Operational Laws

1
Chapter 33

• Operational Laws

2
Exercise 33.1

• During a 10 seconds observation period, 400
  packets were serviced by a gateway whose CPU can
  service 200 pps. What was the utilization of the
  gateway CPU?

3
Exercise 33.1

• During a 10 seconds observation period, 400
  packets were serviced by a gateway whose CPU can
  service 200 pps. What was the utilization of the
  gateway CPU?
• U B/T (Operational Laws/Utilization)
• U (1/200 x 400) / 10
• 2/10
• 20

4
Exercise 33.2

• The throughput of a timesharing system was
  observed to be five jobs per second over a
  10-minute observation period. If the average
  number of jobs in the system was four during this
  period, what is the average response time?

5
Exercise 33.2

• The throughput of a timesharing system was
  observed to be five jobs per second over a
  10-minute observation period. If the average
  number of jobs in the system was four during this
  period, what is the average response time?
• Q X R (Littles Law)
• 4 5 R
• R 0.8 s

6
Exercise 33.3

• During a 10-second observation period, 40
  requests were serviced by a file server. Each
  request requires two disk accesses. The average
  service time at the disk was 30 ms. What was the
  average disk utilization during this period?

7
Exercise 33.3

• During a 10-second observation period, 40
  requests were serviced by a file server. Each
  request requires two disk accesses. The average
  service time at the disk was 30 ms. What was the
  average disk utilization during this period?
• U B/T (Operational Laws/Utilization)
• U (0.03 x 2 x 40) / 10
• 2.4/10
• 24

8
Exercise 33.4

• A distributed system has a print server with a
  printing speed of 60 pages per minute. The
  server was observed to print 500 pages over 10
  minutes observation period. If each job prints
  five pages on the average, what was the job
  completion rate of the system?

9
Exercise 33.4

• A distributed system has a print server with a
  printing speed of 60 pages per minute. The
  server was observed to print 500 pages over 10
  minutes observation period. If each job prints
  five pages on the average, what was the job
  completion rate of the system?
• X C/T
• X (500/5)/(60x10)
• X 1/6

10
Exercise 33.5

• For a timesharing system with two disks (user and
  system), the probability for jobs completing the
  service at the CPU were found to be 0.8 to disk
  A, 0.16 to disk B, and 0.04 to the terminal. The
  user think time was measured to be 5 second, the
  disk service time were 30 and 25 ms, and the
  average service time per visit to the CPU was 40
  ms. Using the network model shown in Figure 32.8.

11
Exercise 33.5

• CPU were found to be 0.8 to disk A, 0.16 to disk
  B, and 0.04 to the terminal.
• gt PCPU, A0.8, PCPU, B0.16, PCPU, 00.04,
• User think time was measured to be 5
• gt Z5
• disk service time were 30 and 25 ms, and average
  service time per visit to CPU was 40 ms.
• gt SA0.030, SB0.025, SCPU0.040

12
Exercise 33.5 (a)

• PCPU, A0.8, PCPU, B0.16, PCPU, 00.04
• Z5
• SA0.030, SB0.025, SCPU0.040
• For each job, what are the visit ratios for CPU,
  disk A, and disk B?
• i) 1VCPUPCPU, 0 gt 10.04VCPU gt VCPU25
• ii) VA VCPUPCPU, A 25 x 0.820
• iii) VB VCPUPCPU, B 25 x 0.164

13
Exercise 33.5 (b)

• PCPU, A0.8, PCPU, B0.16, PCPU, 00.04
• Z5
• SA0.030, SB0.025, SCPU0.040
• VCPU25, VA20, VB 4
• b) For each job, what are total service demand?
• i) DCPU SCPUVCPU 0.040 x 251
• ii) DA SAVA 0.030 x 200.6
• iii) DB SBVB 0.025 x 40.1
• DDCPU DA DB 10.60.11.7

14
Exercise 33.5 (c)

• PCPU, A0.8, PCPU, B0.16, PCPU, 00.04
• Z5, SA0.030, SB0.025, SCPU0.040
• VCPU25, VA20, VB 4
• DCPU 1, DA0.6, DB 0.1
• c) If disk A utilization is 60, what is
  utilization of CPU and disk B?
• UAX DA gt 0.6X 0.6, gt X1
• UCPUX DCPU 1 x 1 1
• UBX DB 1 x 0.1 0.1

15
Exercise 33.5 (d)

• PCPU, A0.8, PCPU, B0.16, PCPU, 00.04
• Z5, SA0.030, SB0.025, SCPU0.040
• VCPU25, VA20, VB 4
• DCPU 1, DA0.6, DB 0.1
• d) If disk B utilization is 10, what is the
  average response time when there are 20 users on
  the system?
• UBX DB gt 0.1X 0.1, gt X1
• RN/X Z 20/1 515

16
Exercise 33.6 (a)

• For the system of Exercise 33.5
• PCPU, A0.8, PCPU, B0.16, PCPU, 00.04
• Z5, SA0.030, SB0.025, SCPU0.040
• VCPU25, VA20, VB 4
• DCPU 1, DA0.6, DB 0.1
• What is the bottleneck device?
• DMAX DCPU , therefore CPU has the highest total
  service demand, it is the bottleneck device.

17
Exercise 33.6 (b)

• For the system of Exercise 33.5
• PCPU, A0.8, PCPU, B0.16, PCPU, 00.04
• Z5, SA0.030, SB0.025, SCPU0.040
• VCPU25, VA20, VB 4
• DCPU 1, DA0.6, DB 0.1, DMAX 1
• b) What is the minimum average response time?
• DDCPUDADB 10.60.11.7s
• R(N)gtD
• Therefore minimum average response time is 1.7s.

18
Exercise 33.6 (c)

• For the system of Exercise 33.5
• PCPU, A0.8, PCPU, B0.16, PCPU, 00.04
• Z5, SA0.030, SB0.025, SCPU0.040
• VCPU25, VA20, VB 4
• DCPU 1, DA0.6, DB 0.1, DMAX 1, D1.7
• c) What is the maximum possible disk A
  utilization for this configuration?
• X(N)ltminN/(DZ), 1/DMAX
• X(N)ltminN/(1.75), 1/1lt1
• UA X DA 1 x 0.6 0.6

19
Exercise 33.6 (d)

• For the system of Exercise 33.5
• PCPU, A0.8, PCPU, B0.16, PCPU, 00.04
• Z5, SA0.030, SB0.025, SCPU0.040
• VCPU25, VA20, VB 4
• DCPU 1, DA0.6, DB 0.1, DMAX 1, D1.7
• d) What is the maximum possible throughput of
  this system?
• X(N)ltminN/(DZ), 1/DMAX
• X(N)ltminN/(1.75), 1/1lt1
• max X(N) 1

20
Exercise 33.6 (e)

• For the system of Exercise 33.5
• PCPU, A0.8, PCPU, B0.16, PCPU, 00.04
• Z5, SA0.030, SB0.025, SCPU0.040
• VCPU25, VA20, VB 4
• DCPU 1, DA0.6, DB 0.1, DMAX 1, D1.7
• d) What change in CPU speed would you recommend
  to achieve a response time of 10 s with 25 users?
  Would you also need a faster disk A or disk B?
• R(N)N/X-Z, 1025/X-5, X5/3
• UmaxX VCPUSCPU, 15/3 x 25 x SCPU,
  SCPU3/1250.024
• UmaxX VASA, 15/3 x 20 x SA, SA3/1000.03 (OK)
• UmaxX VBSB, 15/3 x 4 x SB, SB3/200.06 (OK)

21
Exercise 33.6 (f)

• For the system of Exercise 33.5
• PCPU, A0.8, PCPU, B0.16, PCPU, 00.04
• Z5, SA0.030, SB0.025, SCPU0.040
• VCPU25, VA20, VB 4
• DCPU 1, DA0.6, DB 0.1, DMAX 1, D1.7
• f) Write the expressions for asymptotic bounds on
  throughput and response time.
• X(N) ltminN/(DZ),1/Dmax
• X(N) ltminN/(1.75),1/1ltminN/6.7,1
• R(N) gtmaxD, N Dmax-Z
• R(N) gtmax1.7, N 1-5gtmax1.7, N-5

22
Exercise 33.7 (a)

• For the system of Exercise 33.6
• PCPU, A0.8, PCPU, B0.16, PCPU, 00.04
• Z5, SA0.030, SB0.025, SCPU0.040
• VCPU25, VA20, VB 4
• DCPU 1, DA0.6, DB 0.1, DMAX 1, D1.7
• Which device would be the bottleneck if the CPU
  is replaced by another unit that is twice as
  fast?
• DCPU SCPUVCPU (0.040/2) x 250.5
• DMAX DA

23
Exercise 33.7 (b)

• For the system of Exercise 33.6
• PCPU, A0.8, PCPU, B0.16, PCPU, 00.04
• Z5, SA0.030, SB0.025, SCPU0.040
• VCPU25, VA20, VB 4
• DCPU 1, DA0.6, DB 0.1, DMAX 1, D1.7
• b) Which device would be the bottleneck if disk A
  is replaced by another unit that is twice as
  slow?
• DA SAVA (0.030x 2) x 201.2
• DMAX DA

24
Exercise 33.7 (c)

• For the system of Exercise 33.6
• PCPU, A0.8, PCPU, B0.16, PCPU, 00.04
• Z5, SA0.030, SB0.025, SCPU0.040
• VCPU25, VA20, VB 4
• DCPU 1, DA0.6, DB 0.1, DMAX 1, D1.7
• c) Which device would be the bottleneck if disk B
  is replaced by another unit that is twice as
  slow?
• DB SBVB (0.025x2) x 40.2
• DMAX DCPU

25
Exercise 33.7 (d)

• For the system of Exercise 33.6
• PCPU, A0.8, PCPU, B0.16, PCPU, 00.04
• Z5, SA0.030, SB0.025, SCPU0.040
• VCPU25, VA20, VB 4
• DCPU 1, DA0.6, DB 0.1, DMAX 1, D1.7
• d) Which device would be the bottleneck if the
  memory size is reduce so that the jobs make 20
  times more visit to disk B due to increased page
  fault?
• DB SBVB 0.025 x (420)0.6
• DMAX DCPU