Advanced TCP/IP       Dordal      Jan 28, 2002
Homework 1	due: Feb 8 (Friday)

We have looked at a simple simulation of the congestion
window size as a function of packet loss probability,
for TCP (Tahoe). The full java program is available 
online; the main loop is:

        cwnd = 1;
        for (i=0; i<RUNS; i++) {
                if (frandom() < p) {
                        peakcount ++;
                        cwnd = Math.max(1.0, cwnd/2.0);
                } else {
                        cwnd+= 1/(cwnd==0? 1 : cwnd);
                }
                cwndsum += cwnd;
        }
        average = ((double)cwndsum)/RUNS;

Here, we multiply cwnd by 0.5 with probability p (representing
a loss), and increment by 1.0 otherwise (no loss). This is
known as Additive Increase / Multiplicative Decrease, or AIMD.

What you are to do is to experiment with other decrease factors,
alpha, and other increment values, beta. That is, suppose on
a loss we set cwnd *= alpha, and on no loss we set cwnd += beta.
Call such an algorithm AIMD(alpha, beta). The "standard" algorithm
is thus AIMD(0.5, 1.0). Given a specific AIMD(alpha, beta), 
and a given loss probability p, if we run the simulation
a long time we will see convergence to a specific value of cwnd.

Part 1: For p=0.001 and each of the following alphas,
try to find a corresponding beta such that AIMD(alpha, beta) 
gives the same average cwnd as AIMD(0.5, 1.0).
	alpha= 0.9
	alpha= 0.8
	alpha= 0.7
	alpha= 0.6
	alpha= 0.4
	alpha= 0.25
Note that you will have to make runs with AIMD(0.5, 1.0) in order
to find out the window size to expect for p=0.001; it should be
about 47.

Part 2: determine whether the same beta works with that alpha
with different values for p (eg p=0.01, p=0.0001, and at least
one third value).

You should turn in the program you used for Part 1, plus your data,
plus a brief description of how you proceeded.