Homework 4
Due Friday, November 14

Directions for submission: Combine your .tex and .c files into a .tar.gz.uu file, which upon decoding produces Hwk4.tar.gz.

The problem here will deal with the p-persistent ALOHA system simulation program in the Contention Protocols unit in our pirnted lecture notes. I've put a separate copy of the program in

http://heather.csucdavis.edu/~matloff/Networks/Contention/Sim.c

Do a "state space" analysis of this system along the lines of the one for Go-Back-N ARQ in the unit on sliding-window protocols, for a two-node system. Your states will be 0, 1 and 2, with state i meaning that at the very beginning of a time slot (before idle nodes have a chance to generate new messages) there are i nodes which are active. Denote the long-run state probabilities by pi0, pi1 and pi2. First, derive pi0, pi1 and pi2, carefully explaining your steps. You may wish to let a computer do your algebra, for you, using Mathematica on the ACS machines. I have a short example of equation solving on Mathematica at

http://heather.cs.ucdavis.edu/~matloff/solve.eqns

Then, verify your answers, by making a MINIMAL change to Sim.c. It should only consist of a few lines of code being added (and none subtracted).