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08-Mid_Term-with_solution_-_v2_modified-1

# 08-Mid_Term-with_solution_-_v2_modified-1 - Mid-term Exam...

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Mid-term Exam, Spring Semester, 2008 – Data Networks Professor: Sunghyun Choi 2008-05-06 (Tue), 12:30pm-2:15pm 1. (10 points) We are given a bit transmission facility that transmits each bit correctly with probability 1- p and incorrectly with probability p . The bit errors are independent. We send bits in groups of 7 and we add a parity bit so that the groups of 8 bits that we send always contain an even number of 1’s. What is the probability that a group of 8 bits arrive at the receiver with transmission errors that com not be detected? (10 points) If even number of error occurs, it cannot be detected in this case. P n means the probability which n number of error occurs in the data bits. P 2 : 8 C 2 (1-p) 6 p 2 P 4 : 8 C 4 (1-p) 4 p 4 P 6 : 8 C 6 (1-p) 2 p 6 P 8 : 8 C 8 p 8 Total probability: P 2 + P 4 + P 6 + P 8 = 8 C 2 (1-p) 6 p 2 + 8 C 4 (1-p) 4 p 4 + 8 C 6 (1-p) 2 p 6 + 8 C 8 p 8 2. (20 points) Consider a stop-and-wait system with two-way traffic between nodes A and B . Assume that data frames are all of the some length and require D seconds for transmission. Acknowledgement frames require R seconds for transmission, and there is a propagation delay P on the link. Assume that A and B both have an unending sequence of packets to send, assume that no transmission errors occur, and assume that the time-out interval at which a node resends a previously transmitted packet is very large. Finally, assume that each sends new data packets and acknowledgements as fast as possible, subject of the rules of the stop-and-wait protocol. The rate at which packets are transmitted

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