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. Lau 1 1 The University of Hong Kong 2 University of Calgary

2. Outline  Background  Problem settings  Difficulties  Mechanism design  Performance evaluations  Summary

3. Amazon EC2 Computing resources are packed into VMs by virtualization technology

4. Users demand for Cloud resources

5. Why auction  Users can determine their own VM types  Providers can price according to the current demand and supply relationship  Computing resources are limited

6. Amazon EC2 Spot Instances Demand: a VM instance

7. Amazon EC2 Spot Instances Demand: a VM instance

8. Our work Time-variant resource demands —— a customized VM Start time End time

9. S servers R types of resources, with known capacities T time slots I users For each user i: Demands of user i: Problem settings

10. Power consumption of each server can be formulated Problem settings Horizontal coordinate: resource(e.g., CPU) utilization Vertical coordinate: power consumption

11. When Dynamic Voltage Frequency Scaling (DVFS) server mode is enabled,. Problem settings

12. Dynamic Voltage Frequency Scaling (DVFS) server mode is disabled.

13. Problem settings Server cost is not considered.

14. bid server bid i on s ✔ =1 ✗ =0 time slot resource VM allocation model

15. resource allocation constraint server cost VM allocation model

16. 1. y = allocated resource amount 2.No resource is over-provisioned VM allocation model

17.  VM auction: NP-hard Sever cost consideration Resource 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

18. 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. Otherwise: Reject bid i. Online auction for welfare maximization

19.  Our online auction achieves:  How to update ？ Online auction for welfare maximization

20.  Our online auction achieves:  Truthfulness  Polynomial time complexity  High social welfare ---- competitive ratio  How to update ？ Online auction for welfare maximization

21.  Our online auction achieves:  Truthfulness  Polynomial time complexity  High social welfare ---- competitive ratio  How to update ？ Online auction for welfare maximization

22.  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

23. An online primal-dual framework Primal: Dual: Lagrange relaxation

24. An online primal-dual framework Primal: Dual: Lagrange relaxation Resource price Utility of i

25. 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

26. 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

27. An online primal-dual framework  Competitive analysis: P>= (1/ α )D  P i : The primal objective value after dealing with bid i  D i : The dual objective value after dealing with bid i  In order to get P>= (1/ α )D, we resort to satisfying P i - P i-1 >= (1/ α ) (D i – D i-1 ), given P 0 =D 0 =0.

28. An online primal-dual framework  In order to guarantee P i - P i-1 >= (1/ α ) (D i – D i-1 ), we have:  Solve for each i, r, s, t to minimize α.

29.  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

30. How to intuitively understand

31. 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 C rs ). 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. h rs ~[0.4, 0.6] for CPU, h rs ~[0.005, 0.02] for RAM and disk. β rs ~[1.7, 2.2] for CPU, β rs ~[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].

32. 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.

33. Performance evaluation of welfare maximization

34. 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

35. 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.

36. Thank you Q&A

37. Backup Slides

38. 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. Otherwise: Reject bid i. Online auction for welfare maximization

39. uiui P rs (t) relaxation Lagrange Relaxation Online primal-dual framework

40. uiui P rs (t) relaxation Online primal-dual framework

41. uiui P rs (t) relaxation utility marginal payment Online primal-dual framework

42. uiui P rs (t) relaxation utility marginal payment payment of bid i Online primal-dual framework

43. utility marginal payment payment of bid i Online primal-dual framework

44. utility marginal 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

45. Intuitively, p rs (y rs (t)) is a function of marginal cost under some predicted allocated amount. Why ? Upon Bi’s arrival, for any t, r, s, p rs (t)d ir (t) > f rs (y rs (t)+d ir (t)) – f rs (y rs (t)) ≈ f ’ rs (y rs (t))d ir (t) if How to design p rs (t)

46. Intuitively, p rs (y rs (t)) is a function of marginal cost under some predicted allocated amount. Why ? Exponential function is growing fast! if How to design p rs (t)

47. P i – P i-1 >= 1/ α ( D i – D i-1 ), given P 0 = D 0 =0 P I >= 1/ α D I α is the competitive ratio How to design p rs (t)

48. P i – P i-1 >= 1/ α ( D i – D i-1 ), given P 0 = D 0 =0 P I >= 1/ α D I α is the competitive ratio How to design p rs (t)

49. P i – P i-1 >= 1/ α ( D i – D i-1 ), given P 0 = D 0 =0 P I >= 1/ α D I α is the competitive ratio How to design p rs (t)

50. Show the idea by drawing a picture on the whiteboard How to design p rs (t)

51. >= b max Profit maximization