Automated Bandwidth Allocation Problems in Data Centers

Yifei Yuan, Anduo Wang, Rajeev Alur, Boon Thau LooUniversity of Pennsylvania

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

Bandwidth Allocation Problem

2

Bandwidth Allocation Problem

1G bps 600M bps

500M bps

450M bps

X1

X2 X3

S1 S2 S3 S4

Data Center’s Network

10G bps

10G bps

2

Bandwidth Allocation Problem

1G bps 600M bps

500M bps

450M bps

X1

X2 X3

S1 S2 S3 S4

Data Center’s Network

V1

V2 V3

400M bps

400M bps

Virtual Network

10G bps

10G bps

2

Bandwidth Allocation Problem

1G bps 600M bps

500M bps

450M bps

X1

X2 X3

S1 S2 S3 S4

Data Center’s Network

V1

V2 V3

400M bps

400M bps

Virtual Network

10G bps

10G bps

2

Bandwidth Allocation Problem

1G bps 600M bps

500M bps

450M bps

X1

X2 X3

S1 S2 S3 S4

Data Center’s Network

V1

V2 V3

400M bps

400M bps

Virtual Network

v1 v3 v2

10G bps

10G bps

2

Bandwidth Allocation Problem

1G bps 600M bps

500M bps

450M bps

X1

X2 X3

S1 S2 S3 S4

Data Center’s Network

V1

V2 V3

400M bps

400M bps

Virtual Network

v1 v3 v2

10G bps

10G bps

2

BAP: Facts

• Complexity:– NP-complete: tree for physical network & virtual

network• Existing heuristics:– Pros: efficient– Cons: no guarantee

• Alternative approach: SAT/SMT solving

3

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

Abstraction and Refinement

• Observation: Hierarchical physical network topology in data centers– Tree– Fat-tree

• Idea:– Abstract physical network: small size– Refine subgraphs

5

Abstraction

1 2 4 2

6

Abstraction

1 2 4 2

6

Abstraction

1 2 4 2

3 6

6

Abstraction

3 6

6

Abstraction

3 6

6

Refinement

1 2 4 2

3 6

7

Refinement

1 2 4 2

7

Evaluation: Set up

• Physical network topology: tree with 200 servers:

200

20

4 4 4 4

8

Evaluation: Set up

• Virtual network topology: connected cliques

2

1 1

9

Evaluation: Set up

• Experiment:– Run allocation algorithm– Keep mapping the VN to the PN– Stop when no more VN can be mapped

10

Evaluation: Server Utilization

9 vms 15 vms0

0.2

0.4

0.6

0.8

1

1.2

secondnetsatsat_abs

# of VMs

Avg.

serv

er u

liti-

zatio

n

11

Evaluation: Running Time per VN

9 vms 15 vms0.01

0.1

1

10

100

1000

secondnetsatsat_abs

# of VMs

Runn

ing

time

per

vn (s

econ

ds)

12

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