Game Theory Based Scheduling for Multiple-User Smart Home Systems

1. EE5900: Cyber-Physical Systems Multiple-User Smart Home System

2. Multiple Users in a Community 2

3. Multiple Users • Pricing at 10:00am is cheap, so how about scheduling everything at that time? Energy Accumlation 10:00am 3

4. Game Theory Based Scheduling 4

5. Game Theory Based Scheduling • For every player in a game, there is a set of strategies and a payoff function which is the profit of the player. • Each player chooses from the set of strategies in order to maximize its payoff. • When no player can increase its payoff without decreasing other users’ payoff, Nash Equilibrium is reached. 5

6. Game Formulation in Community Level Players: All users in the community Strategy: Choose power levels and launch time to maximize payoff while satisfying constraints 6

7. Community Size • Small community: Less than 100 users • Medium community: 100 ~5,000 users • Large community: More than 5,000 users 7

8. Small Community: Fully Distributed Architecture In the fully distributed architecture, each customer uses own smart home scheduler to communicate with other users for information exchange and computes smart home scheduling solution. 8

9. Algorithmic Illustration For Small Community Iteration 1 … User1 Usern User2 Usern User1 User2 Embedded Processor Embedded Processor Embedded Processor Embedded Processor Embedded Processor Embedded Processor Communication/Synchronization Iteration 2 … Communication/Synchronization …… Equilibrium/Schedule 9

10. Algorithmic Flow For Small Community • Each user schedules their own appliances separately to maximize payoff using dynamic programming • Appliances • Determine scheduling appliances order • All users share information with each other • Schedule current appliance by dynamic programming • Each user reschedules their own appliances separately by dynamic programming No All appliances scheduled No Equilibrium Yes Yes • Schedule • Schedule 10

11. Problem With The Fully Distributed Architecture • Communication/synchronization problem • Assume that there are 100 iterations needed for the game theory based algorithm. • Communication/synchronization needs to be performed at the end of every iteration. • It is not realistic for big community to deploy the fully distributed architecture due to the complexity of synchronization among a large number of users. Each user performs the game theory based algorithm at their own side and communicates with all other users after every single iteration. 11

12. Medium Community: Fully Centralized Architecture • Users only communicate with computer cluster twice, at the beginning and end. • Communication/synchronization is not needed any more among users. • Communication/synchronization within computers or CPU cores is much easier and faster. Each user sends the scheduling tasks to a computer cluster which compute the scheduling solutions of all users. 12

13. Algorithmic Illustration For Medium Community … • Each core schedules assigned tasks of users in parallel Interface Interface Interface Usern User2 User1 Run iteratively until convergence User2 User1 Usern Parallel Computing Interface Interface Interface • All cores share information with each other to synchronize • Each core reschedules the assigned tasks given the information of other users Equilibrium … • Schedule 13

14. Algorithmic Flow For Medium Community User3 User2 Usern User3 User2 User1 Usern Schedule tasks of users to computers Game theory based algorithm Sort all computers increasingly by ratio of 𝒄/𝒇 • Each computer runs tasks of users in parallel User1 Solve the continuous fashion problem combinatorially Run iteratively Yes Flag all computers to be available • All computers share information with each other to synchronize # iterations = kϒ No Assign task fractionally to the available computer with lowest ratio of 𝒄/𝒇 Users send tasks to computers Computers send back the results to users • Each computer reruns the tasks of users given the information of other users …… …… No Runtime of computer is reaching TC Yes Equilibrium No Flag the computer to be unavailable Yes • Schedule Discretize the continuous solution

15. Problem With The Fully Centralized Architecture • Cannot handle large community • Communication delay • Limited computation power and high maintenance cost • Security concerns 15

16. Large Community: Hierarchical Architecture • There are 10 million users in a big community. It can be partitioned into 2k smaller groups, in which the number of users is 5k. • The communication overhead within each group is acceptable. • There is no flooding packets problem. 16

17. Algorithmic Flow For Intra-Community Optimization … • Each core schedules assigned tasks of users in parallel User2 User1 Userx1 Continue to Inter-community optimization Run iteratively until convergence Parallel Computing Interface Interface Interface • All cores share information with each other to synchronize • Each core reschedules the assigned tasks given the information of other users Equilibrium • Schedule 17

18. Algorithmic Flow For Inter-Community Optimization • Energy consumption summation of Intra-community optimization • Pick k time intervals with the largest total energy consumption • Reduce the k energy consumption by δ • Pick k time intervals with the smallest total energy consumption • Increase the k energy consumption by δ • Continue to Intra-community optimization/Schedule 18

19. Algorithmic Illustration For Large Community … • Each core schedules assigned tasks of users in parallel Userx1 User2 User1 Continue to Inter-community optimization • Energy consumption summation of Intra-community optimization Run iteratively until convergence Parallel Computing Interface Interface Interface • All cores share information with each other to synchronize • Pick k time intervals with the largest total energy consumption • Each core reschedules the assigned tasks given the information of other users • Reduce the k energy consumption by δ • Pick k time intervals with the smallest total energy consumption Equilibrium • Increase the k energy consumption by δ • Schedule • Continue to Intra-community optimization/Schedule 19

20. Thanks 20