This page contains assignment #2 for
Performance Evaluation. This assignment is due on Monday,
September 27 in class. Any solutions that you find "on the web"
must be referenced as such. Please start each problem on a new
sheet of paper and put your name on all sheets of paper. Note
that problem #7 is an extra credit problem.
Go to one of the open PC labs and try-out Mathcad. Spend at least 20
minutes studying the tutorial and otherwise "playing" with Mathcad. Submit
a printed Mathcad sheet showing something of what you did (e.g., simple
equations, plotting, and so on). Tell me what version of Mathcad
you used and in what room. The goal here is for you to see what a
Mathematics package can do and how easy they are to use.
Find the Z-transform for the Poisson distribution. Show your work.
Hint: this summation should look very familiar to you (think calculus):
.
Let U be a random variable that is the sum of N Poisson distributed
random variables. What is the distribution of U? Show your work.
The M/M/1 queue is a very important type of single-server queue that we
will study in this class. Two measures of a queue are its utilizaton (ranging
form 0% to 100%) and system delay (ranging from almost zero to infinity). The
following series is the mean system delay for 10%, 20%, 30%, 40%, 50%, and 60%
utilzation assuming a mean service time of 1.0 second. Using exponential
smoothing, can you predict the mean system delay for 70%, 80%, 90%, and 100%.
Are your predictions reasonable (i.e., what you might expect for an M/M/1 queue
system delay)? Can you see something obviously wrong?
It is very important that you can work with large data sets of measurement
or experimental data. A trace of 500 thousand packets taken on the USF
Internet2 on December 2001 is trace.zip (file size
is about 5,090,365 bytes and it has been compressed with pkzip). The
second to last value in each record is packet length. Determine the minimum,
maximum, mean, variance, and 95%-tile packet length for this trace. Plot a
histogram of packet lengths. Give some insights on the histogram (i.e.,
explain or speculate on why the histogram looks like it does). You are
welcome (and encouraged) to use and modify the tools on the
Christensen
tools page for this and other assignments.
What is the cost (in time) of a function call in C? That is, what
benefit in execution time would I get for inlining code versus putting
it in a function (and having to invoke it with a function call)?
Clearly, the answer is dependent on the machine and operating system. When
doing your study, be sure that your compiler does not automatically inline
functions. Be sure to submit your code (i.e., your measurement
scaffolding).
EXTRA CREDIT: A simple program to find the number of prime numbers
between 2 and MAX is prime.c. When compiled with the
Microsoft Visual compiler (cl) the program executes almost twice as fast as
when compiled with the Borland complier (bcc32). Why is this? I do not know.
I want you to dig into this. The executables from the cl and bcc32 compilers
are... prime_cl.exe and
prime_bcc32.exe. The assembly language listing
(from the compilations) are prime_cl.asm and
prime_bcc32.asm.
.