Server Operational Cost Optimization for Cloud Computing Service Providers over a Time Horizon Haiyang(Ocean)Qian and Deep Medhi Networking and Telecommunication Research Lab (NeTReL) University of Missouri-Kansas City USENIX Hot-ICE 2011 workshop March 29, 2011, Boston 1
Outline • Motivation • Problem Formulation • Evaluation • Conclusion and Future Work 2
On-Demand Cloud Computing Content Scientific Data Web Hosting Delivery Computing Warehousing Service Providers Resource Management VM VM VM VM VM VM VM VM VM Physical Machine Physical Machine Physical Machine Cloud Computing Service Provider’s Infrastructure (Data Center) 3
Demand on CPU Resource • Demand on CPU, Memory, I/O etc. D(t; t + Δ) = max{D(t); … ;D(t + Δ)} Basic Review Point 4
Server Operational Cost Cost due to Cost due to reconfiguration • Wear and Tear over a time (turning on/off cost) horizon horizon Demand most vulnerable part: hard disk The # of servers and at which DVFS: Dynamic frequency at Voltage/Frequency Scaling review points Proportional to the # of servers and the CPU frequency cubic Capacity Energy Energy V e ~f V e : Voltage, f: Frequency 2 x f ~f 3 P~V e P: Power Consumption • Proportional to the # of P=P fixed +P f x f 3 P fixed : Fixed component , P f : Cost Cost Coefficient servers E=P x t E: Energy, t: Time • Positively correlated to CPU frequency 5
Outline • Motivation • Problem Formulation • Evaluation • Conclusion and Future Work 6
Notations System Variables Options Type Set Notation Element Range Notation Z + Server i [1,I] I Frequency Modular value J [1,J] J Z + Time t [1,T] T Capacity Notations C ij C Power Consumption when server i Power Consumption when server i is running at frequency option j Cost Notations V ij Capacity of server i running at (per time unit) frequency option j . + Cost of turning a server on at a Decision Variable: C s review point y ij (t) if server i is turned on and - C s Cost of turning a server off at a operated at frequency j at review point time slot t 7
Minimize the Server Operational Cost over a Time Horizon It is quadratic integer programming! Minimize server power consumption Turning servers on cost � � � j ∈ J C ij · y ij ( t ) + t ∈ T i ∈ I Dependency � � s · � j ∈ J y ij ( t ) · ( � j ∈ J y ij ( t ) − � on + i ∈ I ( C j ∈ J y ij ( t − 1)) + t ∈ T immediate immediate previous � � s · � j ∈ J y ij ( t − 1) · ( � j ∈ J y ij ( t − 1) − � i ∈ I ( C − j ∈ J y ij ( t )) t ∈ T time slot time slot Turning servers off cost Subject to � One server can only be operated at one j ∈ J y ij ( t ) ≤ 1, t ∈ T frequency at one time � � j ∈ J V ij y ij ( t ) ≥ D ( t ) , t ∈ T Demand requirement i ∈ I 8
Linearize the Objective Function Introduce two binary variables to represent turning on/off � j ∈ J y ij ( t ) − � y + (t) y - (t) j ∈ J y ij ( t − 1) − y + ( t ) + y − ( t ) = 0 1 0 0 1 In case of “no change”, two variables should be both 0 0 0 i ( t ) + y − y + i ( t ) ≤ 1 , ∀ i ∈ I, ∀ t ∈ T 1 1 Initialization (assume reshuffling at the beginning of planning) i (1) = � y + y − j y ij (1) i (1) = 0 The objective function becomes + · y + � � � j ∈ J C ij · y ij ( t ) + � � i ( t ) + C − · y − i ∈ I ( C i ( t )) s s t ∈ T i ∈ I t 9
Re-formulate the Problem as Integer Linear Programming Minimize − · y − � � � j ∈ J C ij · y ij ( t ) + � � + · y + i ∈ I ( C i ( t ) + C i ( t )) s s t ∈ T i ∈ I t Subject to � j ∈ J y ij ( t ) ≤ 1 , ∀ i ∈ I, ∀ t ∈ T � � j ∈ J V ij y ij ≥ D, ∀ t ∈ T i ∈ I ij ij i I j J � j ∈ J y ij ( t ) − � j ∈ J y ij ( t − 1) − y + ( t ) + y − ( t ) = 0 , ∀ i ∈ I, ∀ t ∈ T i ( t ) + y − y + i ( t ) ≤ 1 , ∀ i ∈ I, ∀ t ∈ T � + i (1) = j ∈ J y ij (1) , ∀ i ∈ I y y − i (1) = 0 , ∀ i ∈ I Binary i ( t ) , y − y + i ( t ) , ∀ i ∈ I, ∀ t ∈ T y ij ( t ) , ∀ I ∈ I, ∀ j ∈ J, ∀ t ∈ T 10
Outline • Motivation • Problem Formulation • Evaluation • Conclusion and Future Work 11
Evaluation Setup • A 100 homogeneous server cluster with DVFS capability* 1 2 3 4 5 6 7 8 # j 1.4 1.57 1.74 1.91 2.08 2.25 2.42 2.6 Freq. F j .5385 .6038 .6692 .7346 .8 .8645 .9308 1 Cap. V j 60 63 66.8 71.3 76.8 83.2 90.7 100 watts P j .42t .441t .467t .4991t .5376t .5824t .6349t .7t cents Cj • The demand is forecasted and profiled every 5 minutes based on the traces of the demand on CPU – Assume the distribution is exponential with the mean of 20 (20% utilization) • How optimal solution is effected by (and how good it is?) – Granularity: 5 min, 15 min, 30 min, 60 min – DVFS capability: Full, PingPong, Max – Relations between power consumption and turning on/off cost * The CPU frequency is adopted from Chen. et. al . SIGMETRICS 2005 paper [6] 12
Minimum Cost in a 100 Server Cluster Baseline-I: all servers are • Outperforms Baseline cases always on and operated at • Σ local optimum (BL-II) ≠ maximum frequency Baseline-II: the optimization global optimum (our solution) is executed for each time • Finer time granularity, better slot independently (tuning optimum on/off cost is ignored) • Partial gain cancelled out because of the existence of turn on/off cost turn on/off cost • More frequency options improves optimum. But, the improvement from PingPong to Full is marginal. Baseline-I : all servers are always on and operated at maximum frequency (static allocation) Max : operated at maximum frequency only Baseline-II : the optimization is PingPong : operated at maximum and minimum freq. executed for each time slot Full : operated at full spectrum (discrete) independently (tuning on/off cost is 13 ignored) (independent optimization)
Relative Improvement ( R ) Baseline-I : static allocation Baseline-II : independent optim. C b : Cost of baseline C op : Optimal cost R=(C b - C op )/C op • Finer granularity, more improvement • Improvement over Baseline-II diminishes as time granularity gets coarser • Improvement from PingPong to Full is marginal Max : operated at maximum frequency only PingPong : operated at maximum and minimum freq. 14 Full : operated at full spectrum (discrete)
Scaling Factor Vesus Minimum Cost Scaling Factor: the ratio Max : operated at maximum frequency only between turning on/off cost PingPong : operated at maximum and minimum frequenct and power consumption cost Full : operated at full spectrum (discrete) • The gain obtained Finer time granularity goes down as SF increase • Turning on/off cost dominant, less significant impact of time granularity • Power consumption dominant, more significant impact 15
Outline • Motivation • Problem Formulation • Evaluation • Conclusion and Future Work 16
Conclusion • The demand is dynamic over time horizon due to the nature of provisioning service • Multi-time period mathematical model to optimize server operational cost • Leverage turning servers on/off and DVFS in synchronous manner • Significantly reduce the server operational cost compared with static allocation and local optimization • Finer time slot granularity results in better optimum, but the improvement depends on relationships of cost components • Optimization aspects for DVFS chip design and operating system software management 17
Future Work • Heuristics for large scale cloud clusters • Management overhead (such as migration) for reconfiguration cost besides turn on/off cost • Communication cost when allocating resources • Leverage turning on/off and DVFS asynchronously • Uncertainty in demand • We need demand trace/profile/workload in real cloud/cluster computing environment – The demand for resources from individual customers – Customer information 18
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