1. Consider users who share a communication link with transmission rate R. Each

Question

1. Consider users who share a communication link with transmission rate R. Each user is generating data at a rate of D when busy, but is busy only with probability p.

a. What is M, the maximum number of users that can be supported simultaneously under circuit switching? Please give a formula for M in terms of p, R, D.

b. Now consider packet switching and a user population of N users. Give a formula (in terms of p, M, N) for the probability that more than M users are sending data simultaneously. Hint: Use the Binomial distribution.

c. Suppose R = 2.4 Mbps, D = 100 kbps, p = 0.1, N = 50, and M is defined in part a. Calculate the numerical value of the probability in part (b). (You might need to write a small program to do this.)



2. Suppose two hosts, A and B, are separated by 16,000 kilometers and are connected
by a direct link with transmission rate R = 2 Mbps. Suppose the propagation speed over the link
is 2 · 108 meters/sec.

a . Calculate the bandwidth-delay product R · dprop.

b. Consider sending a file of 400,000 bits from Host A to Host B. Suppose the file is sent continuously as one large message. What is the maximum number of bits that will be in the link at any given time?

c. Provide an interpretation of the bandwidth-delay product.

d. What is the width (in meters) of a bit in the link? Is it longer than a football field?

e. Derive a general expression for the width of a bit in terms of the propagation speed s, the transmission rate R, and the length of the link m.

Explanation / Answer

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