An Optimal Control Policy in a Mobile Cloud Computing System Based on Stochastic Data

1. An Optimal Control Policy in a Mobile Cloud Computing System Based on Stochastic Data Xue Lin, Yanzhi Wang, MassoudPedram University of Southern California

2. Cloud Computing and Mobile Devices • Cloud Computing Paradigm • Cloud service provider • Clients • Mobile Device Computing Platform • Compactness, portability, and functionality • Weak computing and storage • Short battery life • Mobile Cloud Computing (MCC) paradigm • Extend capabilities • Improve performance • Reduce energy consumption 2

3. Mobile Devices in MCC Paradigm • Service Request • Local processing • Remote processing by offloading to the cloud • Control Decision • Whether to offload a service request • CPU operating frequency for local processing • Performance and Power Consumption • Higher performance means higher power • A trade-off is desirable 3

4. Outline • Motivation • System Model • MCC system • Battery model • Expected performance sum • Optimal Control Policy • Problem formulation • Dynamic programming algorithm • Experimental Results • Conclusion 4

5. Motivation • Inter-Charging Interval (ICI) • Short ICI length: high performance mode • Long ICI length: low power mode • Only stochastic data is available • Power and Performance Trade-Off • Performance sum: the sum of the performance for all requests processed during an ICI • Maximize the expected performance sum 5

6. System Model: MCC System • A mobile device in the MCC system • : service request generation rate, Poisson • : local processing probability • : local request rate, Poisson • : remote request rate, Poisson 6

7. System Model: Response Time • Average response time of local processing • Average response time of remote processing • Average response time : avg. request processing rate of the CPU : avg. request sending rate in the RF : avg. request sending time : avg. round trip time 7

8. System Model: Power Consumption • Mobile Device Power Consumption • CPU: dynamic and static power • RF: dynamic and static power 8

9. System Model: Battery • Battery is power source during ICI • : length of an ICI, random variable, probability density function (p.d.f) , the i-th time interval , , • The remaining energy in the battery • The operating time of the mobile device, assuming an infinite long ICI, 9

10. System Model: Expected Performance Sum • The performance for processing a request • The expected value of the performance sum where is the indicator function 10

11. Problem Formulation • Derive the optimal control policy for the mobile device, based on the stochastic data of the ICI length, to maximize the expected performance sum • Derive the optimal and for • can only assume values for the set , where the elements are request processing rates corresponding to K CPU frequency values. • The stochastic data about ICI length are given in the form of . 11

12. Optimal Control Policy Problem • Given: (i) the number of discharging time intervals , and (ii) the amount of remaining battery energy after the discharging process. • Find: the and values for . • Maximize: • Subject to: • This is a general problem i.e., problem. • When and , the problem becomes the Optimal Control Policy (OCP) problem. 12

13. Dynamic Programming Algorithm • The optimal substructure property: Suppose that the problem has been optimally solved, and the the energy stored in the battery at time is in that optimal solution. This corresponds to the problem. The optimal solution of the problem contains within it the optimal solution of the problem. • Find the optimal solution of the problem from the optimal solutions of the problems for , which are stored in matrix elements 13

14. Dynamic Programming Algorithm • Maximize the expected performance of the mobile device during the time interval • Given: the battery energy at time is and the battery energy at time is • Find: the and values • Maximize: the expected performance • Subject to: • The maximum expected performance in time interval is denoted by 14

15. Dynamic Programming Algorithm • Find the optimal solution of the problem is then calculated as • The optimal is stored in the matrix entry • The problem is solved as we calculate 15

16. Dynamic Programming Algorithm 16

17. Dynamic Programming Algorithm • The average performance value is a non-increasing function, or equivalently, is a non-decreasing function, over all the time intervals . • Proof: Suppose that function is not a non-decreasing function. Then there must exist two consecutive time intervals i and i+1 satisfying . We exchange the control decisions with , and it will result in the same value but a higher expected value of the performance sum. This is because . 17

18. Experimental Results • Two baseline control policies: • Always chooses the highest CPU operating frequency, and chooses p[i] values to maximize performance. • Always chooses the lowest CPU operating frequency, and chooses p[i] values to maximize performance. • Three probability density functions of ICI length 18

19. Experimental Results • The optimal control policy outperforms two baseline control policies with higher expected value of the performance sum. 19

20. Experimental Results 20

21. Conclustion • The mobile device control decisions should be made according to the ICI length. • We define the expected performance sum as the objective function, which is a trade-off between performance and power consumption and accounts for the ICI length uncertainty. • A dynamic programming algorithm is proposed to derive the optimal control policy. 21

22. Thank you !