Online Auctions in IaaS Clouds: Welfare and Profit Maximization with Server Costs Xiaoxi Zhang 1,...
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![Page 1: Online Auctions in IaaS Clouds: Welfare and Profit Maximization with Server Costs Xiaoxi Zhang 1, Zhiyi Huang 1, Chuan Wu 1, Zongpeng Li 2, Francis C.M.](https://reader035.fdocuments.us/reader035/viewer/2022062304/56649d775503460f94a58619/html5/thumbnails/1.jpg)
Online Auctions in IaaS Clouds: Welfare and
Profit Maximization with Server Costs
Xiaoxi Zhang 1, Zhiyi Huang 1, Chuan Wu 1,
Zongpeng Li 2, Francis C.M. Lau 1
1 The University of Hong Kong2 University of Calgary
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Outline
Background Problem settings Difficulties Mechanism design Performance evaluations Summary
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Amazon EC2
Computing resources are packed into VMs by virtualization technology
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Users demand for Cloud resources
![Page 5: Online Auctions in IaaS Clouds: Welfare and Profit Maximization with Server Costs Xiaoxi Zhang 1, Zhiyi Huang 1, Chuan Wu 1, Zongpeng Li 2, Francis C.M.](https://reader035.fdocuments.us/reader035/viewer/2022062304/56649d775503460f94a58619/html5/thumbnails/5.jpg)
Why auction
Users can determine their own VM types
Providers can price according to the current demand and supply relationship
Computing resources are limited
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Amazon EC2 Spot Instances
Demand: a VM instance
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Amazon EC2 Spot Instances
Demand: a VM instance
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Our work
Our workTime-variant resource demands—— a customized VM
Start time
End time
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• S servers• R types of resources, with known capacities• T time slots• I users• For each user i: • Demands of user i:
Problem settings
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• Power consumption of each server can be formulated
Problem settings
Horizontal coordinate: resource(e.g., CPU) utilizationVertical coordinate: power consumption
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When Dynamic Voltage Frequency Scaling (DVFS)
server mode is enabled, .
Problem settings
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Problem settings
Dynamic Voltage Frequency Scaling (DVFS) server mode is disabled.
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Problem settings
Server cost is not considered.
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bid serv
erbid i on s ✔ =1 ✗ =0
time slot
resource
VM allocation model
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resource allocation constraint
server cost
VM allocation model
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1. y = allocated resource amount
2. No resource is over-provisioned
VM allocation model
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VM auction: NP-hardSever cost considerationResource reusability
Payment: For welfare maximization: it should be a threshold to filer out low-value bids For profit maximization: it should be as close to bidding price as possible
Challenges with online auction
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Upon the arrival of bid i: 1. Use the current price to
calculate the payment on each server: payment(s)= 2. Choose the smallest payment and
the corresponding server . 3. If : Accept bid i. Serve bid i on
. Update . Update . Otherwise: Reject bid i .
Online auction for welfare maximization
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Our online auction achieves:
How to update ?
Online auction for welfare maximization
![Page 20: Online Auctions in IaaS Clouds: Welfare and Profit Maximization with Server Costs Xiaoxi Zhang 1, Zhiyi Huang 1, Chuan Wu 1, Zongpeng Li 2, Francis C.M.](https://reader035.fdocuments.us/reader035/viewer/2022062304/56649d775503460f94a58619/html5/thumbnails/20.jpg)
Our online auction achieves: Truthfulness Polynomial time complexity High social welfare ---- competitive
ratio
How to update ?
Online auction for welfare maximization
![Page 21: Online Auctions in IaaS Clouds: Welfare and Profit Maximization with Server Costs Xiaoxi Zhang 1, Zhiyi Huang 1, Chuan Wu 1, Zongpeng Li 2, Francis C.M.](https://reader035.fdocuments.us/reader035/viewer/2022062304/56649d775503460f94a58619/html5/thumbnails/21.jpg)
Our online auction achieves: Truthfulness Polynomial time complexity High social welfare ---- competitive
ratio
How to update ?
Online auction for welfare maximization
![Page 22: Online Auctions in IaaS Clouds: Welfare and Profit Maximization with Server Costs Xiaoxi Zhang 1, Zhiyi Huang 1, Chuan Wu 1, Zongpeng Li 2, Francis C.M.](https://reader035.fdocuments.us/reader035/viewer/2022062304/56649d775503460f94a58619/html5/thumbnails/22.jpg)
Our online auction achieves: Truthfulness Polynomial time complexity High social welfare ---- competitive
ratio
How to update ? Using an online primal-dual framework
Online auction for welfare maximization
![Page 23: Online Auctions in IaaS Clouds: Welfare and Profit Maximization with Server Costs Xiaoxi Zhang 1, Zhiyi Huang 1, Chuan Wu 1, Zongpeng Li 2, Francis C.M.](https://reader035.fdocuments.us/reader035/viewer/2022062304/56649d775503460f94a58619/html5/thumbnails/23.jpg)
An online primal-dual framework
Primal:
Dual:
Lagrange relaxation
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An online primal-dual framework
Primal:
Dual:
Lagrange relaxation
Resource
priceUtility of i
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An online primal-dual framework
Primal (P): Maximization problem Dual (D): Minimization problem P(or D): Primal(or Dual) objective
value under a feasible primal(or dual) solution
Weak duality: P<=P* <= D*<=D
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An online primal-dual framework
Primal (P): Maximization problem Dual (D): Minimization problem P(or D): Primal(or Dual) objective
value under a feasible primal(or dual) solution
Weak duality: P<=P* <= D*<=D
Competitive analysis: P>= (1/α)D
Tight the gap
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An online primal-dual framework
Competitive analysis: P>= (1/α)D Pi: The primal objective value after
dealing with bid i Di: The dual objective value after
dealing with bid i In order to get P>= (1/α)D, we
resort to satisfying Pi - Pi-1 >= (1/α) (Di – Di-1), given P0=D0=0.
![Page 28: Online Auctions in IaaS Clouds: Welfare and Profit Maximization with Server Costs Xiaoxi Zhang 1, Zhiyi Huang 1, Chuan Wu 1, Zongpeng Li 2, Francis C.M.](https://reader035.fdocuments.us/reader035/viewer/2022062304/56649d775503460f94a58619/html5/thumbnails/28.jpg)
An online primal-dual framework
In order to guarantee Pi - Pi-1 >= (1/α) (Di – Di-1), we
have:
Solve for each i, r, s, t to minimize α.
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What are the goals of our online auction ?
Truthfulness Polynomial time complexity High social welfare ---- competitive ratio
How to update ? Using an online primal-dual framework, we solve , a function of .
Online auction for welfare maximization
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How to intuitively understand
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Evaluation setup
Google Cluster Data contains information including resource demands (CPU, RAM, Disk), job arrival times and durations.
We translate each job into a VM bid, requesting R = 3 types of resources at the demands extracted from the traces (demand here is not much smaller than Crs ).
Default Parameters: Each time slot is 10 seconds, and a bid arrives every [1, 10]
time slot(s). The duration of each VM is between 10 and 3600 time slots.
Ur =50, Lr =1. hrs~[0.4, 0.6] for CPU, hrs~[0.005, 0.02] for RAM and disk. βrs~[1.7, 2.2] for CPU, βrs~[0.5, 1] for RAM and disk.
The capacity of each type of resource and the number of servers are roughly according to the total amount of demand from all bids multiplying a random number in [0.4, 0.8].
![Page 32: Online Auctions in IaaS Clouds: Welfare and Profit Maximization with Server Costs Xiaoxi Zhang 1, Zhiyi Huang 1, Chuan Wu 1, Zongpeng Li 2, Francis C.M.](https://reader035.fdocuments.us/reader035/viewer/2022062304/56649d775503460f94a58619/html5/thumbnails/32.jpg)
Performance evaluation of welfare maximization
Bar colors: difference with average # of time slots between the bid arrival time to its specified VM start time over all the bids.
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Performance evaluation of welfare maximization
![Page 34: Online Auctions in IaaS Clouds: Welfare and Profit Maximization with Server Costs Xiaoxi Zhang 1, Zhiyi Huang 1, Chuan Wu 1, Zongpeng Li 2, Francis C.M.](https://reader035.fdocuments.us/reader035/viewer/2022062304/56649d775503460f94a58619/html5/thumbnails/34.jpg)
Performance evaluation of profit maximization
Bar colors: difference with the ratio between the upper and lower bound of bidding price per unit of resource demand
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Summary
We design an online auction to do Cloud resource provisioning for users with time-variant demands.
We consider heterogeneous resources dynamically allocated, released, and reused.
We maximize social welfare with server cost which achieves a good competitive ratio.
We also apply an approach to maximize provider profit which achieves a good competitive ratio.
![Page 36: Online Auctions in IaaS Clouds: Welfare and Profit Maximization with Server Costs Xiaoxi Zhang 1, Zhiyi Huang 1, Chuan Wu 1, Zongpeng Li 2, Francis C.M.](https://reader035.fdocuments.us/reader035/viewer/2022062304/56649d775503460f94a58619/html5/thumbnails/36.jpg)
Thank you
Q&A
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Backup Slides
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Upon the arrival of bid i: 1. Using the current price of each type of resource
at each time slot within the resource execution duration to calculate the payment on each server:
payment(s)= 2. Choose the smallest payment among all s,
denoted by . The corresponding s is . 3. If : Accept bid i. Allocate resources on
to server bid i. Update . Update . Otherwise: Reject bid i.
Online auction for welfare maximization
![Page 39: Online Auctions in IaaS Clouds: Welfare and Profit Maximization with Server Costs Xiaoxi Zhang 1, Zhiyi Huang 1, Chuan Wu 1, Zongpeng Li 2, Francis C.M.](https://reader035.fdocuments.us/reader035/viewer/2022062304/56649d775503460f94a58619/html5/thumbnails/39.jpg)
uiPrs(t)
relaxation Lagrange
Relaxation
Online primal-dual framework
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uiPrs(t)
relaxation
Online primal-dual framework
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uiPrs(t)
relaxation
utilitymarginal payment
Online primal-dual framework
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uiPrs(t)
relaxation
utilitymarginal payment
payment of bid i
Online primal-dual framework
![Page 43: Online Auctions in IaaS Clouds: Welfare and Profit Maximization with Server Costs Xiaoxi Zhang 1, Zhiyi Huang 1, Chuan Wu 1, Zongpeng Li 2, Francis C.M.](https://reader035.fdocuments.us/reader035/viewer/2022062304/56649d775503460f94a58619/html5/thumbnails/43.jpg)
utilitymarginal payment
payment of bid i
Online primal-dual framework
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utilitymarginal payment
payment of bid i
1. Dual Feasibility P >= 1/α D
P*<=D*<=D P >= 1/α P*2. Complementary Slackness of KKT Optimality Condition:For any user i,
Main idea:
Online primal-dual framework
![Page 45: Online Auctions in IaaS Clouds: Welfare and Profit Maximization with Server Costs Xiaoxi Zhang 1, Zhiyi Huang 1, Chuan Wu 1, Zongpeng Li 2, Francis C.M.](https://reader035.fdocuments.us/reader035/viewer/2022062304/56649d775503460f94a58619/html5/thumbnails/45.jpg)
Intuitively, prs(yrs(t)) is a function of marginal cost under some predicted allocated amount.
Why ?Upon Bi’s arrival, for any t, r, s, prs(t)dir(t) > frs(yrs(t)+dir(t)) – frs(yrs(t))
≈ f ’rs(yrs(t))dir(t)
if
How to design prs(t)
![Page 46: Online Auctions in IaaS Clouds: Welfare and Profit Maximization with Server Costs Xiaoxi Zhang 1, Zhiyi Huang 1, Chuan Wu 1, Zongpeng Li 2, Francis C.M.](https://reader035.fdocuments.us/reader035/viewer/2022062304/56649d775503460f94a58619/html5/thumbnails/46.jpg)
Intuitively, prs(yrs(t)) is a function of marginal cost under some predicted allocated amount.
Why ?
Exponential function is growing fast!
if
How to design prs(t)
![Page 47: Online Auctions in IaaS Clouds: Welfare and Profit Maximization with Server Costs Xiaoxi Zhang 1, Zhiyi Huang 1, Chuan Wu 1, Zongpeng Li 2, Francis C.M.](https://reader035.fdocuments.us/reader035/viewer/2022062304/56649d775503460f94a58619/html5/thumbnails/47.jpg)
Pi – Pi-1 >= 1/α ( Di – Di-1 ), given P0 = D0 =0 PI >= 1/α DI α is the competitive ratio
How to design prs(t)
![Page 48: Online Auctions in IaaS Clouds: Welfare and Profit Maximization with Server Costs Xiaoxi Zhang 1, Zhiyi Huang 1, Chuan Wu 1, Zongpeng Li 2, Francis C.M.](https://reader035.fdocuments.us/reader035/viewer/2022062304/56649d775503460f94a58619/html5/thumbnails/48.jpg)
Pi – Pi-1 >= 1/α ( Di – Di-1 ), given P0 = D0 =0 PI >= 1/α DI α is the competitive ratio
How to design prs(t)
![Page 49: Online Auctions in IaaS Clouds: Welfare and Profit Maximization with Server Costs Xiaoxi Zhang 1, Zhiyi Huang 1, Chuan Wu 1, Zongpeng Li 2, Francis C.M.](https://reader035.fdocuments.us/reader035/viewer/2022062304/56649d775503460f94a58619/html5/thumbnails/49.jpg)
Pi – Pi-1 >= 1/α ( Di – Di-1 ), given P0 = D0 =0 PI >= 1/α DI α is the competitive ratio
How to design prs(t)
![Page 50: Online Auctions in IaaS Clouds: Welfare and Profit Maximization with Server Costs Xiaoxi Zhang 1, Zhiyi Huang 1, Chuan Wu 1, Zongpeng Li 2, Francis C.M.](https://reader035.fdocuments.us/reader035/viewer/2022062304/56649d775503460f94a58619/html5/thumbnails/50.jpg)
Show the idea by drawing a picture on the whiteboard
How to design prs(t)
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>= bmax
Profit maximization