Virtual Gate Test Series: Computer Networks - CSMA

Question

A $8$-node network runs the Carrier Sence Multiple Access $\text{(CSMA) MAC}$ protocol.The maximum data rate of the network is $\text{10 Megabits/sec}.$ Including retries, each node sends traffic according to some unknown random process at an average rate of  $\text{1 Megabits/sec}$ per node. Given that the network's utilization is $0.75.$  No packets get dropped in the network except due to collisions $\text{(including retries)}$ experience a collision _____$\%?$ $\text{(Correct to two decimal places).}$

Comments

$6.25%$ ... ?

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Yes. Now explain plz ☺

Answer 1

If only $1$ Node transmits, then in $1$ sec $\left \{ B = 1 Mb/s \right \}$ .

If all the 8 Nodes transmit, then in 1 sec $\left \{ B = 8 Mb/s \right \}$ .

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Throughput of this shared network = Efficiency of the network * Bandwidth of the  network = $0.75 * 10 Mb/s = 7.5 Mb/s$ .

At an average, Out of $10$ Mb/s, we receive throughput of only $7.5$ Mb/s .

When, all the $8$ Nodes are simultaneously transmitting, Bandwidth of only $8$ Mb/s can be reached, but at the end throughput can be only $7.5$ Mb/s $\left \{ Successful\ Transmission \right \}$.

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Hence, Fraction which receives a collision = $\frac{8 - 7.5}{8} * 100 = 6.25 $% .

Comments

One typo. 0.75*10 should be there.

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Thanks !! Corrected !