# Packet switching network used,optimum packet size?

#1

In a packet switching network, packets are routed from source to destination along a single path having two intermediate nodes. If the message size is 24 bytes and each packet contains a header of 3 bytes, then the optimum packet size is:

#2

In a packet switching network, packets are routed from source to destination along a single path having two intermediate nodes. If the message size is 24 bytes and each packet contains a header of 3 bytes, then the optimum packet size is:

But after a certain limit reducing the packet size may increase the transmission time also.

Let transmission time to transfer 1 byte for all nodes be t. The first packet will take time = (packet size)3t. After the first packet reaches the destination, remaining packets will take time equal to (packet size)*t due to parallelism.

If we use 4 bytes as packet size, there will be 24 packets
Total Transmission time = Time taken by first packet +
Time taken by remaining packets
= 34t + 234t = 104t

If we use 6 bytes as packet size, there will be 8 packets
Total Transmission time = 36t + 76t = 60t

If we use 7 bytes as packet size, there will be 6 packets
Total Transmission time = 37t + 57t = 56t

If we use 9 bytes as packet size, there will be 4 packets
Total Transmission time = 39t + 39t = 54t