Resource Pricing and Provisioning Strategies in Cloud Systems: A Stackelberg Game Approach
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1 Resorce Pricing and Provisioning Strategies in Clod Systems: A Stackelberg Game Approach Valeria Cardellini, Valerio di Valerio and Francesco Lo Presti
2 Talk Otline Backgrond and Motivation Provisioning Model and Assmptions Pricing schemes Optimal Pricing as IaaS/SaaS Stackelberg Game Existence of eqilibria Eqilibria comptation Nmerical Examples Conclsions 1
3 Backgrong and Motivation Software as a Service SaaS Provider s applications rnning on a clod infrastctre Infrastctre as a Service IaaS Compte, storage and network resorces as on-demand service Virtalization techniqes - VMs SaaS Acqire VMs SaaS IaaS 2
4 Backgrong and Motivation Isses Dynamic Resorce Provisioning Pricing Schemes vs Action Reserved, on demand, spot SaaS provider strategies, IaaS strategy SaaS Acqire VMs SaaS IaaS 3
5 Backgrong and Motivation Isses Dynamic Resorce Provisioning Pricing Schemes vs Action Reserved, on demand, spot SaaS provider strategies, IaaS strategy 4
6 Related work Too many to mention with different settings and assmptions Action Welfare maximization Profit maximization Game Theory/Mechanism Design Single rond Eqilibria Mltiple ronds Bidding strategies» MDP, Reinforcement Learning Closest to or (which inspired this work) Generalized Nash Eqilibria (Ardagna et al, TSC 13) 5
7 Contribtions Formlate the spot VM pricing and provisioning problem as a Stackelberg game Provide proof of existence of game eqilibria nder sitable assmptions Algorithms for compting eqilibria 6
8 Problem Setting and Assmptions SaaS providers offer service to end sers Service are hosted on a IaaS Clod Assme al VMs are eqal Same CPU, memory, etc. Revene/penalty depends on the performance offered to their cstomers (SLA) Performance depends on workload and nmber of allocated VMs Captred by a sitable Utility Fnction Saas Providers want to maximize their tility SaaS tility strictly concave fnction of nmber of VMs and twice differentiable Diminishing retrns 7
9 Problem Setting and Assmptions IaaS provider sells VMs to SaaS Providers Different VMs pricing schemes (~ Amazon EC2 offer) Flat instances Reserved instances, One time payment + fixed time nit rate f On Demand instances Fixed time nit rate d Spot instances Variable rate s Typically d > f >> s Iaas Provider wants to maximize its revene 8
10 Provisioning Model Periodic Provisioning SaaS provision VMs periodically (e.g., every hor) based on (expected) workload Each SaaS has a fixed amont of flat it acqired in the past At the beginning of each time interval: 1. Each SaaS provider determines: Nmber of flat instances (he owns) to se (fixed price f) Nmber of on demand to by (fixed price d) How many spot instances to by (variable price s) 2. IaaS provider determines: Spot price s 9
11 Provisioning Model 2 step Provisioning 1 step: SaaS providers decide how many flat VMs to se and how many on demand VMs to by As to optimize their tility Assme IaaS provider has enogh resorces to satisfy flat and on demand VMs reqests no competition in this step 2 step: IaaS IaaS provider sells its nsed capacity as spot VMs Cheap Finite amont -> competition We stdy the game arising in the 2 provisioning step 10
12 Two Spot instances Pricing schemes SaaS annonce maximm price they wold accept ~ bdget constraint Same Spot Price Model (SSPM): IaaS sets a niqe spot price for all SaaS providers Users whose max price is lower than actal price will not get any spot instances Mltiple Spost Price (MSPM): IaaS can set different price for different SaaS providers Price will not exceed SaaS max price 11
13 Step 2: Different spot prices IaaS PROVIDER SaaS ser s s max s Θ spot price max spot price nmber of spot VMs tility fnction Max s åss Sbject to: s min s s max SaaS PROVIDER 1 PROBLEM Max s1 Θ 1 (s 1,σ 1 ) Sbject to: å residal cap. s... SaaS PROVIDER n PROBLEM Max sn Θ n (s n,σ n ) Sbject to: å residal cap. s 12
14 Step 2: Same spot prices for all SaaS providers IaaS PROVIDER Max s å ss Sbject to: s min s SaaS PROVIDER 1 PROBLEM Max s1 Θ 1 (s 1,σ) Sbject to: å residal cap. s s 1 =0 if s 1 >σ 1 max... SaaS PROVIDER n PROBLEM Max sn Θ n (s n,σ) Sbject to: å residal cap. s s n =0 if s n >σ n max 13
15 Step 2 as Stackelberg game IaaS PROVIDER Max s åss Sbject to: s min s s max STACKELBERG GAME LEADER Maximizes its revene by adjsting the spot price(s) SaaS sbgame IaaS provider sets the spot price(s) SaaS providers retrn the eqilibrim nmber of spot VMs SaaS PROVIDER 1 PROBLEM Max s1 Θ 1 (s 1,σ 1 ) Sbject to: å residal cap. s... STACKELBERG GAME FOLLOWERS Play a non-cooperative game to maximize their tility SaaS PROVIDER n PROBLEM Max sn Θ n (s n,σ n ) Sbject to: å residal cap. s 14
16 SaaS sbgame Fixed spot price vector, compte SaaS eqilibrim SaaS PROVIDER 1 PROBLEM Max s1 Θ 1 (s 1,σ 1 ) Sbject to: å residal cap. s... SaaS PROVIDER n PROBLEM Max sn Θ n (s n,σ n ) Sbject to: å residal cap. s Generalized Nash Game strategy space depends on other players Jointly Convex Gen. Nash Game Eqilibrim can be compted solving the associated Variational Ineqality (VI) Associated VI fnction is strongly monotone 15
17 SaaS sbgame SaaS PROVIDER 1 PROBLEM Max s1 Θ 1 (s 1,σ 1 ) Sbject to: å residal cap. s... SaaS PROVIDER n PROBLEM Max sn Θ n (s n,σ n ) Sbject to: å residal cap. s Theorem: there is exactly one variational eqilibrim of the followers sbgame 16
18 IaaS Problem IaaS PROVIDER Max s åss Sbject to: s min s s max SaaS sbgame SaaS PROVIDER 1 PROBLEM Max s1 Θ 1 (s 1,s -1,σ 1 ) Sbject to: å residal cap. s IaaS provider sets the spot price... SaaS providers retrn the eqilibrim nmber of spots VMs SaaS PROVIDER n PROBLEM Max sn Θ n (s n,s -n,σ n ) Sbject to: å residal cap. s 17
19 IaaS Problem IaaS PROVIDER Max s åss Sbject to: s min s s max is the soltion of the SaaS sbgame Theorem: there is at least one Stackelberg eqilibrim of the IaaS game Under both pricing schemes 18
20 IaaS Problem: MSPM Max s Sbject to: IaaS PROVIDER åss s min s s max IaaS Problem is Mathematical Problem with Eqilibrim Constraints Cannot be directly solved Soltion compted by solving a seqence of pertrbed (smooth) problem [Facchinei et al 99] 19
21 IaaS Problem: SSPM IaaS PROVIDER Need to resort to a brte force approach Max åss 1. Discretize the spot s price interval 2. Compte SaaS sbgame Sbject to: eqilibrim s min s 1. Easy, it trns ot to be a potential game 3. Pick p the price that corresponds to the largest IaaS revene 20
22 Nmerical examples: Homogeneos Scenario SaaS provider capacity 160 VMs 10 SaaS homogenoes providers, max price 0.5$ Spot price vs SaaS load Nmber of available and sold spot VMs dring the 2 stage Optimal spot price 21
23 Nmerical examples: Heterogenos Scenario SaaS provider capacity 160 VMs 10 SaaS heterogenos provider, same tility fnction bt max price=[0:1; 0:14; 0:18; 0:22; 0:26; 0:30; 0:34; 0:38; 0:42; 0:46]$ Spot price vs SaaS load Nmber of available and sold spot VMs dring the 2 stage Optimal spot price 22
24 Nmerical examples: Heterogenos Scenario SaaS provider capacity 160 VMs 10 SaaS heterogenos provider, same tility fnction bt max price=[0:1; 0:14; 0:18; 0:22; 0:26; 0:30; 0:34; 0:38; 0:42; 0:46]$ MSPM vs SSPM optimal spot price MSPM SSPM 23
25 Conclsions Stdied Clod Resorce Provisioning problem Formlated the spot pricing as a Stackelberg game IaaS as leader SaaS providers as followers Considered two pricing schemes Provided proof of existence of eqilibria Presented algorithms for eqilibria comptation Ftre work Stdy mlti IaaS/SaaS problem Extend the work to other provisioning/pricing schemes Compare the reslts with action based schemes 24
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