Problem $5(12$ marks$)$: Consider a time$-$slotted local area network where connected stations employ a $1-$

persistent carrier sense multiple access $($CSMA$)$ scheme to access the physical medium. Assume that the

following linear backoff algorithm is employed after a collision:

The delay is an integral multiple of the slot duration $T,$ the latter being equal to twice the

maximum propagation delay across the medium.

The number of slot times to delay before the $i-$th retransmission attempt is chosen as a random

integer $r,$ uniformly distributed in the range $L{P}_{i}i-1i{P}_{i}L=20r,$ where $Lis$ a positive integer.

$a$