GATE | GATE CS 2021 | Set 2 | Question 64

Consider a network using the pure ALOHA medium access control protocol, where each frame is of length 1,000 bits. The channel transmission rate is 1 Mbps (=10⁶ bits per second). The aggregate number of transmissions across all the nodes (including new frame transmissions and retransmitted frames due to collisions) is modelled as a Poisson process with a rate of 1,000 frames per second. Throughput is defined as the average number of frames successfully transmitted per second. The throughput of the network (rounded to the nearest integer) is ______________ .
(A) 130 to 140
(B) 140 to 150
(C) 120 to 130
(D) 100 to 110


Answer: (A)

Explanation:

General Formula of Efficiency of Pure Aloha 

= G x e-2G

Where G is number of requests send in given time slot

So now Tt

= L/BW
= 1000/106
= 1 millisecond

For 1000 frames it will be 1000*1 millisecond = 1 second

So now in 1 second total 1000 frames send ,So G =1

Value of e = 2.71(Mathematical constant)

So efficiency 

= 1* 2.71^(-2+1) 
= 0.1353

Now for 1000 frames it would be 1000*0.1353 = 135.3 
(Closest Integer=135)

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