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Tutorial 1

Q3​

Suppose we want to send a file of 160,000 bits from Host A to Host B over a circuit-switched network. Suppose that all links in the network use FDM with 12 frequency bands of the same bandwidth. Assume that the 12 frequency bands together can support a total bit rate of 1.536 Mbps. Also suppose that it takes 600 msec to establish an end-to-end circuit before Host A can begin to transmit the file. How long does it take to send the file?

160000 / (1.536 * 1000000 / 12) + 600 / 1000

= 1.85

Q4​

Suppose users share a 3 Mbps link. Also suppose each user requires 150 kbps when transmitting, but each user transmits only 10 percent of the time.

a. When circuit switching is used, how many users can be supported?​

3 * 1000 / 150

= 20

b. For the remainder of this problem, suppose packet switching is used. Find the probability that a given user is transmitting.​

0.1 (from question)

c. Suppose there are 120 users. Find the probability that at any given time, exactly n users are transmitting simultaneously​

X∼B(120,0.1)X \sim B(120, 0.1) P(X=n)=C(120,n)0.1n0.9120−n\begin{align*} P(X = n) &= C(120, n) 0.1^n 0.9^{120 - n} \end{align*}