Question

Computer Network Performance (20 Points) 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). 1111 Font Family . Format B I u 1) What is the transmission time for the last packet? Solution: 2) What is the queue delay for the 4th packet? Solution: 3) What is the average queue delay for the first three packets? Solution: 4) What is the average transmission delay for the last three packets? Solution: 5) What is the total delay for 10th packet including queue delay and transmission delay? Solution: L/R

Answer 1

Number of packets = N
Length of packet = L
Transmission rate = R

(1)Transmission time of last packet = L/R
(2)Queue delay for the 4th packet = Time taken to transmit first 3 packets = (3*L)/R
(3)Queue delay for the first packet = 0
Queue delay for the second packet = L/R
Queue delay for the first packet = 2L/R

Total delay = (0 + L/R + 2L/R) = 3L/R
Average delay = (3L/R)/3 = L/R

(4)
Transmission delay of last packet = N*L/R
Transmission delay of second last packet = (N-1)*L/R
Transmission delay of third last packet = (N-2)*L/R

Average delay = 1/3(N*L/R + (N-1)*L/R + (N-2)*L/R)
=> (N-1)*L/R

(5)Total delay for 10th packet = (10L)/R