Consider sending a large file of F bits from Host A to B. There are N switches and N+1 links serially connected between hosts A and B, and all the links are uncongested. Host A segments the file into S bit segments (assume that F is an integer multiplier of S) and adds a header H to each segment. Each link has a transmission rate of R bps.

a) Find the value of S that minimises the total delay in sending the file from A to B. Disregard the propagation delay, the processing delays and queuing delays in each node. Clearly state any additional assumption you have made.

b) Verify your answer to part a) by plotting the total delay vs the segment size for F= 1000 bytes, N=4, R= 10 kbps and H = 20 bytes.