Suppose N packets arrive simultaneously towards a router for transmiision over a

Question

Suppose N packets arrive simultaneously towards a router for transmiision over a link at which no packets are currently being transmitted or queued. Each packet is of length L and the link has transmission rate R and propagation delay D. Assume that the processing delay is negligible. Draw a timing diagram and explain the diagram that shows how these N packets are transmitted over the single hop represented by this link . What is the average queuing delay for the N packets?
What is the total delay for transmitting all N packets over this hop?

Explanation / Answer

The queuing delay is 0 for the first transmitted packet 0, for the second transmitted packet, and, generally, for the nth transmitted packet. Thus, the average delay for the N packets is

(L/R+2L/R+....+(N-1)L/R)/N=L/RN(1+2+.....+(N-1))=LN(N - 1)/2RN = (N - 1)L/2R

The transmission delay for each case is The total delay is the queuing delay plus the transmission delay.

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