128 views
20 Gbps link each user using 5Gbps when active<20% time the user is active>

Max. users that the network can be used by?
Using circuit switching?
| 128 views
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4 users ?
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I also think it should be 4
No more devices can work in parallel?

$\rightarrow$ Consider a time interval of  100 seconds.and it is divided into partition of 20 seconds like

 ${\color{Red} 2}{\color{Red} 0}{\color{Red} s}{\color{Red} e}{\color{Red} c}$ ${\color{Green} 2}{\color{Green} 0}{\color{Green} s}{\color{Green} e}{\color{Green} c}$ ${\color{Cyan} 2}{\color{Cyan} 0}{\color{Cyan} s}{\color{Cyan} e}{\color{Cyan} c}$ ${\color{DarkOrange} 2}{\color{ DarkOrange } 0}{\color{ DarkOrange } s}{\color{ DarkOrange } e}{\color{ DarkOrange } c}$ ${\color{Orchid} 2}{\color{ Orchid } 0}{\color{ Orchid } s}{\color{ Orchid } e}{\color{ Orchid } c}$

20% time the user is active

$\rightarrow$ In the ${\color{Red} 1^{st}}$ ${\color{Red} s}{\color{Red} l}{\color{Red} o}{\color{Red} t}$ of ${\color{Red} 2}{\color{Red} 0}{\color{Red} s}{\color{Red} e}{\color{Red} c}$

• $User 1$ , $User 2$ , $User 3$ , $User 4$ are active and each uses 5 Gbps
•  Together they use 5 Gbps + 5 Gbps+ 5 Gbps + 5 Gbps  = 20 Gbps for the ${\color{Red} 2}{\color{Red} 0}{\color{Red} s}{\color{Red} e}{\color{Red} c}$ and after this they will become inactive for the rest 4 intervals of 20 seconds each i.e. for the next 80 seconds.

$\rightarrow$ In the next  ${\color{Green} 2^{nd}}$ ${\color{Green} s}{\color{Green} l}{\color{Green} o}{\color{Green} t}$ of  ${\color{Green} 2}{\color{Green} 0}{\color{Green} s}{\color{Green} e}{\color{Green} c}$

• $User 5$ ,$User 6$ ,$User 7$ ,$User 8$ are active and each uses 5 Gbps
•  Together they use 5 Gbps + 5 Gbps+ 5 Gbps + 5 Gbps  = 20 Gbps for the next ${\color{Green} 2}{\color{Green} 0}{\color{Green} s}{\color{Green} e}{\color{Green} c}$ and after this they will become inactive for the next 4 intervals of 20 seconds each i.e. for the next 80 seconds.

$\rightarrow$ In the next ${\color{Cyan} 3^{rd} }$ ${\color{Cyan} s}{\color{Cyan} l}{\color{Cyan} o}{\color{Cyan} t}$   of  ${\color{Cyan} 2}{\color{Cyan} 0}{\color{Cyan} s}{\color{Cyan} e}{\color{Cyan} c}$

• $User 9$ , $User 10$ , $User 11$ ,$User 12$ are active and each uses 5 Gbps
•  Together they use 5 Gbps + 5 Gbps+ 5 Gbps + 5 Gbps  = 20 Gbps for the next ${\color{Cyan} 2}{\color{Cyan} 0}{\color{Cyan} s}{\color{Cyan} e}{\color{Cyan} c}$ and after this they will become inactive for the next 4 intervals of 20 seconds each i.e. for the next 80 seconds.

$\rightarrow$ In the ${\color{DarkOrange} 4^{th} }$ ${\color{DarkOrange} s}{\color{ DarkOrange } l}{\color{ DarkOrange } o}{\color{ DarkOrange } t}$   of   ${\color{DarkOrange} 2}{\color{ DarkOrange } 0}{\color{ DarkOrange } s}{\color{ DarkOrange } e}{\color{ DarkOrange } c}$

• $User 13$ ,$User 14$,$User 15$ , $User 16$ are active and each uses 5 Gbps
•  Together they use 5 Gbps + 5 Gbps+ 5 Gbps + 5 Gbps  = 20 Gbps for the next ${\color{DarkOrange} 2}{\color{ DarkOrange } 0}{\color{ DarkOrange } s}{\color{ DarkOrange } e}{\color{ DarkOrange } c}$ and after this they will become inactive for the next 4 intervals of 20 seconds each i.e. for the next 80 seconds.

$\rightarrow$ In the ${\color{Orchid} 5^{th} }$ ${\color{Orchid} s}{\color{ Orchid } l}{\color{ Orchid } o}{\color{ Orchid } t}$ of  ${\color{Orchid} 2}{\color{ Orchid } 0}{\color{ Orchid } s}{\color{ Orchid } e}{\color{ Orchid } c}$

• $User 17$ ,$User 18$ ,$User 19$ , $User 20$ are active and each uses 5 Gbps
•  Together they use 5 Gbps + 5 Gbps+ 5 Gbps + 5 Gbps  = 20 Gbps for the next   ${\color{Orchid} 2}{\color{ Orchid } 0}{\color{ Orchid } s}{\color{ Orchid } e}{\color{ Orchid } c}$ and after this they will become inactive for the next 4 intervals of 20 seconds each i.e. for the next 80 seconds.

$\rightarrow$ After  this again $User 1$ , $User 2$ , $User 3$ , $User 4$ are active and each uses 5 Gbps  and the loop repeats.

$\therefore$ Max. users that the network can be used by is 20.

by Boss (24k points)
edited by
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But this isn't the right way, I mean this way if you keep increasing from 100ms time, you will get more users.
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No because after 80 time units the previous users will become active again. I have just assumed time unit to be in second. You can take it in ms also.

@manisha11 Can you please explain how we can get more users ?

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But deciding time frame is also not valid

What if all the users are active simultaneously

@MiNiPanda

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Try yourself @manisha11

Suppose if 30 users try to access simultaneously then only 4 users will be able to access it and for next 80 time units they will become inactive

same process goes on and at most 20 user will be able to access it

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@manisha11

Take any time interval say 200 s. We know that a user stays active for 20% of the time. So user1 will stay active for 40 s (20% of 200 s). Also, simultaneously 4 users can use the channel as each of them uses 5 Gbps and the bandwidth is 20 Gbps.

Answer would have been 4 if the question had not mentioned that a user is active for 20% of the time. But now with this additional info. our answer might not be same anymore right?

We will divide it into 5 slots each getting 40 s where in each of these slots we will have 4 users who can use the channel at the same time (increasing the time slot doesn't increase the bandwidth of channel so we cannot increase the no. of users using it. It will remain same. Just the time of access increases) . So 5 slots each with 4 users. In a given time interval, atmost 20 users can be active.

Comment if you find this wrong..

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Right in parallel only 4

So 4 is a better answer?