ENERGY EFFICIENT CONTROL OF VIRTUAL MACHINE CONSOLIDATION UNDER UNCERTAIN INPUT PARAMETERS FOR GREEN CLOUDS

Transcription

1 ENERGY EFFICIENT CONTROL OF VIRTUAL MACHINE CONSOLIDATION UNDER UNCERTAIN INPUT PARAMETERS FOR GREEN CLOUDS

2 ENERGY SAVING IN VIRTUALIZED DATACENTERS Assume small datacenter, 1064 Servers LighWng UPS 588 Cooling Compute Out of the 588 KW for Compute/Network 44% are for processor, server power supply and other server components (in total 258 kw), à This is what we try to opwmize 4% for storage 4% for communicawon equipment Saving 1 W for processing saves addiwonal 1.84 W for other components

3 ENERGY SAVING IN VIRTUALIZED DATACENTERS For example, save 20% energy for this datacenter results in: Total CO2 footprint avoided per year 846t California 690t Sweden 1387t China 1407t Australia Monetary savings per year USD for California SEK for Sweden Yuan for China $ for Australia

4 VM CONSOLIDATION: MOTIVATION VM Workload Varies over Wme due to unpredictable workload May require VM resizing, VM creawon, VM terminawon Result in the physical servers to be UnderuWlized OveruWlized Consequences for Cloud Operators SLA ViolaWons versus Minimum Energy ConsumpWon Case Study Evaluated Workload of 6 VMs in KAU Compute Service Department

5 VM CONSOLIDATION: KAU WORKLOAD TRACES EXAMPLE: KAU workload traces VMDatacenter Demand Varies over /me

6 VM CONSOLIDATION: KAU WORKLOAD TRACES VM Demand Varies within bounds

7 VM CONSOLIDATION - REVISITIED VM1 VM2 VM3 VM4 60% 40% 20% 50% VM demands vary over Wme SLA may be violated!!! GOAL: Provide a soluwon that is robust against input variability VM1 VM3 80% VM2 VM4 105% 90%

8 VM CONSOLIDATION - REVISITED VM1 VM2 VM3 VM4 60% 40% 20% 50% VM demands vary over Wme SLA may be violated!!! GOAL: Provide a soluwon that is robust against input variability DeterminisWc OpWmizaWon: Too conservawve Apply robust opwmizawon theory VM1 VM3 80% VM2 VM4 40% 50% Higher energy consumpwon and more unused resources Less probability of SLA viola/on

9 CLASSICAL OPTIMIZATION FRAMEWORKS Almost all models for Cloud (any?) OpWmisaWon (e.g. VM ConsolidaWon) assume perfect knowledge! MIN ct(x) s.t. Ax<=b Once x* calculated, it is used BUT: Many factors not known precisely, e.g. VM Resource Demands Energy Model of Servers We can only assume incomplete knowledge in A, b, c Consequence (Ben Tal+Nemirovski, 2000): Small errors in parameters can make x* highly unfeasible

10 ROBUST OPTIMIZATION PARADIGM Assume uncertainty model for data is known (e.g. bounds) Define a soluwon is robust feasible as one that is guaranteed to remain feasible for all admissible data values (out of uncertainty set U) OpWmize objecwve over set of approximate robustly feasible soluwons Robust counterpart ai i-th row of uncertain matrix objecwve Nominal boundary robust x*à nominal becomes infeasible

11 ROBUST VM CONSOLIDATION MODEL ROBUST Mixed Integer Linear Problem SoluWon x* is robust feasible if it sawsfies all uncertain constraints Robust counterpart Typically has infinite number of constraints Depends on uncertainty set U SoluWon typically has worse objecwve value Tries to miwgate adverse effects of uncertainty Special case: cardinality constraint uncertainty set (Bertsimas, Sim) Polyhedral uncertainty set, budget of uncertainty in terms of cardinality constraints Each coefficient in matrix is within, max Γi coefficients deviate Robust counterpart becomes aqer duality

12 UNCERTAINTY ON SERVER POWER MODEL Power of server can be modeled as linear funcwon of resource uwlizawon (e.g. CPU load, etc) But errors up to 10-14% due to processor opwmizawons, etc Power consumpwon is random variable from uncertainty set symmetrically distributed between with zero mean Decision variable Constraints depend on VM uwlizawon, see next slide

13 UNCERTAINTY ON VM RESOURCE DEMANDS Power consumpwon depends on resource demands of VMs, which are uncertain Resource demand is random variable symmetrically distributed with zero mean plus fixed demand UWlizaWon Resource demands of Old assignment VMs migrawng towards server Budget constraint VMs migrawng away Overprovisioning Factor

14 UNCERTAINTY MODEL PRICE OF ROBUSTNESS Uncertainty set for cardinality constraint Defines deviawons from nominal values, i.e. mean values plus deviawon bounds ProtecWon from deviawon by introducing hard constraints that cut-off feasible soluwons that may become unfeasible ones for some deviawons Price of robustness Cloud Operator can tradeoff by modifying Γ Higher risk aversion à consider more unlikely deviawons à higher protecwon à higher energy consumpwon OpportunisWc soluwon à less protecwon à less energy consumpwon

15 HOW MUCH RISK TO TAKE? TUNING OF Γ Probability of constraint violawon ω coefficients may deviate Upper bound can be computed according to (Bertsimas, Sim) For small ω need to ensure full protecwon (sesng Γ to max) to ensure small violawon probability

16 EVALUATION ImplementaWon in Matlab with IBM CPLEX Not suitable for online opwmizawon Benchmark for heuriswcs Small example to demonstrate model capabiliwes 0.1 CPU = 1 core 0.1 RAM = 512 MB

17 CPU DEMANDS UNCERTAIN (Δ=5%) Γ=0 Γ=50 Pr(viol)=52% Pr(viol)<1% Cloud Operator can tradeoff by modifying Γ CONSERVATIVE SOLUTION = TOTAL PROTECTION LEVEL (MAX Γ) = HIGHEST ENERGY PROTECTION AGAINST UNCERTAINTY OF 50 UNITS HIGHER ENERGY = PRICE OF ROBUSTNESS OPPORTUNISTIC SOLUTION (NO PROTECTION) = LESS ENERGY CONSUMPTION

18 CPU DEMANDS UNCERTAIN

19 CPU DEMANDS UNCERTAIN LARGE INSTANCE (100/14) ADDITIONAL POWER, NO OVERBOOKING EXPECTED POWER, 50% DEMAND UNCERTAINTY RELATIVE POWER, 40% UNCERTAINTY ON DEMAND SLA VIOLATION, 50% DEMAND UNCERTAINTY

20 CONCLUSIONS AND FUTURE WORK Conclusions Applied Robust OpWmizaWon Framework to cope with unknown and imprecise input data to VM ConsolidaWon problem Uncertainty on VM resource demands and Power model of servers Γ uncertainty and constraint violawon probability gives Cloud operators a tool to tradeoff robustness versus energy efficiency Many more results with enhanced model with e.g. resource overbooking Future work Comparison with robust heuriswcs IntegraWon of network model and NFV concept (service chain) Apply Robust OpWmizaWon to 5G Network OpWmizaWon

21 THANK YOU FOR YOUR ATTENTION! Thank you for your axenwon! ANDREAS KASSLER ACROSS WORKSHOP, 11TH SEPTEMBER 2015, GHENT, BELGIUM