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Suppose you are a service provider with 120KHz of bandwidth

which you must allocate between voice and data users. The voice users require 20Khz of bandwidth, and

the data users require 60KHz of bandwidth. So, for example, you could allocate all of your bandwidth to

voice users, resulting in 6 voice channels, or you could divide the bandwidth to have one data channel and

three voice channels, etc. There are six independent voice users in the system: each of these users requests a voice channel with probability .8 and pays $.20 if his call is processed. There are two independent data users in the system:

each of these users requests a data channel with probability .5 and pays $1 if his call is processed. How

should you allocate your bandwidth to maximize your expected revenue?

solution

This is a problem from a textbook , I have found the solution online and would very appreciate it if someone can answer my question.

  1. What is the term for this kind of probability, I would like to research more about it but not sure about the keyword

2.case 2 said d=1 but why the solution also include the prob of having two data user? The same with prob of having more than 3 voice users

3.is this solution correct?

Thanks so much, any help would greatly appreciated

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    $\begingroup$ Welcome to MSE. It is in your best interest that you type your questions (using MathJax) instead of posting links to pictures. $\endgroup$ – José Carlos Santos Feb 24 at 11:12

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