b. (10 points) Consider a router buffer preceding an outbound link. In this prob

Question

b. (10 points) Consider a router buffer preceding an outbound link. In this problem, you will use Little's formula, a famous formula from queueing theory. Let N denote the average number of packets in the buffer plus the packet being transmitted. Let a denote the rate of packets arriving at the link. Let d denote the average total delay (i.e, the queueing delay plus the transmission delay) experienced by a packet. Little's formula is N = A × d. Suppose that on average, the buffer contains 10 packets, and the average packet queueing delay is 10 milliseconds. The link's transmission rate is 100 packets/sec

Explanation / Answer

We know that, N = A x d

So, A = N/d   -------------(1)

The average number of packets N = 10

The link transmission rate, l = 100 packets/sec = 1 packet/.01 sec

The link transmission rate is 0.01 sec for one packet.

l=0.01

Queueing delay, q = 10msec = .01 sec

Average total delay d = l + q = .02 sec

Now apply the value of N and d we will get,

A = 10 packets/(.02 sec) = 500 packets/sec

Therefore the Average Packet Arrival rate is 500 packets/sec.

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