Introduction of network Please help me 5 When a packet switch receives a packet,

Question

Introduction of network

Please help me

5 When a packet switch receives a packet, it determines the outbound link to which the packet should be forwarded. Suppose when a particular packet arrives, one other packet is one quarter done being transmitted on this outbound link and four other packets are waiting to be transmitted. Packets are transmitted in order of arrival. Suppose all packets are 2,000 bytes and the link rate is 15 Mbps. What is the queuing delay for the packet? More generally, what is the queuing delay when all packets have length k, the transmission rate is T, p bits of the currently-being transmitted packet have been transmitted and q packets are already in the queue?

Explanation / Answer

The queuing delay is 0 for the first transmitted packet, k/T for the second transmitted packet, and generally, (q-1)k/T for the qth transmitted packet. Thus, the average delay for the Q packets is
(k/T + 2k/T + ....... + (Q-1)k/T)/Q
= k/(TQ) * (1 + 2 + ..... + (Q-1))
= k/(TQ) * Q(Q-1)/2
= kQ(Q-1)/(2TQ)
= (Q-1)k/(2T)

= (4.25-1)(2000)/(15*106)

= 0.43 ms
Note that here we used the well-known fact that
1 + 2 + ....... + Q = Q(Q+1)/2

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