Aloha

Question

You have two computers, $A$ and $B$, sharing a wireless network in your room. The network runs the slotted Aloha protocol with equal-sized packets. You want $B$ to get twice the throughout over the wireless network as $A$ whenever both nodes are backlogged. You configure $A$ to send packets with probability $p$. What should you set the transmission probability of $B$ to, in order to achieve your throughout goal?

1. $p/(1+p)$
2. $p/(1+2p)$
3. $2p/(1+p)$
4. $1/2$

Comments

http://web.mit.edu/6.02/www/s2010/handouts/lectures/L16-notes-2.pdf(16.3, concept )

http://web.mit.edu/6.02/www/f2010/handouts/q3review/f09quiz3-soln.pdf(q.5)

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Is the ans C ? @ParimalAndhalkar or @Amsar ?

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yes, I m getting C..

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You can always google before posting question. :)

https://gateoverflow.in/34586/aloha

Answer 1

Option C is correct.

slotted Aloha - Time is divided in slots, so, either A or B transmits only at beginning of a slot.

Given, A's probability to transmit = p

 Let B's probability to transmit = x

So, probability of unsuccessful transmission = probability that both A & B transmit = x * p

probability of successful transmission by A =  P(A)  - P(A∩B) = p - xp 

probability of successful transmission by B =  P(B)  - P(A∩B) = x - xp

Now, since B should have twice the throughput of A, this gives 

    x - xp = 2* (p - xp)

=>   x + xp = 2p

=>  x= 2p/ (1+p)   Option C (Ans).

Comments

Can do in this way too :

Probability of A's transfer is P .

Now since throughput of B is twice that of A so transfer probability becomes twice ie 2p .

Now denominator should be  2p + (1-p)  ( B transmitting successfully and A could not transmit within that slot ) .

So B' overall transmission probability is  2p / (2p + (1-p) ) = 2p / (p+1) .