## Question

Suppose M=20 users are sharing B Mbps link. Also suppose each user requires b=0.2 Mbps when transmitting, but each user transmits only p=2% of the time. Suppose packet switching (i.e. statistical multiplexing) is used. Find the minimum value of B such that the probability of packet queuing is less than 0.5%. You may assume B is a multiple of b, i.e. if b is 0.2 Mbps, B would be 0.2 Mbps, 0.4 Mbps, 0.6 Mbps, etc. Also, you may assume 1 Mbps = 10^6 bps.

a. What is your answer to the question underlined above? Justify your answer by attaching a screenshot of the execution of your program below.

b. As M increases while other conditions stay the same, how does the value of the min of B that satisfies the probability requirement underlined above react? Justify your answer by populating the table below.

M B (Mbps)

20

30

40

50

60

70

80

90

Note: b=0.2, p=2%

c. As b increases while other conditions stay the same, how does the value of the min of B that satisfies the probability requirement underlined above react? Justify your answer by populating the table below.

b (Mbps) B (Mbps)

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Note: M=20, p=2%

d. As p increases while other conditions stay the same, how does the value of the min of B that satisfies the probability requirement underlined above react? Justify your answer by populating the table below.

p (%) B (Mbps)

2

3

4

5

6

7

8

9

Note: M=20, b=0.2

What to turn in?

a. This word document with all your answers.

b. The source code file of your program.

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