Please help me with this problem for computer networks, thank you! Consider two

Question

Please help me with this problem for computer networks, thank you!

Consider two active nodes, A and B, on an ethernet with lots of frames to send. Each node tries to senod its first frame and they collide, send their jamming signal and calculate a back-off time in the interval 0,1] slots. Let A be the node that chooses a back-off time 0 and B chooses a back-off time of 1 slot (if botlh pick the same slot, they collide again). So A sends its first frame successfully and B decides to wait 1 slot. However during the next time slot when B tries to send its first frame, A also tries to send its second frame so they collide again. Answer the following questions 2 pts each: (a) After the last collision (A's second frame colliding with B's first frame), what are the back-off intervals (b) What is the probability that B wins over A and can send its first frame successfully? c) If A wins that round, do you think that B has a fair chance to win the next round? Explain why

Explanation / Answer

Q (a). After the last collision (A's second frame colliding with B's first frame), what are the back-off intervals nodes A and B are choosing from?

Solution : For A's second frame this is second try but for B's first frame this is the third try

so A chooses a random no between (0 to 2n -1) where n is tries number = 2

= (0 to 22-1)

= (0, 1, 2, 3)

and B chooses a random no between (0 to 2n-1) where n is tries number = 3

= (0 to 23-1)

= (0,1,2,3, 4, 5, 6, 7)

A's Backoff interval= (0, 1, 2, 3)

B's Backoff interval = (0,1,2,3, 4, 5, 6, 7)

Q (b) What is the probability that B wins over A and can send its first frame successfully?

Solution: There are 32 combination form because A's has 4 option to choose and B has 8 option to choose like

(0,0), (0,1), (0,2), (0,3), (0,4),(0,5),(0,6),(0,7)

(1,0), (1,1), (1,2),(1,3),(1,4),(1,5),(1,6),(1,7)

(2,0),(2,1),(2,2),(2,3),(2,4),(2,5),(2,6),(2,7)

(3,0),(3,1),(3,2),(3,3),(3,4),(3,5),(3,6),(3,7)

probability of B's win over A's = 6/32 //where 6 is combinations where value of B's is less than A's//

Q(c) If A wins that round, do you think that B has a fair chance to win the next round? explain why.

solution: No, Because chance to win A is more than B in next round.

Here A will choose third frame to send but B first freme is still pending. This ist the first tryof A's third freme and fourth try of B's first frame so A will choose no between (0 to 21-1) and B will choose no between ( 0 to 24-1).

So A's backoff interval = ( 0,1)

and B's backoff interval = (0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15)

so A has more chance to win over B

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