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日期:2020-10-13 11:38

CS3201 Computer Networks

Homework 1

Due on October 9 at 23:59

Please submit your solution as a PDF on Canvas.

Make sure to include enough details to make it clear how you have arrived at your

answers.

1. Suppose that Alice and Bob are connected by a direct link that has a transmission rate

of 40 kbps and a propagation delay of 10msec. They plan to use the go-back-N

protocol with a send window of size N=5 to ensure that Alice can send messages

reliably to Bob. What is the minimum packet size that ensures a link utilization of at

least 75%? Justify your answer.

2. Consider the figure below, which follows the analogy between store-and-forward

link transmission and propagation of bits in a packet along a link, and cars in a

caravan being serviced at a toll booth and then driving along a road to the next

tollbooth, as discussed in the lecture (see slides 1-39 and 1-40).

Suppose the caravan has 20 cars, and that the tollbooth services (that is, “transmits”) a

car at a rate of one car per 2 seconds. Once a car has been serviced, it proceeds to the

next tool both, which is 200 kilometers away, at a rate of 10 kilometers per second.

Also, assume that whenever the first car of the caravan arrives at a tollbooth, it must

wait at the entrance to the tollbooth until all of the other cars in its caravan have

arrived, and lined up behind it before being serviced at the toll booth. That is, the

entire caravan must be “stored” at the tollbooth (like a packet at a router) before the

first car in the caravan can pay its toll and begin driving towards the next tollbooth.

a. How long does it take for the entire caravan to receive service at the tollbooth

(that is the time from when the first car enters service until the last car leaves

the tollbooth)?

b. Once the first car leaves the tollbooth, how long does it take until it is serviced

at the next tollbooth?

3. Suppose that the selective repeat protocol is used. The sequence number space is

{0,1,2,3}. Assume that the sender window size is N=3. At the start, the sender sends

packets with sequence numbers in 0, 1, and 2, respectively. The receiver receives

these packets and sends ACK 0, ACK 1, and ACK 2, respectively. However, these

three ACK messages are lost.

a. After the timeout interval for packet 0, the sender retransmits packet 0.

Suppose that the receiver receives the packet. What happens when the receiver

receives this packet? Moreover, will the application layer process on the

receiving host receive exactly the same data as it was sent by the application

process on the sending host?

b. In general, given a sequence number space of size K, what is the maximum

size we can choose for the sender window N ? Justify your answer by

describing a concrete scenario where the protocol behaves incorrectly if we

make the window too large.

4. Suppose that a user clicks on a link to obtain a Web page. Initially, the IP address for

the associated URL is not cached in the user’s machine, so a DNS lookup is necessary

to obtain the IP address. Suppose that three DNS servers are visited before the user’s

host receives the IP address. (From that point on, you can assume that the user’s host

stores the IP address for future use.) The first DNS server visited is the local DNS

cache, with an RTT delay of RTT0 = 2 msecs. The second and third DNS servers

contacted have RTTs of 40 and 23 msecs, respectively. Assume that the RTT between

the local host and the Web server containing the object is RTTHTTP = 26 msecs.

Moreover, suppose the HTML base file references 8 objects on the same server, and,

assume that the client is configured to support a maximum of 5 parallel TCP

connections, with persistent HTTP. All the web objects are very small and hence we

neglect their transmission times. How much time (in msec) elapses from when the

client clicks on the URL until the base object and the 8 objects have been received

from the web server?

5. Suppose that we want to distribute a file of F bits that is located at a server to N

clients using a client-server architecture. In this question, we will study concrete

distribution schemes. Just like in the lecture, we assume that the server has an upload

rate of us and that the i

th client can download at a rate of at most di. Recall that it is

possible that multiple clients download the file from the server in parallel, as long as

the sum of the rates at which clients are downloading does not exceed us and the

individual rate of the client i

th doesn’t exceed di, at any point in time. We make the

(realistic) assumption that di ≤ us, for all i.

a. A possible distribution scheme is as follows: Order the clients from 1 to N.

Initially, the 1st client downloads the file from the server at the (maximum

possible) rate of d1. Once the download has completed, the 2nd client starts

downloading the file at a rate of d2, and so forth. How long will it take until

every client has received the file under this distribution scheme?

b. Assume that dmin ≥ us / N, where dmin is the minimum download rate of any

client. Give a concrete distribution scheme where the distribution time is

exactly N F / us.


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