CS244a: An Introduction to Computer Networks

Transcription

1 Do not write in this box MCQ 13: /10 14: /10 15: /0 16: /0 17: /10 18: /10 19: /0 0: /10 Total: Name: Student ID #: Campus/SITN-Local/SITN-Remote? CS44a Winter 004 Professor McKeown CS44a: An Introduction to Computer Networks Final Exam: Thursday March 18, 004 You are allowed 3 hours to complete this exam. (i) This exam is closed book and closed notes. However, you may refer to a sheet of 8.5"x11" paper (double-sided) of your own design. (ii) Write your solution directly onto this exam. Be sure to write your name and student ID clearly on the front of the exam. (iii) Don t panic! Be sure to start by reading the exam all the way through. Then answer the questions in whatever order you choose. (iv) Show your reasoning clearly. If your reasoning is correct, but your final answer is wrong, you will receive most of the credit. If you just show the answer without reasoning, and your answer is wrong, you may receive no points at all. The Stanford Honor Code In accordance with both the letter and spirit of the Honor Code, I didn't cheat on this exam. Signature: Page 1 of 13

2 Multiple Choice Questions. Instructions: in the following questions, check all listed assertions that appear to be correct. There is at least one correct assertion per question, but there may be more. Each correct assertion checked will earn you one point. For each incorrect assertion you check, you will lose one point. If you don t know an answer, checking no assertion will neither earn you nor lose you any points. 1. General. What transmission rate is needed to transmit a 4" x 6" color photograph (uncompressed, and with a resolution of 100 dots per inch and 4 bits per pixel) in 4 seconds? (a.) 691,00kb/s (b.) 8.8kb/s (c.) 07.36Mb/s (d.) 89Mb/s (e.) None of the above.. Coding. Suppose a 10Mb/s network interface card sends into a link an infinite stream of 0 s using Manchester encoding. The signal emerging from the adapter will have how many transitions per second? (a.) 10 million transitions per second. (b.) 5 million transitions per second. (c.) 0 million transitions per second. (d.) No transitions. (e.) None of the above. 3. Error Control. A link has a bit error rate of If bit errors are independent of each other, what is the probability that 1 million bit file will be transferred over the link without error? (a.) (b.) 0 (c.) 0.5 (d.) About (e.) < CRC. Two computers exchange messages over a link and agree to use a CRC with the generator x to detect errors. One computer wishes to send the message What remainder should it append to the message? (a.) (b.) (c.) (d.) e -1 R = 000 R = 0100 R = 100 R = 001 (e.) none of the above. Page of 13

3 5. Routing. Loops are prevented in the path taken by packets in a BGP network because: (a.) Routers in a BGP network use Dijkstra s algorithm to build a spanning tree. (b.) Operators construct their network so there are no loops. (c.) Packets carry a list of routers visited and are dropped if they visit the same router twice. (d.) Advertized paths contain a list of the AS s, and the packet contains the list of AS s it has visited. (e.) Advertised paths contain a list of the AS s that a packet will visit, and a sending router will not send a packet along a path with a loop. 6. Elasticity Buffer. An elasticity buffer is used to store bits arriving at a network interface. If the receiving station uses a 00-bit elasticity buffer and the clocks of the transmitter and receiver have a minimum frequency of MHz and a maximum frequency of MHz, which of the following statements are true: (a.) All packets have to be less than or equal to 1,500 bytes long. (b.) All packets have to be less than or equal to 4500 bytes long. (c.) The clocks have a tolerance of ±100 ppm. (d.) The clocks have a tolerance of ±1000 ppm. (e.) The transmitter s clock is always faster than the receiver s clock. 7. Fair Queueing. Which of the following are true: (a.) A fair queueing scheduler in a router always transmits one bit at a time before moving onto the next packet. (b.) If traffic arriving at each router in a network is leaky-bucket constrained, and if each router uses weighted fair queueing schedulers, then bounds can be placed on the end-to-end delay of each packet. (c.) If a fair queueing scheduler calculates the finishing time of two packets, A and B, such that A is scheduled to depart before B, then at a later time as new packets arrive, the scheduler may change its mind and schedule B before A. (d.) Weighted fair queueing (WFQ) allows a router to provide each flow with a weighted share of the link capacity. 8. TCP Congestion Control. A TCP source starts sending packets using the Slow-Start algorithm, starting with one transmitted packet in the first RTT. Assume that the source sends N packets, and that N is sufficiently small so that the source never leaves Slow-Start. Which of the following are true: (a.) All of the packets are sent consecutively before the first ACK is received. (b.) Assuming a fixed RTT, the time taken to transmit all the packets is approximately RTT log ( N). (c.) Assuming a fixed RTT, the time taken to transmit all the packets is approximately RTT N. (d.) The window size is increased by one each time a complete window of data is acknowledged. 9. Error Control. Which of the following are true: (a.) A CRC of length R is calculated over a message of length M bits. The CRC will detect all errors in the message. (b.) The strings and have a Hamming distance of one. (c.) If a single parity bit is added to a message, the resulting code set has a minimum Hamming distance of two. (d.) A larger Hamming distance is needed to detect errors than to correct errors. Page 3 of 13

4 10.Channel capacity. The capacity of a channel is: (a.) The maximum achievable error-free data rate that can be achieved over the channel. (b.) The length of the channel multiplied by the data rate. (c.) The bandwidth of the channel in Hertz. (d.) The volume of the channel measured in cubic feet. 11. TCP. Which of the following are true statements about TCP: (a.) The Slow-Start algorithm increases a source s rate of transmission faster than "additive increase". (b.) A source s retransmission timeout value (RTO) is always set equal to the measured RTT. (c.) If RTO is too small, it might lead to unnecessary retranmissions. (d.) A source s retranmission timeout value is set to a value that increases with the variance in measured RTT values. 1. TCP: Which of the following are true statements about TCP: (a.) TCP segments can only be lost when router queues overflow. (b.) If the window size of a TCP connection (measured in seconds) is smaller than the RTT, the link will operate very efficiently. (c.) There is no performance benefit to having a window size (measured in seconds) larger than the RTT. (d.) A receiver reduces the advertized window size in response to congestion at routers along the path. Long Questions 13. (10 points) A CD Shop. A shop that sells music CDs decides to try and save money by only recording CDs when the customer makes a purchase. When the customer places an order, the songs are downloaded over the network from a centralized server and written onto the CD. When digitized into digital audio format, the music is sampled 44,000 times per second, with 16-bits per sample per channel. (a.) If a CD can hold 70minutes of stereo music (i.e. two channels), write down its storage capacity in bytes. (b.) If a CD has a total capacity of B bytes, which corresponds to M minutes of music, write down an expression for the bit-rate, R, (in bits per second) that is required between the central server and the shop so that a disc can be downloaded in less than N minutes? Page 4 of 13

5 (c.) The network between the remote central server and the shop supports weighted fair queueing, and allows a customer to agree a service quality with the network provider using the RSVP protocol. The central server ensures that the data it sends into the network is leaky-bucket constrained; i.e. that in any interval τ, it sends no more than σ + Rτ bits, where R is the same as in part (b). The network provides the flow with sufficient data rate and buffering to ensure that no data is lost along the way. The shop uses a playback buffer to store the data before writing it a fixed rate onto a blank CD for the customer. Assuming there is only one router in the network, write down an expression for the minimum size of the playback buffer. 14. (10 points) Spanning trees. A network of bridges (or Ethernet switches) uses the spanning tree algorithm discussed in class. The bridges exchange configuration messages of the form (sender's ID, root ID, sender's distance to root). If the root ID and advertised distance are identical, the sender's bridge ID is used as a tie breaker. (a.) Why is the sender s ID used as a tie breaker for messages advertising equal cost to reach the root? (b.) If a bridge receives messages that have identical root ID and advertised distance, could the message to keep instead be chosen randomly, without using the tie breaker described above? If so, why? If not, explain why not, and sketch a simple topology that illustrates your point. Page 5 of 13

6 15. (0 points) Token Passing Networks. N computers are connected to the same shared bus network, as shown below. Access to the bus is controlled by a modified token passing protocol. This protocol operates like the "release after transmission" (RAT) Token Ring protocol discussed in class. When computer Ci receives the token, it may hold the token while it transmits one packet. The computer then passes the token to computer C(i+1). When the token reaches computer CN, it is passed back to computer C1. You may assume: (i) That the distance between each computer equals l, (ii) It takes PROP seconds for a bit to propagate from C1 to CN in Figure 1, (iii) On average, it takes TRANSP to transmit a packet. C1 C C3 CN l l (a.) Find an expression for the efficiency, η TB, of the network. C1 C5 C3 (b.) Now assume that the computers are renumbered randomly and arranged in a ring as shown below. Each computer is assigned a number between C1 and CN by picking a number uniformly and at random, with each computer having a unique number. The figure below shows an example of how they might be numbered. As before, the token is passed clockwise in sequence from C1 to C, and so on to CN. Assume a propagation time of PROP around the Page 6 of 13

7 ring.show that the effficiency of this network is given by: PROP a = TRANSP η TR a , where (c.) When N is large, how many times more efficient is the RAT Token Ring network than the token ring network in part (b)? Express your result as a function of a. Briefly explain your result. 16. (0 points) Parity. In class, we saw how a parity-bit appended to a data word allows a receiver to detect single-bit errors. Suppose now we extend the scheme to two-dimensional parity as shown below. D data bits are split into i rows each of length j bits (D is assumed to divide exactly by i and j). Parity bits are calculated for each row and each column, resulting in i + j + 1 parity bits. d 1, 1 d 1 j d, 1 d j, d 1, j + 1, d, j + 1 d i, 1 d i j d i + 1 1, d i 1, d i, j + 1 +, j d i + 1, j (a) The general scheme: D bits are divided into i rows, each of length j bits. Parity is calculated along each row and each column. (b) An example: the 15-bit data word has parity calculated according to the table above. Page 7 of 13

8 (a.) Is the scheme above even parity or odd parity? (b.) Assume that the highlighted bit "1" in the table above is corrupted (i.e. an error in the channel turns it into a "0" instead of a "1" at the receiver). Show how the error can be detected and corrected. (c.) Prove that all single-bit errors can be detected and corrected by this scheme. Page 8 of 13

9 (d.) Prove that not all two-bit errors can be corrected by this scheme. (e.) Find an example of a two-bit error that can be detected by this scheme. Can all two-bit errors be detected? Page 9 of 13

10 17. (10 points) Dijkstra s Shortest-Path First Routing Algorithm. Consider the network topology shown below. R1 1 1 R R R R5 R R7 R8 1 (a.) Using Dijkstra s algorithm, find the shortest-path spanning-tree for routing packets from router R 1 to every other router. Clearly show each step of the algorithm, including the evolution of the candidate set, C, and the shortest-path set, S. (The candidate set is defined to be the set of all routers that are exactly one hop away from the routers in S). Page 10 of 13

11 18. (10 points) Queues. Every minute, on average three new customers arrive at a supermarket checkout. There are, on average, six customers waiting at the checkout. The checkout clerk mistypes and has to reenter every other checked item. (a.) What is the average time a customer waits in line? (b.) When the customers have checked out, they have to wait in a second security line before leaving the store. Customers from nine other identical checkouts (with identical arrival rates) also wait in the same security line. There are, on average, 75 people in the security line. How long does a typical customer wait in line? 19. (0 points) TCP Congestion Control. [This question is similar to a question on the midterm, but here we re interested in the rate at which the source sends.] In this question we ll explore how fast a source sends packets. We ll be using the network with the topology shown above. A single TCP source has an ACKs Source R >> C Link (a) B C Link (b) Dest infinite supply of equal-sized packets that it wants to send to a single destination over links (a) and (b). Link (a) is very fast and runs at rate R packets/s, whereas link (b) is much slower, runs at C packets/s and is the "bottleneck" link. The path is therefore congested, the bufer fills, and packets are dropped. Packets are only dropped when the buffer fills. Whenever the Destination receives a packet, it sends an ACK packet back to the Source. There is no congestion or queueing on the path taken by ACKs. We will assume that the round-trip propagation delay over the links from Source to Dest and back again is PROP seconds. Page 11 of 13

12 (a.) If the buffer never goes empty, write down an expression for how long it is from the start of one packet on link (b) to the start of the next packet? (b.) If the buffer never goes empty, write down an expression for how long it is from start of when one ACK arrives at the Source until the next one arrives (when no packet is dropped)? (c.) Sketch the rate at which the Source sends packets as a function of time. Clearly distinguish two cases on your graph: (i) When ACKs are received, and (ii) When the packet was dropped at the buffer, and no ACK is received. (d.) On the same graph as part (c), sketch the evolution (as a function of time) of the round-trip time from the Source to the Destination and back again. Page 1 of 13

13 (e.) Explain (in words) how your sketch in part (c) would change if the router uses RED to drop packets at random intervals, instead of only when the buffer is full. 0. (10 points) Leaky-buckets. In class we learned that the cumulative arrival process of leaky bucket constrained traffic with parameters ( σ, ρ) satisfies A( t) σ + ρt, t 0. Now consider an arrival process constrained by: A( t) σ + ρt 1. (a.) If such a flow arrives to a server of capacity C, find conditions on C and the buffer size, B, so that the buffer won't overflow. (Hint: Find an expression for the maximum queue occupancy). (b.) Explain why it is difficult to modify the leaky-bucket regulator we saw in class to constrain traffic in this way. Page 13 of 13