Calculating throughput for slotted ALOHA

Question

Consider a system generating 20 bit frames and connected through a shared 20kbps channel. Find throughput in percent if slotted ALOHA is used and frame rate is 1000 fps.

Answer 1

Frame size = L = 20 bits
Rate = R = 20kbps
Transmission time,T = L/R = 1 * 10^-3 s
Throughput, S = G e-G, where G= Number of frames per T
So, G = 1000 * 10^-3 = 1
Therefore, S = e-1 = 0.368 = 36.8%

Comments

FPS=1000, ie: (number of frames)/time=1000, right?

Which is Number of frames per T?

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Thats a number of frames per transmission time.

Answer 2

Answer :

As we know efficiency in slotted  aloha = G * e^-G

where G=no of stations who can transmit in Transmission Time

Here transmission time = L/BW = 20 bit / 20 Kbps = 1ms

As BW is 20 Kbps so bits that can be transferred in 1 ms = 20 bits

This means only 1 station can transmit data in time equal to one transmission time

i.e G=1

As throughput is asked in percentage which indicates they are asking indirectly for efficiency

So throughput in percentage = 1 * e ^ -1 =0.3678 i.e 36.78 %

Extending the question :

Throughput = Efficiency * Bandwidth

                  = 0.3678 * 20 Kbps

                 =  7.35 Kbps

Answer 3

$\large S_{slotted} = G \times e^{-G}$

$\large G = N \times fps \times T_{fr}$

$\text{frame size} = 20 \ \text{bit} $

Here number of stations are not given and frames generated by whole system is given which is $1000 fps$

so, $G = 1000 \ \times \frac{20}{ 20 \times 10^3} $

$G = 1$

$\large S_{slotted} = 1 \times e^{-1} = 0.368 = 36.8 \text{%}$

Comments

Where did u this formula bro ? please refer