# (Solved Homework): Suppose there are exactly two routers between a sending host and a receiving host. As shown below, the tra…

Suppose there are exactly two routers between a sending host and a receiving host. As shown below, the transmission rate of each link is R. Suppose N packets simultaneously arrive to router 1 and no other packets are currently being transmitted or queued in the network. Each packet is of length L. a) What is the average queuing delay for the N packets at router 1? b) What is the average queuing delay for the N packets at router 2?

a)

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N number of packets are there

So, rate of transfer for each packet is L/t….(t is time required for each packet)

There for queuing delay for packet is q1 = L/R, q2 =L/R*2, q3 =L/R*3,…………qN =L/R*(N-1)………(1)

N-1 because there no queuing delay for first packet).

Average queuing delay is given by    (q1 + q2+ q3…… qN+)/N

Put the values from equation …(1)

(L/R+ L/R*2+ L/R*3……..+ qN =L/R*(N-1))/N

Average queuing delay at router 1 for N packet is (L/R+ L/R*2+ L/R*3……..+ qN =L/R*(N-1))/N

b)

Transmission rate for each link is same that is R

Number of packet and its size is also same that is N and L

So , Average queuing delay at router 2 for N packet is (L/R+ L/R*2+ L/R*3……..+ qN =L/R*(N-1))/N

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