Consider sending a large file of F bits from host A to host

Consider sending a large file of F bits from host A to host B. A and B are connected by a route of L links, and the links are not congested (that is, no queuing delays). Host A partitions the file into segments of S bits each (assume F is a multiple of S) and adds H bits of header to each segment, forming packets of S + H bits. Each link has a transmission rate of R bps. Find the value of S that minimizes the delay of moving the file from host A to host B, neglecting propagation delay.

Solution

Solution ::

Host A(S) --> router (R)---> router (R) ---> Host B

Host A sends a file to Host B.File is very large so the file is partitioned into segments S bits each and add H bits of header to the each segment,forming the packets

of S+H bits.Now we have find the value of S.
Transmission Delay in Packet Switching ::
The principle of packet switching is Store and Forward.
Packets are completely received before being transmitted to the next node.

Consider Each segment as a packet and consists of S bits.
It takes L/R seconds to transmit S bits on to the link (or) R bps.
Entire the packet will be arrive at router before it can be transmitted on next link.

Now,the transmission delay is : 3S/R (assume that the propagation delay is zero)

Transmission delay = 3*S/R
Transmission delay * R = 3*S

Therefore, S = (Transmission delay * R) / 3

If transmission delay is minimum then we minimizes the delay of moving the file from Host A to Host B.

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