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15-441: Computer Networks Homework 1
Assigned: Sep 2, 2011 Due: Sep 15, 2011 1:30 PM in class Lead TAs: Athula Balachandran Wolf Richter

1 1 1 1

Byte KByte Mbps GHz

Units 8 bits 210 bytes 106 bits per second 109 Hz

1. [Sec 1.5] Calculate the total time required to transfer a 1500 KByte file in the following cases, assuming a RTT of 10ms, a packet size of 1500 bytes, and an initial 3 RTT of handshaking before the actual data is sent. (a) The bandwidth is 10 Mbps and data packets can be sent continuously. (b) The bandwidth is 10 Mbps, but after we finish sending each data packet we must wait one RTT before sending the next (c) The bandwidth is infinite, i.e., the transmit time is zero, but only up to 25 packets can be sent per RTT 2. [Sec 2.6.2] This problem illustrates possible danger of incorporating randomization in design. 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 backoff base unit. Suppose A and B simultaneously attempt to send frame 1, collide, and happen to choose backoff times of 0 x T and 1 x T, respectively. As a result, A 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 x T or 1 x T, while B backs off for time equal to one of 0 x T, ..., 3 X T. (a) Give the probability that A wins this second backoff race immediately after its first collision. (b) Suppose A wins the second backoff race. A transmits A3 and, when it is finished, A and B collide again as A tries to transmit A4 while B tries once more to transmit B1 . Give the probability that A wins this third backoff race immediately after the first collision. (c) Give a reasonable lower bound for the probability that A wins all the remaining backoff races. (d) What then happens to the...
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