product
will be over priced, not enough buffering and its performance will be poor.
due to excessive packet losses during periods of high load. In either case,
your job will be on the line. Welcome to the real world!
Requirement:
If each packet is 53-bytes in length (the length of an ATM cell for those
that want to know!), how much memory is needed to have less than 2% packet
loss at 70% offered load? If the same 2% packet loss percentage is also
required for 80% and 90% offered load, how much memory is needed (two
answers, one for 80% offered load and one for 90% offered load). Also,
give the mean number of packets in the switch for each of the three offered
loads for the case of no packet loss (i.e., "infinite" size buffers).
Guidelines and hints:
The M/M/1 simulation handed-out in class (and also available on the
code page is a good place to start. Submit
your program listing (both hardcopy and softcopy) and six numerical answers
(memory sizes and mean number of packets per the above requirement).
Be sure to run your simulation for a sufficient amount of time to get
a "good" answer. This is very important!
Extra Credit: (10 points)
A theoretical answer is possible for the mean number of packets
in the system given no loss. Find the theoretical answers for
the above 70%, 80%, and 90% offered loads. The "formula" is not
in the text book. You will have to look in a book on performance
modeling or queueing theory. There are plenty such books in the
library. This is exactly the purpose of this extra credit problem,
to get you to dig into the more advanced material on the subject.
You might like it (and want to go the graduate school!!! :-) ).
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Last updated by
Ken Christensen on JANUARY 31, 1999