A Resource Allocation Mechanism of Data Center for Public Cloud Service

1. A Resource Allocation Mechanism of Data Center for Public Cloud Service 指導教授：王國禎 學生：連懷恩 國立交通大學資訊工程系 行動計算與寬頻網路實驗室

2. Outline • Background and scenario review • Basics of linear programming • A simple linear programming approach • Conclusion

3. Background and Scenario Review • Dealing with Number of active servers, number of VMs for each application, VM placement problem, and optimization over a series of time slots. • Applying an existing load-prediction method to get the forecast of resource demand of each application over a series of time slots.

4. Background and Scenario Review • To reduce the problem complexity, we split it into a two-phase problem. • In phase 1, we only consider the number of active servers and VMs for each app in each time slot. That is, set the VM migration cost to 0 thus ignoring the VM placement problem. • We have showed a branch-and-bound approach for the phase 1 problem last time. This time we try a different way using a linear programming approach to solve the phase 1 problem.

5. Basics of Linear Programming • A standard form of a minimization problem: minimize cx subject to Ax ≤ b, x ≥ 0 where A is a m × n matrix over reals, with m ≤ n, x is an n-dimensional column vector over reals, c is an n-dimensional row vector over reals, and b is an m-dimensional column vector over reals. • n variables in x form a convex polytope in a n-dimension space. • Three possible conditions; try to find optimal solution on vertices.

6. Basics of Linear Programming By the state-of-the-art interior method, we can solve the real number linear programming problem in . But an integer programming problem is NP-hard. A typical approach would be: Integer programming relax => Linear programming => Real number solution rounding => Integer solution

7. A Simple Linear Programming Approach – The Power Consumption Model

8. A Simple Linear Programming Approach - Denotations • PVM = Energy cost of a VM in a time slot • Pserver = Basic energy cost of a idle server in a time slot • δVM= Switching cost to switch on/off a VM • δServer= Switching cost to switch on/off a server • Each server can host at most capacity VMs • Total N apps, infinite number of free servers • Forecast of resource demand is up to T time slots

9. Basics of Linear Programming Minimize Subject to

10. Basics of Linear Programming – Solving the Linear Programming Problem Add free variables to transform the absolute form into linear form, and inequality into equality, ex. Transform into , in which Totally, we need 5T(N+1) - 3N - 3 variables. Note that we have a running time .

11. A Simple Linear Programming Approach – Rounding to Integer Solution If we round up to the closest integer Since Optreal ≤ Optinteger ≤ Rounding, and αOptreal≥ Rounding → αOptinteger≥ Rounding → α = Not a constant performance ratio. It depends on the input size. If we can estimate the frequency of break-event time event, the performance ratio will be lower.

12. A Simple Linear Programming Approach – Rounding to Integer Solution • We can further improve the performance ratio if we use threshold 0.5 to round # of VMs. • In every VM break-even time event, the increment of switching cost ≤ δVM, the amortized increment of energy cost is 0.

13. Conclusion • Try to improve the performance ratio. • As a baseline approach comparing with our heuristic approach. • How to combine the linear programming approach with the phase 2 algorithm?

14. Reference [1] A Taxonomy and Survey of Energy-Efficient Data Centers and Cloud Computing Systems - Advances in Computers, Vol 82, Anton Beloglazov, RajkumarBuyya, Young ChoonLee, and Albert Zomaya