# Computer Capacity Planning: Quantifying Performance Models

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## 3.6 Exercises

1. A computer system is monitored for one hour. During this period, 7,200 transactions were executed and the average multiprogramming level is measured to be equal to 5 jobs. What is the average time spent by a job in the system once it is in the multiprogramming mix (i.e., the average time spent by the job in the system once it is memory resident)?

2. Measurements taken during one hour from a Web server indicate that the utilization of the CPU and the two disks are: UCPU = 0.25, Udisk1 = 0.35, and Udisk2 = 0.30. The Web server log shows that 21,600 requests were processed during the measurement interval. What are the service demands at the CPU and both disks, what is the maximum throughput, and what was the response time of the Web server during the measurement interval?

3. Consider the Web server of Exercise 3.2. Draw a graph of the Web server's throughput as a function of the number of concurrent requests. Comment on observations.

4. A computer system is measured for 30 minutes. During this time, 5,400 transactions are completed and 18,900 I/O operations are executed on a certain disk that is 40% utilized. What is the average number of I/O operations per transaction on this disk? What is the average service time per transaction on this disk?

5. A transaction processing system is monitored for one hour. During this period, 5,400 transactions are processed. What is the utilization of a disk if its average service time is equal to 30 msec per visit and the disk is visited three times on average by every transaction?

6. The average delay experienced by a packet when traversing a computer network is 100 msec. The average number of packets that cross the network per second is 128 packets/sec. What is the average number of concurrent packets in transit in the network at any time?

7. A file server is monitored for 60 minutes, during which time 7,200 requests are completed. The disk utilization is measured to be 30%. The average service time at this disk is 30 msec per file operation request. What is the average number of accesses to this disk per file request?

8. Consider the database server of Example 3.2. Using ClosedQN.XLS, what is the throughput of the database server, its response time, and the utilization of the CPU and the three disks, when there are 5 concurrent transactions in execution?

9. A computer system has one CPU and two disks: disk 1 and disk 2. The system is monitored for one hour and the utilization of the CPU and of disk 1 are measured to be 32% and 60%, respectively. Each transaction makes 5 I/O requests to disk 1 and 8 to disk 2. The average service time at disk 1 is 30 msec and at disk 2 is 25 msec.

• Find the system throughput.

• Find the utilization of disk 2.

• Find the average service demands at the CPU, disk 1, and disk 2.

• Use ClosedQN.XLS to find the system throughput, response time, and average queue length at the CPU and the disks when the degree of multiprogramming is n, for n = 0, ..., 4.

• Based on the above results, what is a good approximation for the average degree of multiprogramming during the measurement interval?

10. An interactive system has 50 terminals and the user's think time is equal to 5 seconds. The utilization of one of the system's disk was measured to be 60%. The average service time at the disk is equal to 30 msec. Each user interaction requires, on average, 4 I/Os on this disk. What is the average response time of the interactive system?

11. Obtain access to a UNIX or Linux machine and become acquainted with the command iostat, which displays information on disk and CPU activity. The data in Table 3.4 shows a typical output report from iostat. Each line displays values averaged over 5-second intervals. The first three columns show activity on disk sd0. The kps column reports KB transferred per second, the tps column shows the number of I/Os per second, and the serv column shows average disk service time in milliseconds. The next four columns display CPU activity. The us column shows the percent of time the CPU spent in user mode. The next column shows the percent of time the CPU was in system mode followed by the percent of time the CPU was waiting for I/O. The last column is the percent of time the CPU was idle. Compute the disk and CPU utilizations.

#### Table 3.4. Data for Exercise 3.9

sd0

cpu

kps

tps

serv

us

sy

wt

id

25

3

6

19

3

0

78

32

4

7

13

4

0

83

28

2

7

20

3

0

77

18

2

8

24

2

0

74

29

3

9

18

5

0

77

33

4

12

23

3

0

74

35

4

8

25

5

0

70

25

4

10

32

4

0

64

26

3

11

28

4

0

68

34

4

12

22

6

0

72

12. You are planning a load testing experiment of an e-commerce site. During the experiment, virtual users (i.e., programs that behave like real users and submit requests to the site) send requests to the site with an average think time of 5 seconds. How many virtual users you should have in the experiment to achieve a throughput of 20 requests/sec with an average response time of 2 seconds?