DISCRETE TIME ADAPTIVE LINEAR CONTROL
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1 DISCRETE TIME ADAPTIVE LINEAR CONTROL FOR SOFTWARE SYSTEMS Martina Maggio Lund University
2 From wikipedia: CONTROL THEORY Control theory is an interdisciplinary branch of engineering and mathematics that deals with the behavior of dynamical systems with inputs, and how their behavior is modified by feedback.
3 Plant
4 Actuators Measurements Plant
5 Actuators Measurements Linear Model
6 Actuators Measurements Linear Model
7 Objectives Actuators Measurements Linear Model
8 Objectives Error Actuators Measurements + - Linear Model
9 Objectives Error Actuators Measurements + Controller Linear Model -
10 Adaptation Linearization Objectives Error Actuators Measurements + Controller Linear Model - Automated design of self-adaptive software with control theoretical formal guarantees A. Filieri, H, Hoffmann, M. Maggio; ICSE 2014
11 Adaptation Linearization Objectives Error Actuators Measurements + Controller Linear Model - Adaptive control: updating the controller online based on data from the software
12 FORMAL GUARANTEES Stability: objectives reached when feasible No-overshooting: without overshooting Short settling time: in a short time Robustness: despite model inaccuracies
13 CONTROLLING THE CLOUD BROWNOUT
14 BROWNOUT A brownout is an intentional or unintentional drop in voltage in an electrical power supply system. Intentional brownouts are used for load reduction in emergency conditions.
15 BROWNOUT A brownout is an intentional or unintentional drop in voltage in an electrical power supply system. Intentional brownouts are used for load reduction in emergency conditions. Tokyo Tower Brownout
16 PREDICTABILITY: MOTIVATION 82% of end-users give up on a lost payment transaction* 25% of end-users leave if load time > 4s** 1% reduced sale per 100ms load time** 20% reduced income if 0.5s longer load time*** *JupiterResearch, **Amazon, ***Google
17 STATE OF THE ART Increase capacity Public cloud
18 BROWNOUT DISABLE NON-ESSENTIAL CONTENT ON DEMAND
19 Adaptation Linearization Objectives Error Actuators Measurements + Controller Linear Model -
20 Adaptation Linearization Objectives Error Actuators Measurements + Controller Software -
21 Adaptation Linearization Bounded Response Times Error Actuators Measurements + Controller Software - The 95th percentile of the responses should be produced in less than 1 second
22 Adaptation Linearization Bounded Response Times Error Dimmer Measurements + Controller Software - The dimmer denotes the percentage of requests served with the optional computation enabled
23 Adaptation Linearization Bounded Response Times Error Dimmer Measurements + Controller Software - We need to measure the 95th percentile of the response times to know how far we are from our objective
24 Adaptation Linearization Bounded Response Times Error Dimmer Measurements + Controller Software - The adaptation strategy linearizes the system and takes care of runtime changes (like slow downs due to memory leaks)
25 Software equation-based model: y(k + 1) = y(k)+ u(k) +
26 Software equation-based model: The value of α determines the runtime behavior of the metric that is monitored y(k + 1) = y(k)+ u(k) +
27 Equation-based controller: u(k + 1) = u(k)+ 1 ˆ p e(k) +
28 Equation-based controller: u(k + 1) = u(k)+ 1 ˆ p e(k) The controller uses an online estimate of α (corresponds to linearizing around the operating point) +
29 Closed loop system: G(z) = 1 z p p +
30 Closed loop system: G(z) = 1 z p p The value of p controls the speed of convergence time +
31 Robustness to model inaccuracies: =ˆ +
32 Robustness to model inaccuracies: =ˆ 0 apple apple 2 1 p +
33 BROWNOUT Single replica Graceful degradation Minimally intrusive (<200 lines of code) Application developers mark optional code Automatic control strategy to select when the optional computations should be turned on and off
34 EXAMPLE: E-COMMERCE WEBSITE 10 Latency [s] Dimmer Resources [% CPU]
35 EXAMPLE: E-COMMERCE WEBSITE 10 Latency [s] Dimmer Resources [% CPU]
36 EXAMPLE: E-COMMERCE WEBSITE 10 Latency [s] Dimmer Resources [% CPU]
37 AUTOMATIC CONTROL STRATEGY Compute statistics from response times Use statistics as a feedback signal Update the current model of the system (linearization) Control strategy: selects the probability of executing the optional code (dimmer) Brownout: building more robust cloud applications C. Klein, M. Maggio, K.-E. Årzén, F. Hernández-Rodriguez, ICSE 2014
38 AUTOMATIC CONTROL STRATEGY Implemented and tested: Adaptive PI controller Adaptive PID controller Deadbeat controller Feedforward plus feedback controller Control strategies for predictable brownouts in cloud computing M. Maggio, C. Klein, K.-E. Årzén, IFAC WC 2014
39 AUTOMATIC CONTROL STRATEGY Implemented and tested: Adaptive PI controller Adaptive means that the controller behavior changes depending on the current system s behavior via identification and linearization Adaptive PID controller Deadbeat controller Feedforward plus feedback controlle Control strategies for predictable brownouts in cloud computing M. Maggio, C. Klein, K.-E. Årzén, IFAC WC 2014
40 EXPERIMENTAL VALIDATION EXPERIMENT WITH RUBBOS AND VARYING USERS/RESOURCES Latency [s] resources [% CPU], number of users 400, , , , , time [s] Dimmer
41 STATISTICAL VALIDATION With control Without control
42 SCALING UP Multiple replicas Needs load balancing: - Based on latencies - SQF - Brownout-aware Control-theoretical load-balancing for cloud applications with brownout J. Dürango, M. Dellkrantz, M. Maggio, C. Klein, A.V. Papadopoulos, F. Hernández- Rodriguez, E. Elmroth, K.-E. Årzén, CDC 2014
43 IMPROVING FAULT-TOLERANCE Replica 4 fails Replica 3 fails Replica 2 fails Replica 1 fails Replica 1 restored Replica 2 restored Replica 3 restored Replica 4 restored non-brownout Timeouts [req/s] brownout Timeouts [req/s] Dimmer [%] Only replica 0 during this interval Time [s] Dimmer [%] Improving Cloud Service Resilience using Brownout-Aware Load-Balancing C. Klein, A.V. Papadopoulos, M. Dellkrantz, J. Dürango, M. Maggio, K.-E. Årzén, F. Hernández-Rodriguez, and E. Elmroth, SRDS 2014
44 CONCLUSION Bounded response times and improved fault tolerance Formal guarantees Minimally intrusive Application developer should only mark optional computations
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