15-441 Homework #1 (2006)

Assigned: Friday Feb 17, 2006. Due: Friday Feb 24, 2006, 5pm.

Homeworks must be returned electronically - see the course syllabus for details. We will post an announcement on the bboard when the directories are ready.

Problem 1: Transmission Overheads

Consider sending a file of F kbytes in the following settings. Setting 1 consists of two computers A and B, each equipped with a modem that is capable of sending/receiving at 33.3kbits/sec. For A to send a file to B, it must first establish a dial-up connection with B, which takes 30 seconds. It can then send the file in 128-byte packets, with a one-byte checksum attached to each packet. The propagation delay of the phone line is negligible. Assume that A and B are directly connected, i.e. there are no intervening routers. Setting 2 consists of two computers C and D, connected by an established wireless connection that can transmit at 8kbits/sec through a satellite, with a quarter-second (0.25 second) propagation delay. In setting 2 files are transmitted without being split into packets.

(a)

If F=16, how long does it take to send the file from A to B? How long does it take to send the file from C to D?

(b)

Now do the same computation as in (a), but for the case of F=64.

(c)

Which link is better with respect to total time? Briefly justify your answer.

(You may assume there are no errors during each transmission and you may ignore acknowledgements, i.e., consider only bits flowing from the sending computer to the receiving computer. Also note that 1k bytes=1024 bytes and 1kbits/sec = 1000 bit/second and most people agree that 1 byte = 8 bits.)

Problem 2: Ethernet

Problem 43 in the textbook, page 159, but rReplace part (c) by the following:

(c) How might the specification be modified so as to allow a smaller minimum packet size.

Problem 3: Network configuration

Suppose you are in charge of building a LAN in your department, where 7 machines are placed in a row, evenly spaced by 6 meters. The machine in the middle is a file server.

(a)

Suppose you are to build a 10-Mbps thin-net. Given the prices below, how much is it going to cost? You may ignore the costs of the BNC connectors on the coax runs and the cost of the T connector at each station.

(b)

Now assume your boss is not satisfied with the performance of thin-net because there are too many collisions and wants you to replace it with a 10-Mbps 8-port twisted-pair repeater. If the repeater will be co-located with the server (i.e., have the same distances to other clients as the server has) and will be connected to the server via a 1-meter twisted-pair run, how much will this setup cost? You may ignore the costs of the RJ-14 connectors on the twisted-pair runs.

(c)

Assuming each client communicates with only the server and not with other clients, will this upgrade noticeably increase performance? Why or why not?

(d)

If we choose to upgrade our original thin-net installation using an Ethernet switch instead, how much would this cost? Assume that the Ethernet switch has 8 10-Mbps ports (1 for each of the 6 clients and 2 empty) and one 100-Mbps "backbone" port (to which we will attach the server).

(e)

Approximately what is the best throughput increase we could expect to see with the switch configuration compared to the thin-net configuration? Briefly justify your answer.

Problem 4: Frequency Division Multiplexing

You need to multiplex 3 connections onto a single link: The first is a music channel which plays music in the range of 15Hz - 20kHz (for simplicity assume 0 Hz - 20kHz). The second is a telephone line which transmits voice in the range 400Hz - 3400Hz. The third is a data line which transmits 10Kbps of data.

How might you assign the frequencies to multiplex all 3 connections at their full desired rate, minimizing the total frequency used? Assume that channels are separated by 2kHz guard bands.

In working out this problem, assume no noise and assume the Nyquist Limit (from lecture) applies to translating between bps and the width of the frequency band.

Problem 5: Link Speed

(a)

a T1 (1.5 Mbits/sec)

(b)

a OC-3 (155 Mbits/sec)

(c)

a OC-48 (2.5 Gbit/sec)

(d)

a OC-192 (10 Gbit/sec - common today)

(e)

If increasing the link speed does not decrease the latency of a file transfer, then why are carriers spending billions of dollers to replace their links with faster ones?