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consider the speed of propagation of a signal along a cable is 2*10^8m/s and metwork has 10Mbps CSMA/CD network interconnecting 10 computers shown in below image.each computer is connected to the hub with a cable of different length .Computer H1 is connected via a 100m cable,computer H2 via 200m cable…….(ignore requirement of repeater due to signal degradation).Assume hub introduces a delay of 2.5 microseconds.what is the shortest packet length Lmin of this network in order to ensure that the CSMA/CD functions properly?

 

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IN CSMA/CD, We need to consider the longest path, Here $H_9$ and $H_{10}$ will have path length of 900 m and 1000 m from the hub, so total distance = 1900 m.

A signal needs to travel from  $H_9$ to $H_{10}$ so total distance is 1900, along with that hub adds delay of 2.5 $\mu s$.While transmitting to  $H_{10}$ if the collision happens near $H_{10}$, a collision signal will again take 2.5 $\mu s$ hub delay to come back to $H_{9}$. Hence a hub will add a total of 5 $\mu s$ delay overall.

Hence,

$T_t \geq 2*T_P + 2*T_{hub}$

where,

$T_{hub} = 2.5 \mu s$

Propagation time = $\frac{distance}{velocity} = \frac{1900}{2*10^8} =  9.5 * 10^{-6} = 9.5 \ \mu s$

$L \geq (2*T_P + 2*T_{hub})B = (2*9.5 \mu s + 2*2.5 \mu s)10*  10^{6}bps= 240 \ bits$ .
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