1. IBM T.J. Watson Research Center Sigmetrics 2008 Tutorial: Introduction to Control Theory and Its Application to Computing Systems Self-Tuning Memory Management of A Database System Yixin Diao diao@us.ibm.com

2. IBM T.J. Watson Research Center © 2008 IBM Corporation 2 SIGMETRICS 2008: Introduction to Control Theory. Abdelzaher, Diao, Hellerstein, Lu, and Zhu. DB2 Self-Tuning Memory Management Technical problems –Large systems with varying workloads and many configuration parameters –Autonomic computing: systems self-management DB2 UDB Server Agents Memory pools Disks DB2 Clients Memory pools Challenges from systems aspects –Heterogeneous memory pools –Dissimilar usage characteristics Challenges from control aspects –Adaptation and self-design –Reliability and robustness

3. IBM T.J. Watson Research Center © 2008 IBM Corporation 3 SIGMETRICS 2008: Introduction to Control Theory. Abdelzaher, Diao, Hellerstein, Lu, and Zhu. Load Balancing for Database Memory Resource Consumer 1 Resource Consumer N Load Balancer Measured Output N Measured Output 1 Resource Resource Allocation 1 Resource Allocation N Load Balancing Fairness optimal ? Common measured output ? 010002000300040005000 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 Entry size (Page) Benefit (sec/page) OLTP Saved System Time (x i ) simPages savedTime BenefitPerPage (y i ) Memory Pool Size (u i )

4. IBM T.J. Watson Research Center © 2008 IBM Corporation 4 SIGMETRICS 2008: Introduction to Control Theory. Abdelzaher, Diao, Hellerstein, Lu, and Zhu. Constrained Optimization and Regulatory Control Saved Disk Time ( x i ) MemoryPool1 Mem pool 1 (x 1 ) Overall Saved System Time (x i ) Optimal memory allocation BenefitPerPage (y 1 ) Mem pool 2 (x 2 ) Mem size 1 (u 1 ) Mem size 2 (u 2 ) Constrained Optimization Karush-Kuhn-Tucker conditions Regulatory Control

5. IBM T.J. Watson Research Center © 2008 IBM Corporation 5 SIGMETRICS 2008: Introduction to Control Theory. Abdelzaher, Diao, Hellerstein, Lu, and Zhu. Dynamic State Feedback Controller State space model Control error Integral control error Feedback control law

6. IBM T.J. Watson Research Center © 2008 IBM Corporation 6 SIGMETRICS 2008: Introduction to Control Theory. Abdelzaher, Diao, Hellerstein, Lu, and Zhu. Incorporating Const of Control into Controller Design Disk Memory Pool A before after write dirty pages to disk Remove these pages Memory Pool B before allocate extra memory OS Major cost: write dirty, move memory, victimize hot Linear quadratic regulation (LQR) J = [e T (k) e T I (k)] Q [e T (k) e T I (k)] T + u T (k) R u(k) Define Q and R regarding to performance Cost of transient load imbalances Cost of changing resource allocations Pool Size Benefit Ts=12449 Ts=15703 Ts=24827

7. IBM T.J. Watson Research Center © 2008 IBM Corporation 7 SIGMETRICS 2008: Introduction to Control Theory. Abdelzaher, Diao, Hellerstein, Lu, and Zhu. Adaptive Controller Design Decentralized integral controlLocal linear model DB2 Memory Pool DB2 Clients Memory Statistics Collector Response Time Benefit MIMO Control Algorithm MIMO Control Algorithm Fixed Step 4-Bit (Oscillation) Model Builder Model Builder Accurate Interval Tuner Interval Tuner Y N Entry Size Step Tuner Response Time Benefit Greedy (Constraint)

8. IBM T.J. Watson Research Center © 2008 IBM Corporation 8 SIGMETRICS 2008: Introduction to Control Theory. Abdelzaher, Diao, Hellerstein, Lu, and Zhu. Experimental Assessment squid.torolab.ibm.com Machine: IBM7028-6C4 CPU:4x 1453MHz Memory: 16GB Disk: 25x 9.1G OLTP workload: multiple (20) buffer pools Response time benefits Memory sizes Throughput Increase TP from ~100 to ~250 DSS workload: various query lengths STMM tuning Ts = 10680s ConfigAdvisor settings Ts = 26342s > 2x improvement DSS workload: index drop Execution time for Query 21 (10 stream avg) 0 1000 2000 3000 4000 5000 6000 7000 12345678910111213141516171819202122232425262728293031323334 Order of execution Time in seconds avg= 959 avg= 2285 avg= 6206 Some indexes dropped Reduce 63%

9. IBM T.J. Watson Research Center © 2008 IBM Corporation 9 SIGMETRICS 2008: Introduction to Control Theory. Abdelzaher, Diao, Hellerstein, Lu, and Zhu. Comparing Control and Optimization Techniques Control-based approachOptimization-based approach Similarity in a simplified scenario Differences in design considerations Step length (modified Armijo rule) Projected gradient (quasi-Newton) Gradient method Constraint enforcement (projection method) Decentralized integral control Local linear model Pure average vs. convex sum Pole location vs. Armijo rule Steady-state gain vs. Hessian matrix Less dependence on the model Strictly applies constrained optimization

10. IBM T.J. Watson Research Center © 2008 IBM Corporation 10 SIGMETRICS 2008: Introduction to Control Theory. Abdelzaher, Diao, Hellerstein, Lu, and Zhu. Simulation Study: Comparison with Optimization Approach Control-based approachOptimization-based approach More robust and better uncertainty management Faster convergence, but more sensitive to noise Without noise (single run) Effect of noise (multiple runs) Memory size Total saved time Control intervals WL change

11. IBM T.J. Watson Research Center © 2008 IBM Corporation 11 SIGMETRICS 2008: Introduction to Control Theory. Abdelzaher, Diao, Hellerstein, Lu, and Zhu. Summary DB2 self-tuning memory management –Interconnection, heterogeneity, adaptation and robustness, cost of control Constrained optimization with a linear feedback controller Experimental assessment for OLTP and DSS workloads