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Raziel Hess-Green 1 A small intro Raziel Hess-Green 2 More known as: “ski-rental problem” Stairs: takes time S Elevator: takes time L<S The ultimate question: How long to wait? 3 Competitive ratio – Alg/OPT ◦ worst case over all possible events ◦ Alg = cost of algorithm ◦ OPT = optimal cost in hindsight. 4 Wait until elevator comes ◦ What if it’s broken? Take stairs immediately ◦ Bad competitive ratio - S/L 5 Wait until you should have taken the stairs, then take the stairs Case 1: ◦ Elevator comes before time S-L: optimal. Case 2: ◦ Elevator comes after: you paid 2S-L, OPT paid S. Ratio = 2 - L/S. 6 Elevator arrives right after you give up: ◦ If you wait longer, numerator goes up but the denominator stays the same, so your ratio is worse. ◦ If you wait less, then the numerator and the denominator go down by the same amount, worse. 7 BP: ◦ Given N items with sizes s1, s2,…, sN, where 0 si 1. The bin packing is to pack these items in the fewest bins, given that each bin has unit capacity. On-line bin packing: ◦ Each item must be placed in a bin before the size of the next item is given. Stay tuned for more.. 8 9 Young Choon Lee, Albert Y. Zomaya 10 2000 – 2005 ◦ Doubled! ◦ 2005 cost 7.2 bn US$ 2005-2010 ◦ Predicted by the EPA at 2007 to double again ◦ Actually added around 56% (J. Koomey) Mainly due to 2008 recession 2011 ◦ 2% of USA electricity 11 Electricity Bill 12 Cloud Computing allows for fuller utilization of hardware Energy consumption is turning into a major issue Costly CO2 emission Must hold enough resources to handle peak demand Energy grows linearly with utilization 13 20% utilization Idle servers can use 60% of full utilization Turning off is problematic ◦ Long turn on time ◦ May increase failure rate 14 Must have the server totally unutilized to enable sleep mode Dynamic Voltage and Frequency Scaling (DVFS) ◦ Intel SpeedStep ◦ AMD PowerNow! Started in laptops and mobile devices Now used in servers Much more research on this: ◦ PowerNap (ASPLOS ’09) 15 Cloud Application Energy 16 Resources ◦ set R of r resources/processors fully interconnected Homogeneous ◦ Communication ◦ Same DC Live Migration 17 IaaS, SaaS or PaaS regarded as tasks Assumed: known time and CPU demand ◦ IaaS has predefined time/CPU requirements ◦ For SaaS and PaaS- obtain estimates from history and/or from consumer 18 linear relationship with processing time and utilization: 𝑈𝑖 = 𝑛𝑗=1 𝑢𝑖,𝑗 ◦ 𝑢𝑖,𝑗 - utilization of task t j on 𝑟𝑖 𝐸𝑖 = 𝑈𝑖 𝑃𝑚𝑎𝑥 − 𝑃𝑚𝑖𝑛 + 𝑃𝑚𝑖𝑛 Energy during Power Save mode: 10% 𝑃𝑚𝑖𝑛 19 Assigning a set N of n tasks to a set R of r cloud resources Maximize resource utilization ◦ In order to minimize energy consumption ◦ By enabling resources to sleep Without violating constraints ◦ time ◦ Usage ◦ Hard constraints 21 Two algorithms presented, differ only in cost function ECTC ◦ Explicitly computes energy consumption MaxUtil ◦ Average utilization during processing time of the task to schedule ◦ Increase consolidation density 22 23 𝑓𝑖,𝑗 = (𝑝∆ . 𝑢𝑗 + 𝑝𝑚𝑖𝑛 )τ0 – ((𝑝∆ . 𝑢𝑗 + 𝑝𝑚𝑖𝑛 )τ1 +𝑝∆ . 𝑢𝑗 .τ2) 𝑊ℎ𝑒𝑟𝑒 ◦ ◦ ◦ ◦ ◦ 𝑝∆ = 𝑝𝑚𝑎𝑥 − 𝑝𝑚𝑖𝑛 𝑢𝑗- utilization rate of the task 𝑡𝑗 τ0 - total processing time of the task τ1- time task will run alone τ2- time task will run in parallel 24 0 fi , j U 1 i 0 Maximize average consolidation density ◦ Over all processing time of task j 25 26 27 Random ECTC MaxUtil 1,500 experiments ◦ 50 different number of tasks 100-5,000 with intervals of 100 ◦ 10 mean inter-arrival times (10 -100) Poisson process 28 Three usage patterns ◦ Random Uniformly distributed between 0.1 and 1 ◦ Low Gaussian, mean utilization rates of 0.3 ◦ High Gaussian, mean utilization rates of 0.7 29 Task processing time ◦ Exponential distribution 𝑃𝑚𝑎𝑥 = 30, 𝑃𝑚𝑖𝑛 = 20 ◦ Assume: 300-200 watt active mode consumption _m ◦ Adding migration 30 Relative energy savings ◦ MaxUtil ◦ ECTC Different resource usage patterns ◦ Low ◦ High ◦ Random 31 32 33 34 35 Important problem Strict modeling ◦ All demands known exactly (time, usage) ◦ Communication is “free” And yet: No sophisticated algorithms No “make sense” for results No comparing to previous work ◦ “existing task consolidation algorithms are not directly comparable to our heuristics” 36 Stochastic Bin Packing (SBP) problem ◦ each virtual machine's bandwidth demand is treated as a random variable. ◦ both offline and online versions are treated ◦ assumption: VMs' bandwidth consumption obeys normal distribution ◦ show a 2-approximation algorithm for the offline version ◦ (2+Ɛ)-competitive algorithm for online version 37