Homework 1 Solution

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Problem 1. (adapted from Chapter 1 Exercise 15 in PBook)

For each of the following operations on a remote file server, discuss whether they are more likely to be delay sensitive or bandwidth sensitive:

  1. Open a file.

  1. Read the contents of a file.

  1. List the contents of a directory.

  1. Display the attributes of a file.

  1. Upload a new video file to the remote fil server.

Problem 2. (adapted from Chapter 1 Exercise 16 in PBook)

Calculate the latency (from first bit sent to last bit received) for the following:

  1. 100-Mbps Ethernet with a single store-and-forward switch in the path and a packet size of 10,000 bits. Assume that each link introduces a propagation delay of 20 s and that the switch begins retransmitting immediately after it has finished receiving the packet.

  2. Same as (a), but with three switches.

  1. Same as (a), but assume the switch implements “cut-through” switching; it is able to begin transmit the packet after the first 200 bits have been received.

Problem 3. Consider a network consisting of three nodes, hosts A and B, and switch S.

A is connected to S via a 100 Mbps link with 20 s delay.

B is connected to S via a 50 Mbps link with 30 s delay.

S is a store-and-forward device: it begins transmit a received packet 40 s after it has finished receiving it.

  1. How long does it take to send a 10,000-bit packet from A to B?

  1. Suppose that A starts transmitting 10,000-bit packets to B at the maximum rate possible on the link from A to S. How much buffering does S need to provide such that packets won’t be dropped until after 100 ms has elapsed?

  1. Suppose that B immediately signals A to stop sending packets after it receives the first packet. Assume that this “signal” packet experiences the minimum possible delay. A stops sending packets immediately after receiving the signal packets. How many packets has A sent?

Problem 4. (Chapter 1 Exercise 22 in PBook)

Suppose that a certain communications protocol involves a per-packet overhead of 50 bytes for headers and framing. We send 1 million bytes of data using this protocol; however, one data byte is corrupted and the entire packet containing it is thus lost. Give the total number of overhead + loss bytes for packet data sizes of 1000, 10,000, and 20,000 bytes. Which size is optimal?

Problem 5. The Unix utility ping can be used to find the round-trip time (RTT) to various Internet hosts. Read the man page for ping,

  1. Use it to find the RTT to www.syracuse.edu in Syracuse, NY and www.cam.ac.uk in UK, and report these results.

  2. What do you think accounts for the differences?

Problem 6. (adapted from Chapter 5 Problem 1 in KBook)

Suppose the information content of a packet is the bit pattern 1010 1010 1100 1101 and an even parity scheme is being used. What would the value of the field containing the parity bits be for the case of a two-dimensional parity scheme? Your answer should be such that a minimum-length checksum field is used.

Problem 7. Suppose we want to transmit the message 1011 0010 011 and protect it from errors using the CRC polynomial x4 + x + 1.

  1. Use polynomial long division to determine the message that should be transmitted.

  1. Suppose the channel introduces an error pattern 1000 1000 0000 000 (i.e., a flip from 1 to 0 or from 0 to 1 in position 1 and 5). What is received? Can the error be detected?

  2. Repeat part (b) with error pattern 1001 1000 0000 000.

Problem 8. Consider the 10-bit message 1100 1010 01,

  1. Calculate the minimum number of parity bits needed for Hamming code.

  1. Calcuate the Hamming code of this message (assume even parity, position starts from the left).

Problem 9. The Stop-and-Wait protocol is used for a 10 Mbps link over a 2000 km long cable to send frames of 1000 bytes each. The signal propagation speed is 2 108 meters per second. Suppose ACK send time and processing time for both send and receive are negligible. What is the link utilization?

Problem 10. (adapted from Chapter 2 Exercise 25 in PBook)

Suppose you are designing a sliding window protocol for a 1-Mbps point-to-point link to the stationary satellite revolving around the Earth at an altitude of 3 104 km. Assuming that each frame carries 1000 bytes of data, what is the minimum number of bits you need for the sequence number in the following cases? Assume the speed of light is 3 108 m/s.

  1. Go-back-N, where RWS=1

  1. Selective repeat, where RWS=SWS