Question

Suppose N packets arrive simultaneously to a router at which no packets are currently being transmitted or queued. Each packet is of length L and the link has transmission rate R (simple proof is needed).

Answer 1

Solution:

Given,

=>Number of packets = N

=>Each packet length = L

=>Transmission rate = R

(1)

Explanation:

=>Transmission delay will be equal for all N packets.

=>Transmission delay for last packet = packet length/transmission rate

=>Transmission delay for last packet = L/R

(2)

Explanation:

=>As all N the packets arrive at the router simultaneously so there will be queuing delay based on the order in which they are.

=>For 1st packet, queuing delay = 0

=>For 2nd packet, queuing delay = transmision delay for 1st packet.

=>For 2nd packet, queuing delay = L/R

=>For 3rd packet, queuing delay = transmission delay for 1st packet + transmission delay for 2nd packet

=>For 3rd packet, queuing delay = L/R +L/R

=>For 3rd packet, queuing delay = 2L/R

=>For 4th packet, queuing delay = transmission delay for 1st packet + transmission delay for 2nd packet + transmission delay for 3rd packet

=>For 4th packet, queuing delay = L/R + L/R + L/R

=>For 4th packet, queuing delay = 3L/R

(3)

Explanation:

=>Average queuing delay for first three packets = (queuing delay for first packet + queuing delay for second packet + queuing delay for 3rd packet)/3

=>Average queuing delay for first three packets = (0 + L/R + 2L/R)/3

=>Average queuing delay for first three packets = 3L/R/3

=>Average queuing delay for first three packets = L/R

(4)

Explanation:

=>Average transmission delay for last three packets = (transmisison delay for Nth packet + transmission delay for (N-1)th packet + transmission delay for (N-2)th packet)/3

=>Average transmission delay for last three packets = (L/R + L/R + L/R)/3

=>Average transmission delay for last three packets =3L/R/3

=>Average transmission delay for last three packets = L/R

(5)

Explanation:

=>Total delay for 10th packet = queuing delay for 10th packet + transmission delay for 10th packet

=>Total delay for 10th packet = 9L/R + L/R

=>Total delay for 10th packet = 10L/R

I have explained each and every part with the help of statements attached to it.