Quiz 2 ECE/CSC 570 - Fall 2010, Section 001, 601

Q1. Markov Model Consider the following numerical values for the slotted ALOHA system. The arrival process at each station is an independent Poisson process, with rate 0.05 (arrivals/slot time). Backlogged stations attempt re-transmission with a probability of 0.02 in each frame slot. Use the model given for the rigorous analysis of slotted ALOHA, with all the assumptions listed there. Assume that there are 20 stations on the medium, and at the end of a given timeslot, 12 of them are backlogged. What is the probability that 12 or more stations will be backlogged at the end of the next timeslot? qa = 1 - e-l/m = 1 – e-0.05 = 1 – 0.95 = 0.05 qr = 0.02 For 12 or more to be backlogged, we must have either an idle slot, OR collision (any combination of new transmissions and retransmissions), OR one new transmission, successful That is, must exclude only the case of one successful retransmission Probability of that is (0.95)8 12C1 (0.98)11 0.02 = 0.13 Therefore required probability is 0.87 Copyright Rudra Dutta, NCSU, Fall, 2009

Q2. Error Free Routing In the network shown below, part of the FIBs of each of the four nodes is shown. Complete any entries in the tables that can have only one possible value in order for the whole routing to be correct.  A B - C D Only the three shown inside the tables in bold are forced. The two entries in D’s table are obvious – D only has one option. The entry for B in C’s table is forced to be B, because the other option (A) would create a loop between A and C. The other two entries are NOT forced, since multiple combinations would produce correct routes (shown in matched colors). A - B C D A B B B C A B C - D C D A B C D - B A B Copyright Rudra Dutta, NCSU, Fall, 2009