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A 8-node network runs the carrier sense Multiple Access (CSMA) MAC protocol. The maximum data rate of the network is 10 Megabits/s. Including retries, each node sends traffic according to some unknown random process at an average rate of 1 Megabit/s per node. Given that the network's utilization is 0.75 No packets get dropped in the network except due to collisions, and each node's average queue size is 5 packets. What fraction of packets sent by the nodes (including retries) experience a collision?_________% (correct to two decimal places).
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0.625 ??
it is 6.25%.

Max data rate = 10Mbps

each node data rate = 1Mbps

so 8 nodes would be = 8Mbps

Now, it is given in the question that efficiency is 7.5%.

Throughput = 7.5 * 10 Mbps

7.5 Mbps.

which means that (8 - 7.5) 0.5Mbps are wasted due to the collisions.

So, 0.5Mbps / 8 Mbps = 0.0625 ~ 6.25%
Good @subhanshu:)

1 Answer

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Given,Bandwith of Network=10Mbps.

Packet size=10000bits.

So,Number of packets can be transmitted through network per second=10Mbps/10000bits=1000 packets.

Since Network utilization is .75 so efficient number of packets that can be transmitted through network per second=.75*1000=750 packets.

Now talking about each nodes.

Average rate of each of each node=1Mbps.

packet size=10000bits.

So,number of packets sent by each node in 1 sec=1Mbps/10000bits=100packets.

Total number of packets sent by all 8 node combined=800 packets.

Therefore, Fraction of collision = (800-750)/800=50/800=6.25%

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