LPV model identification for power management of Web service systems Mara Tanelli, Danilo Ardagna, Marco Lovera

Transcription

1 LPV model identification for power management of Web service systems Mara Tanelli, Danilo Ardagna, Marco Lovera, Politecnico di Milano {tanelli, ardagna,

2 Outline 2 Reference scenario: autonomic computing LPV modelling for web server dynamics State space LPV model identification Experimental setting Validation results Conclusions

3 Reference scenario 3 Large service centers providing computational capacity on demand Problems: Workload fluctuations Quality of Service (QoS) guarantees Energy (and related) costs Solutions: Autonomic self-management techniques Reconfiguration of service center infrastructures in order to determine Performance vs. Energy trade-off

4 Autonomic computing infrastruncture 4 ws 1 ws 2 ws 3 Free server pool Internet

5 Autonomic self-management techniques 5 Utility Based Approach: Queueing Network model + Optimization framework (e.g., IBM s Tivoli) Multiple decision variables Long term time horizon (several minutes) Control Theory Approach Short time frame (minutes, seconds) System identification used to develop models for: Capturing system transients Taking into account workload variability Advanced control design techniques used to: Ensure closed-loop stability Guarantee performance (QoS) levels a priori

6 System Identification: problem statement 6 Use experimental data to construct dynamical models for performance control of Web services Single class Web server with FIFO scheduling λ k : requests arrival rate s k : service time, CPU time required to serve a single request T k : response time, overall time a request stays in the system X k : system throughput, requests service rate Dynamic voltage scaling (DVS) modeling: s u,k =s k /u k effective service time Queuing theory: Steady state assumption Average response time:

7 LPV state-space models 7 Linear Parameter Varying systems are a class of time-varying systems. In discrete-time state space form: δκ u k LPV System y k Time varying systems, the dynamics of which are functions of a measurable, time varying parameter vector δ. Models for LTV systems or linearizations of non linear systems along the trajectory of δ gain scheduling control problems.

8 LPV state-space models for web server dynamics 8 w k T k s k δκ λ k Arrival rate X k U Throughput Utilization u k LPV System y k We use models with: Affine parameter dependence (LPV-A), that is and similarly for the B, C and D matrices Input-Affine (LPV-IA) parameter dependence, i.e., only the B and D matrices are parametrically varying

9 State space LPV identification algorithms 9 The problem is set up as in the classical output error minimization framework The system is described by a set of parameters θ, identification is perfomed minimising the cost function with respect to θ Minimization carried out via a gradient search method (Levenberg-Marquardt algorithm)

10 Iterative refinement of the estimates 10 The SMI-LPV estimates can be used as a starting point for an iterative refinement: where (see Verdult, Lovera, Verhaegen 2004 for details).

11 Experimental setting 11 A workload generator Apache JMeter custom extension Micro benchmarking web application CPU service time generated according to deterministic (identification), exponential, lognormal, Pareto (validation) distributions Application instrumentation (otherwise, ARM API or kernelbased measurement) Validation: synthetic workload inspired by a real-world usage (Politecnico di Milano Web site, 24 hours)

12 Workload and performance metrics 12 Performance metrics: Variance accounted for (VAF) Average simulation error (e avg )

13 Results: validation data, sampling time 1 min 13 light load heavy load

14 Results: validation data, sampling time 10s 14 light load heavy load

15 Conclusions and future work 15 LPV model identification seems suitable to model Web-servers dynamics Also tested recursive identification algorithms (i.e., for on-line application), with promising results Future work along two different lines Control design for single-class systems Extension to multi-class virtualized environments (MIMO systems) benchmark application implementation design of experiments identification and modeling