Question

Think of the differences between circuit-switching and packet-switching paradigms in the Internet core design. Assume an Internet Service Provider (ISP) has an access link with 500 Mbps capacity and, at any given time, only 1% of its customers are active. However, during that active period, users generate data at a constant rate of 20 Mbps. Assume that there is a total of 100 customers of this ISP.

i. What is the maximum number of users the ISP can serve if it is implementing a circuit-switching strategy?
ii. What is the probability that 1 user will be active?
iii. What is the probability that more than 1 users will be active?
iv. What is the probability that more than 2 users will be active?
v. What is the probability the ISP will not be able to serve some users (i.e., more than 25 users being active) if it is implementing a packet-switching strategy?

Answer 1

1. 25 users

2. 0.3697

3. 0.2643

4. 0.079

Explanation:

1. The maximum users the isp can serve = 500/20 = 25 users

2. The probability 2 user will be active

Total number of customers = 100

P = 1/100

P+t = 1

T = 1 -p

T = 99/100

Using binomial distribution

X = 1

100C1 x (1/100)¹ (99/100)⁹⁹

= 100 x 0.01 x 0.3697

= 0.3697

3. Probability of more than 1 active user

1-[100C1 x (1/100)⁰(99/100)¹⁰⁰ + 0.36973]

= 1-(0.3660+0.3697)

= 1-0.7357

=0.2643