Question

A company has a dedicated link of 100 Mbps. Each employee, when online, transmits continuously at 12 Mbps when active, but each user is active only 20 percent of the time. 1. How many users can the link support when circuit switching is used? 2. For the remainder of this problem, suppose packet switching is used. What is the probability that more than 2 users are transmitting at the same time? 3. Now suppose that the system will drop any packets if it is being utilized at 100% capacity without queuing them. If we need to guarantee a probability of at most 0.05 of messages being lost, what is the maximum number of users we can support under packet switching. (Hint: You can use a programming language like Python or just solve analytically. In both cases you will receive full marks. Points will be given if you describe the correct reasoning without ending up with a correct solution)

Answer 1

Answer: (a) 8 users

(b) 51.5%

Explanation:

(a) Bandwidth = 1000 Mbps = 1000*100 = 100000 Kbps

Employee requirement = 12 Mbps = 12*1000 = 12000 Kbps

Total users = 100000/12000 = 8 Users approx

(b) P(x>2) = 1-(P(x=0)+P(x=1)+P(x=2))

= (8CO * 0.80^8) + (8C1 * 0.80^7*0.20) + (8C2 * 0.80^6*0.20^2)

=51.5%