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# Quantitative Comparison of Packet Switching & Circuit Switching

Consider the two scenarios below:

A circuit-switching scenario in which Ncs users, each requiring a bandwidth of 20 Mbps, must share a link of capacity 100 Mbps.

A packet-switching scenario with Nps users sharing a 100 Mbps link, where each user again requires 20 Mbps when transmitting, but only needs to transmit 20 percent of the time.

a. When circuit switching is used, what is the maximum number of circuit-switched users that can be supported? Explain your answer.

For the remainder of this problem, suppose packet switching is used. Suppose there are 9 packet-switching users (i.e., Nps = 9).

b. Can this many users be supported under circuit-switching? Explain.

c. What is the probability that a given (specific) user is transmitting, and the remaining users are not transmitting?

d. What is the probability that one user (any one among the 9 users) is transmitting, and the remaining users are not transmitting? When one user is transmitting, what fraction of the link capacity will be used by this user?

e. What is the probability that any 5 users (of the total 9 users) are transmitting and the remaining users are not transmitting? (Hint: you will need to use the binomial distribution [1, 2]).

f. What is the probability that more than 5 users are transmitting? Comment on what this implies about the number of users supportable under circuit switching and packet switching.

#### Solution Preview

a. When circuit switching is used, what is the maximum number of circuit-switched users that can be supported? Explain your answer.
When circuit switching is used, the maximum number of circuit-switched users that can be supported is 100/20=5. The reason is that each user will be allocated 20 Mbps bandwidth but only 100 Mbps of line capacity can be allocated.
For the remainder of this problem, suppose packet switching is used. Suppose there are 9 packet-switching users (i.e., Nps = 9).
b. Can this many users be supported under circuit-switching? Explain.
No, 9 users can not be supported under circuit-switching. The reason is that each user will be allocated 20 Mbps which will result ...

#### Solution Summary

The solution gives detailed steps on finding the maximum number of circuit-switched users that can be supported, computing the probability that given user is transmitting and the remaining users are not transmitting and and then commenting on the number of users supportable under packet switching.

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