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.
ser
ver u
litiza
-tio
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