GATE IT 2004 | Question: 85

Question

Consider a simplified time slotted MAC protocol, where each host always has data to send and transmits with probability $p$ = $0.2$ in every slot. There is no backoff and one frame can be transmitted in one slot. If more than one host transmits in the same slot, then the transmissions are unsuccessful due to collision. What is the maximum number of hosts which this protocol can support if each host has to be provided a minimum throughput of $0.16$ frames per time slot?

• A. $1$
• B. $2$
• C. $3$
• D. $4$

Comments

https://gateoverflow.in/1263/gate2007-65

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very imp line 

 if each host has to be provided a minimum throughput of 0.16 frames per time slot

then n host = 0.16n

 

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GO to the Root of Concept: Video Explanation with timestamp: Derivation Efficiency & Throughput of Aloha | In-Depth | GATE 2021, 2004, 2007 PYQs | With NOTES

Answer 1

I have read all answers above and there still some ambiguity among aspirants.Let me clear it for you.

Here probability of sending a frame in a time slot by a host is 0.2.

But what is the probability of success in sending a frame in a time slot by a host ?

Psucces = 0.2*(0.8)^(N-1) i.e all other host (N-1 hosts) must be not be sending.

what reciprocal of this probability (1/Psuccess) tells us?

It tells about minimum number of time slots required by a host to successfully send 1 frame.

Now let us understand what is throughput?

Throuhput is data send over an interval of time. Here it is 0.16 frame per time slot by a host.

So, in how many time slots are required by a host to send 1 frame ?

It will be 1/0.16=number of time slots required for successful transfer by a host which we have calculated earlier.

1/0.16 = (1/Psuccess) = 1/(0.2*(0.8)^(N-1))

.16=0.2*(0.8)^(N-1)

Therefore, N=2.

Correct choice B

Comments

Yeah.Then why didn't you consider n in Psucces

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Becauuse at one time slot anyone of hosts can only send a frame for successful transmission.

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The probability of n*success is about different successful possibilities that could take place.

Answer 2

Try to feel what the question is demanding.

It really helps

I have felt that

A------------------------------------B

There are n number of hosts sitting at A and they can use the transmission medium to send packet to B.

Now we are asked what are the maximum number of hosts which can send the packet to B at probability of sending packet = 0.2 so that Throughput is 0.16

 

This means one host should send the packet and rest should not

0.16 = $0.2^{1}*0.8^{n-1}$

Just solve for n

You will get n=2

The image clearly explains everything