GATE Overflow Test Series | Computer Networks | Test 1 | Question: 15

Question

A pure ALOHA network transmits $\text{100-bit}$ frames on a shared channel of $100\;\text{Kbps}$. The number of frames that will probably survive if system produces $250$ frames per second is ________ (rounded to the nearest integer)

Answer 1

Transmission time $(T_t) = \frac{100}{100 \times 10^3} = 1\; \text{ms}$
    
  $1$ second $\rightarrow 250$ frames
    
 $1$ frame $\rightarrow 1/250$ second or $4\; \text{ms}$
    
 So, $1\;\text{ms} \;\rightarrow  1/4$ frame
    
Average number of frames generated by the system during one frame transmission time is $G = 1/4.$   

Throughput of ALOHA $ = G\times e^{-2G}$
    
 $\qquad = 1/4 \times e^{-1/2} = 0.1516$    

 Number of frames expected to survive $ = 0.1516 \times 250 = 37.9$ out of $250$ frames.

Comments

is”nt it 2tx in pure aloha the valnarable time ??

Answer 2

Step 1: Find frame transmission Time

L/B which is 1ms

Then find number of frames in 1ms

250 frames in 1 second

how many frames in 1/1000 second?

0.25 frames in 1ms

it means G is 0.25

solve by standard formula $g$ * $e^{-2g}$

we will get 37.9