1. Automated Bandwidth Allocation Problems in Data Centers Yifei Yuan, Anduo Wang, Rajeev Alur, Boon Thau Loo University of Pennsylvania

2. Motivation Managing network resources is the key computational problem in Data Centers. Applying verification/synthesis tool to network resource management? – Benefits: exact solutions, correctness guarantees – Challenges: efficiency This work: bandwidth allocation by SAT/SMT solvers 1

3. Bandwidth Allocation Problem 2

4. 1G bps600M bps 500M bps 450M bps X1X1 X2X2 X3X3 S1S1 S2S2 S3S3 S4S4 Data Center’s Network 10G bps 2

5. Bandwidth Allocation Problem 1G bps600M bps 500M bps 450M bps X1X1 X2X2 X3X3 S1S1 S2S2 S3S3 S4S4 Data Center’s Network V1V1 V2V2 V3V3 400M bps Virtual Network 10G bps 2

6. Bandwidth Allocation Problem 1G bps600M bps 500M bps 450M bps X1X1 X2X2 X3X3 S1S1 S2S2 S3S3 S4S4 Data Center’s Network V1V1 V2V2 V3V3 400M bps Virtual Network 10G bps 2

7. Bandwidth Allocation Problem 1G bps600M bps 500M bps 450M bps X1X1 X2X2 X3X3 S1S1 S2S2 S3S3 S4S4 Data Center’s Network V1V1 V2V2 V3V3 400M bps Virtual Network v1v1 v1v1 v3v3 v3v3 v2v2 v2v2 10G bps 2

8. Bandwidth Allocation Problem 1G bps600M bps 500M bps 450M bps X1X1 X2X2 X3X3 S1S1 S2S2 S3S3 S4S4 Data Center’s Network V1V1 V2V2 V3V3 400M bps Virtual Network v1v1 v1v1 v3v3 v3v3 v2v2 v2v2 10G bps 2

9. BAP: Facts Complexity: – NP-complete: tree for physical network & virtual network Existing heuristics: – Pros: efficient – Cons: no guarantee Alternative approach: SAT/SMT solving 3

10. SAT/SMT Encoding: A Glimpse X(v,s): VM v is mapped to server s Y(l,e): physical link l is reserved bandwidth virtual link e R(l,e,k): physical link l is the k-th edge on the routing path for virtual link e Server capacity: – ∑ v X(v,s) < c(s), for every server s Link capacity: – ∑ e Y(l,e) < b(l), for every physical link l 4

11. Abstraction and Refinement Observation: Hierarchical physical network topology in data centers – Tree – Fat-tree Idea: – Abstract physical network: small size – Refine subgraphs 5

12. Abstraction 12 42 6

13. 12 42 6

14. 12 42 36 6

15. 36 6

16. 36 6

17. Refinement 12 42 36 7

18. 12 42 7

19. Evaluation: Set up Physical network topology: tree with 200 servers: 200 20 4444 8

20. Evaluation: Set up Virtual network topology: connected cliques 2 1 1 9

21. Evaluation: Set up Experiment: – Run allocation algorithm – Keep mapping the VN to the PN – Stop when no more VN can be mapped 10

22. Evaluation: Server Utilization 11

23. Evaluation: Link Utilization

24. Evaluation: Running Time per VN 12

25. Summary Alternative approach solving network resource allocation problem: using SAT/SMT solvers Abstract&refinement for scalability Strength: optimal solution Weakness: efficiency – Possible scenario: Optimal reallocation 13