Let A and B be two stations attempting to transmit on an Ethernet. Each has a steady queue of frames ready to send; A's frames will be numbered A1, A2, and so on, and B's similarly. Let T = 51.2 μs be the exponential back off base unit. Suppose A and B simultaneously attempt to send frame 1, collide, and happen to choose back off times of 0 × T and 1 × T, respectively, meaning A wins the race and transmits A1 while B waits. At the end of this transmission, B will attempt to retransmit B1 while A will attempt to transmit A2. These first attempts will collide, but now A backs off for either 0 × T or 1 × T, while B backs off for time equal to one of 0 × T, ... , 3 × T.
(a) Give the probability that A wins this second back off race immediately after this first collision; that is, A's first choice of back off time k × 51.2 is less than B's.
(b) Suppose A wins this second back off race. A transmits A3, and when it is finished, A and B collide again as A tries to transmit A4 and B tries once more to transmit B1. Give the probability that A wins this third back off race immediately after the first collision.
(c) Give a reasonable lower bound for the probability that A wins all the remaining back off races.
(d) What then happens to the frame B1? This scenario is known as the Ethernet capture effect.