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Bounds on Performance

Bounds on Performance. CSE 807. Significance of Bounds. Provide valuable insight into the primary factors affecting the performance of computer system. Can be computed quickly and therefore serve as a first cut modeling technique. Several alternatives can treated together. Model Parameters.

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Bounds on Performance

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  1. Bounds on Performance CSE 807 CSE 807 Bounds on Performance

  2. Significance of Bounds • Provide valuable insight into the primary factors affecting the performance of computer system. • Can be computed quickly and therefore serve as a first cut modeling technique. • Several alternatives can treated together. CSE 807 Bounds on Performance

  3. Model Parameters • K, The number of service centers. • Dmax, Max service demand at any server. • D, Sum of the service demands at the centers. • Type customer (batch, terminal, and transaction) • Z, Average think time. CSE 807 Bounds on Performance

  4. Asymptotic Bounds • Requests may be served by one or more service centers • Finite population model (Closed system) CSE 807 Bounds on Performance

  5. Trans. Workloads • Recall: Uk= XkSk, and if we denote arrival rate as , then Xk = Vk => Uk= Dk, where Dk= VkSk So, throughput bound is the smallest arrival rate sat at which any center saturates. CSE 807 Bounds on Performance

  6. Trans. Workloads (cont’d) => Umax() =  Dmax, < 1 => sat= 1/ Dmax Note: System is unstable if  > sat For response time: D<R() CSE 807 Bounds on Performance

  7. Two Extreme Cases • Best: No customer ever interferes with any other. So, System response time of each customer = D. • Worst: n customers arrive together every n/ time units. Customers must Q and thus experience large response time. • Note: For any pessimistic bound forecasted, it is possible to pick a batch size n sufficiently large that the bound is exceeded, regardless of how small the arrival rate  is. CSE 807 Bounds on Performance

  8. Batch and Terminal Workloads • Consider the heavy load case: • Uk(N) = X (N) Dk< 1 • => X (N)< 1 / Dmax • Now, consider the light load • Case: • At the Extreme, a single customer alone in system attains a throughput of 1/(D+Z) • As more Customers added to the system, there are 2 boundaries situations: CSE 807 Bounds on Performance

  9. Batch and Terminal Workloads (cont’d) • Smallest possible throughput: • For each customer is 1/(ND+Z) ; for N customers. • We have N / (ND+Z) • Largest possible throughput occurs when no time is spent queueing: • For each customer is 1/(D+Z), and N customers • We have N / (D+Z) CSE 807 Bounds on Performance

  10. Batch and Terminal Workloads (cont’d) Note: Asymptotic Bounds on system throughput summarized: N* (population size) crossover Pt. If N < N*, Optimistic Bound applies. If N > N*, Pessimistic (Heavy Load) Bounds Applies CSE 807 Bounds on Performance

  11. Batch and Terminal Workloads (cont’d) We can obtain bounds on response time R(N) by transforming our throughput bounds using Little’s law. We begin by rewriting the previous equation: Inverting each component to express the bounds on R(N) yields: CSE 807 Bounds on Performance

  12. Workload Type bounds batch X terminal transaction batch R terminal transaction Summary of Asymptotic Bounds CSE 807 Bounds on Performance

  13. Batch throughput: ND X(N) 1 N* N Asymptotic Bounds on Performance CSE 807 Bounds on Performance

  14. Batch Response Time: ND R(N) NDmax D 1 N* N Asymptotic Bounds on Performance (cont’d) CSE 807 Bounds on Performance

  15. Asymptotic Bounds on Performance Terminal Throughput: X(N) 1 N* N CSE 807 Bounds on Performance

  16. Asymptotic Bounds on Performance Terminal Response Time: ND R(N) NDmax-Z D 1 N* N CSE 807 Bounds on Performance

  17. Example of a Modeling Study:IBM Equip. Through a combination of this information, “live” measurements of existing 3790 systems, and benchmark experiments on two of the systems (3790 and 8140), the following service demand were determined: Service demands, seconds System CPU disk 4.6 5.1 3.1 4.0 1.9 1.9 3790 (observed) 8130 (estimated) 8140 (estimated) CSE 807 Bounds on Performance

  18. Terminals CPU Disk Case Study Model Example of a Modeling Study:IBM Equip. (cont’d) CSE 807 Bounds on Performance

  19. Example of a Modeling Study:IBM Equip. (cont’d) • K, the number of service centers (2); • Dmax , the largest service demand (4.6 seconds for the 3790, 5.1 for the 8130) and 3.1 for the 8140); • D, the sum of the service demands (8.6, 7.0, and 5.0, respectively); • the type of customer class (terminal); • Z, the average think time (an estimate of 60 seconds was used). CSE 807 Bounds on Performance

  20. Throughput: 0.30 8140 3790 X(N) 0.20 8130 0.10 10 15 20 25 30 5 N Asymptotic Bounds in the Case Study CSE 807 Bounds on Performance

  21. Response Time: 40 30 R(N) 3790 20 8130 8140 10 10 15 20 25 30 5 N Asymptotic Bounds in the Case Study CSE 807 Bounds on Performance

  22. Throughput: 0.30 X(N) 0.20 0.10 4 8 12 16 20 N Secondary and Tertiary Asymptotic Bounds CSE 807 Bounds on Performance

  23. Response Time: 40 30 R(N) 20 D 10 4 8 12 16 20 N Secondary and Tertiary Asymptotic Bounds CSE 807 Bounds on Performance

  24. Throughput: 0.30 Improving primary X(N) 0.20 Original Improving secondary 0.10 4 8 12 16 20 N Relative Effects of Reducing Various Service Demands CSE 807 Bounds on Performance

  25. Response Time: 40 30 R(N) 20 Original Improving primary 10 Improving secondary 4 8 12 16 20 N Relative Effects of Reducing Various Service Demands CSE 807 Bounds on Performance

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