Let a denote the rate of packets arriving at a link in packets/sec, and let denote the link's transmission rate in packets/sec. Based on the formula for the total delay (i.e., the queuing delay plus the transmission delay) derived in the previous problem, derive a formula for the total delay in terms of a P1 5. and Consider a router buffer preceding an outbound link. In this problem, you will use Little's formula, a famous formula from queuing theory. Let N denote the average number of packets in the buffer plus the packet being P16. transmitted. Let a denote the rate of packets arriving at the link. Let d denote the average total delay (i.e., the queuing delay plus the transmission delay) experienced by a packet. Little's formula is N a d. Suppose that on aver age, the buffer contains 10 packets, and the average packet queuing delay is 10 msec. The link's transmission rate is 100 packets/sec. Using Little's formula, what is the average packet arrival rate, assuming there is no packet loss P17. a. Generalize Equation 1.2 in Section 1.4.3 for heterogeneous processing rates, transmission rates, and propagation delays. b. Repeat (a), but now also suppose that there is an average queuing delay of dqueue at each node. P18. Perform a Traceroute between source and destination on the same continert at three different hours of the day a. Find the average and standard deviation of the round-trip delays at each of the three hours. b. Find the number of routers in the path at each of the three hours. Did the paths change during any of the hours? c. Try to identify the number of ISP networks that the Traceroute packets pass through from source to destination. Routers with similar names and/ or similar IP addresses should be considered as part of the same ISP. In your experiments, do the largest delays occur at the peering interfaces between adjacent ISPs? d. Repeat the above for a source and destination on different continents. Compare the intra-continent and inter-continent results