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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