### Homework Assignment 1 Solutions

For each problem create a spread sheet that contains labeled fields for the inputs, and for any important constanst, and then computes the output. Each calculated cell should be labeled both with the name of the value AND the equation used to compute it. (See Example.xls)

1. 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?

The number of packets needed, N , is⌈106 /D⌉, where D is the packet data size. Given that overhead = 50×N and loss = D (we have already counted the lost packet’s header in the overhead), we have overhead+loss = 50 × ⌈106 /D⌉ + D.

 D overhead+loss 1000 51000 10000 15000 20000 22500

2. For the following, assume that no data compression is done, although in practice this would almost never be the case. For (a) to (c), calculate the bandwidth necessary for transmitting in real time:

• (a) Video at a resolution of 640 × 480, 3 bytes/pixel, 30 frames/second.
• (b) Video at a resolution of 160 × 120, 1 byte/pixel, 5 frames/second.
• (c) CD-ROM music, assuming one CD holds 75 minutes’ worth and takes 650 MB.
• (d) Assume a fax transmits an 8 × 10-inch black-and-white image at a resolution of 72 pixels per inch. How long would this take over a 14.4-kbps modem?

• (a) 640 × 480 × 3 × 30 bytes/sec = 26.4 MB/sec
• (b) 160 × 120 × 1 × 5 = 96,000 bytes/sec = 94KB/sec
• (c) 650MB/75 min = 8.7 MB/min = 148 KB/sec
• (d) 8 × 10 × 72 × 72 pixels = 414,720 bits = 51,840 bytes. At 14,400 bits/sec, this would take 28.8 seconds (ignoring overhead for framing and acknowledgments).
Topic revision: r2 - 2015-10-04 - JimSkon

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