Suppose you are using packet switching. What is the maximum number of users that

Question

Suppose you are using packet switching. What is the maximum number of users that can be supported if the required blocking probability is strictly less than .05. Users share a 2Gbps link and each user requires 400 Mbps when transmitting, but only transmits 30% of the time.

So I understand:

P(transmitting) = .3

P(not transmitting) = .7

I also know that P(n users simultaneously transmitting) = (total users "choose" n) (.3^n) * (.7^(total users - n))

But I have no idea how to proceed with the problem. Thank you for your help in advance.

Explanation / Answer

Solution : According to the question -

It is given that the blocking probability is strictly less than 0.05.

Users share 2Gbps and each user require 400Mbps.

Transmit 30% only.

As we known - [ 1 = 0.3 + 0.7 ]

So, Firstly convert 400Mbps into Gbps. i.e.; 1000Mb = 1Gb

400 Mb = xGb

We get, xGb = 400/1000 = 0.4Gb

Then we can calculate the maximum number of users = 20Gbps/0.4Gbps

= 5Gbps

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