Com Sci 230 Homeworks for the Current Quarter

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Written Exercise #1

Hand in this written exercise by electronic mail to ilia@cs. Send it by 7:30 AM, Tuesday 10 October. See homework instructions for more detail.

Do Problems 1.4, 1.5, 1.6, and 1.10 from pages 35-36 of the text.

• In Problem 1.5, the equations 1.1 and 1.2 that you must generalize are on page 39.
• There appears to be an error in Problem 1.6. Part (c) makes no sense to me if the hit rate is fixed at 0.95. The whole point of part (c) is to choose an amount of cache memory that makes the hit rate big enough to give the required average access time. For this purpose, use the relation of hit ratio to relative memory size given by the "Strong Locality" curve in Figure 1.25 on page 41. Calculate the required hit rate carefully, using Equation 1.1. Then, use a ruler to estimate the appropriate relative memory size from Figure 1.25. Precision in this part is not required.
• In Problem 1.10, the "background" programs are assumed to be running all the time at top priority: they cannot be stopped in order to do the I/O.

Discussion Assignment #1

Discuss the following problems on HyperNews. I will provide a starting comment, under the Class Work article, for each one. There is no particular due date, but there should be significant ideas posted in the next week. See the Written Exercise #2

Hand in this written exercise by electronic mail to ilia@cs.uchicago.edu. Send it by 7:30 AM, Monday 16 October. See homework instructions for more detail.

Do Problems 2.1, 2.2, 2.5 on page 96 of the text.

• In Problem 2.1, T stands for the number of seconds in a "computation period". There is no special meaning to "computation period", it's just some arbitrary length of time that is useful for stating the problem. The phrase, "Define the following quantities," is part of the problem statement; it is not a task for you to do. Although the statement of the problem seems to indicate that (a) and (b) are two different sets of problems, if jobs always behave according to (a), the results are precisely the same as if they always behave according to (b). To make the problem interesting, assume that each job alternates between (a) on odd-numbered computation periods, and (b) on even-numbered computation periods. You may assume that N is even, to avoid silly complications in your formulae.

  So, you must provide 9 simple formulae, expressed in terms of N and T, giving the Turnaround, Throughput, and CPU Utilization under 1, 2, and 4 simultaneous jobs. First, draw a picture of the CPU and I/O activity. Assume that all jobs are submitted at the same time. Each job exercises a different I/O channel, so all of them may do I/O simultaneously, but only one can use the CPU at a given time. Draw your picture in units of T/4. For example, the picture for 1 job by itself looks like this:

  CPU:   11 11   11 11   11 11  ...
  I/O: 11  1  111  1  111  1  1 ...
  

  For more than one job, each job gets its own I/O line in the picture, but all 2 or 4 must interleave on the single CPU line. Use round-robin scheduling, where the CPU serves job 1, then 2, then 3, then 4, then 1, etc. If you draw the picture through four computation periods for each job, you should see the pattern, and you should be able to work out the formulae intuitively. For Turnaround time, give the time for the last job to complete. The Turnaround for the first job, and the average, are a bit more complicated, but the difference between the completion of the first job and the last is always less than 2T, so the Turnaround for the last job gives a pretty clear idea of the trend. Since the longest Turnaround is the same as the total time to complete all the jobs, the Throughput is just the number of jobs divided by the Turnaround. The Utilization is the total CPU time divided by the Turnaround: since each job spends time NT/2 on the CPU, this is pretty easy, too.

  The exact formulae in terms of N and T are rather simple ratios, but some of them contain a small amount of noise that obscures the important trend. After working out the exact formulae, approximate some of them on the assumption that N is very large. For very large N, N+1 is approximately the same as N. If you do all of this correctly, it should be easy to see that the Turnaround increases slightly from 1 job to 2, and then essentially doubles for 4 jobs. The Throughput increases by a substantial factor from 1 job to 2, and essentially doubles from 1 job to 4. The Utilization is low for 1 job, a large fraction for 2, and essentially 1 for 4.
  
  

• In Problem 2.5, please limit your discussion to one page. It is possible to make the key points in a few sentences, so don't feel obligated to even fill up the page. Getting to the few essential points is preferable to wading through peripheral or irrelevant detail.

  Project #1, Threads and Synchronization

  Due Wednesday, 8 November 1995, at 7:30 AM.

  Project #2, Address Spaces and Multiprogramming

  Due Wednesday, 29 November 1995, at 7:30 AM.

  Project #3, Virtual Memory and Demand Paging

  Due Friday, 15 December 1995, at 7:30 AM.