Consider the discussion in Section 1. Suppose that the 1 Mbps link is replaced by a 1 Gbps link. Now consider packet switching and a user population of M users. Give a formula in terms of p,M,N for the probability that more than N users are sending data. Consider a packet of length L which begins at end system A and travels over three links to a destination end system.

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Consider the discussion in Section 1. Suppose that the 1 Mbps link is replaced by a 1 Gbps link. Now consider packet switching and a user population of M users. Give a formula in terms of p,M,N for the probability that more than N users are sending data. Consider a packet of length L which begins at end system A and travels over three links to a destination end system.

These three links are connected by two packet switches. Suppose now the packet is 1, bytes, the propagation speed on all three links is 2. For these values, what is the end-to-end delay? Further suppose the packet switch does not store-and-forward packets but instead immediately transmits each bit it receives before waiting for the entire packet to arrive. What is the end-to-end delay? A packet switch receives a packet and determines the outbound link to which the packet should be forwarded.

When the packet arrives, one other packet is halfway 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 1, bytes and the link rate is 2 Mbps.

What is the queuing delay for the packet? More generally, what is the queuing delay when all packets have length L, the transmission rate is R, x bits of the currently-being-transmitted packet have been transmitted, and n packets are already in the queue?

Each packet is of length L and the link has transmission rate R. What is the average queuing delay for the N packets? What is the average queuing delay of a packet? Thus, the average delay of a packet across all batches is the average delay within one batch, i.

Consider the queuing delay in a router buffer. Provide a formula for the total delay, that is, the queuing delay plus the transmission delay. Based on the formula for the total delay i. Consider a router buffer preceding an outbound link. 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. Suppose that on average, the buffer contains 10 packets, and the average packet queuing delay is 10 msec. Generalize Equation 1. Repeat a , but now also suppose that there is an average queuing delay of dqueue at each node. Perform a Traceroute between source and destination on the same continent at three different hours of the day.

Find the average and standard deviation of the round-trip delays at each of the three hours. Find the number of routers in the path at each of the three hours. Did the paths change during any of the hours? Try to identify the number of ISP networks that the Traceroute packets pass through from source to destination.

In your experiments, do the largest delays occur at the peering interfaces between adjacent ISPs? Repeat the above for a source and destination on different continents.

Compare the intra-continent and inter-continent results. Do it your self. Visit the site www. How many links are the same in the two traceroutes? Is the transatlantic link the same? Repeat a but this time choose one city in France and another city in Germany. Pick a city in the United States, and perform traceroutes to two hosts, each in a different city in China.

How many links are common in the two traceroutes? Do the two traceroutes diverge before reaching China? Use websites hosted in countries said in question.

Consider the throughput example corresponding to Figure 1. Now suppose that there are M client-server pairs rather than Assume all other links have abundant capacity and that there is no other traffic in the network besides the traffic generated by the M client-server pairs. Figure 1. Consider Figure 1. Now suppose that there are M paths between the server and the client.

No two paths share any link. If the server can only use one path to send data to the client, what is the maximum throughput that the server can achieve? If the server can use all M paths to send data, what is the maximum throughput that the server can achieve? Given that there are M paths between server and client.

Also No two paths share any link. To achieve Maximum throughput, one has to choose the Maximum throughput out of all the available paths.

Suppose that each link between the server and the client has a packet loss probability p,and the packet loss probabilities for these links are independent. What is the probability that a packet sent by the server is successfully received by the receiver?

If a packet is lost in the path from the server to the client, then the server will re-transmit the packet. On average, how many times will the server re-transmit the packet in order for the client to successfully receive the packet? Suppose we send a pair of packets back to back from the server to the client, and there is no other traffic on this path.

Assume each packet of size L bits, and both links have the same propagation delay dprop. What is the packet inter-arrival time at the destination? That is, how much time elapses from when the last bit of the first packet arrives until the last bit of the second packet arrives? Now assume that the second link is the bottleneck link i.

Is it possible that the second packet queues at the input queue of the second link? Now suppose that the server sends the second packet T seconds after sending the first packet. How large must T be to ensure no queuing before the second link? Given that the bottleneck link is Rs, the first link. Yes, it is possible.

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