1. Scalable Load-Distance Balancing
EE Department The Technion, Haifa, Israel
Scalable Load-Distance Balancing
Edward Bortnikov, Israel Cidon, Idit Keidar

2. Service Assignment Assign (many) users to (a few) servers
Service Assignment
Assign (many) users to (a few) servers
Applications:
Content/game servers
Internet gateways in a wireless mesh network (WMN)
The increased demand for real-time access  multiple service points (servers)
Gives rise to the problem of service assignment – associating each user with a server s.t. the QoS is improved
Many technologies

3. Load-Distance Balancing (LDB)
Load-Distance Balancing (LDB)
Two sources of service delay
Network delay – due to user-server distance
e.g., depends on the number of network hops
Congestion delay – due to server load
General monotonic non-decreasing function
Total delay = Network delay + Congestion delay
The Load-Distance Balancing problem (LDB)
Minimize the maximum total delay (cost)
NP-complete (a 2-approximation exists)

4. LDB versus LB Network distance OK Congestion high Network distance OK
LDB versus LB
Network distance OK
Congestion high
Network distance OK
Congestion OK
Network distance high
Congestion OK

5. Distributed LDB Distributed assignment computation Requirements
Distributed LDB
Distributed assignment computation
Initially, users report locations to closest servers
Servers communicate and compute the assignment
Synchronous failure-free communication model
Requirements
Eventual quiescence
Eventual stability of assignment
Constant α-approximation of the optimal cost
α ≥ 2 is a parameter (trade communication/time for cost)
At startup, every user is assigned to the nearest server
Servers can communicate and change assignment
Eventually, the following conditions must hold:
inter-server communication stops
Assignment stops changing
An a-approximation of the optimal assignment is computed….

6. What About Locality? Extreme global solution Extreme local solution
What About Locality?
Extreme global solution
Collect all data and compute assignment centrally
Guarantees 2-approximation of optimal cost
Excessive communication/network latency
Extreme local solution
Nearest-Server assignment
No communication
No approximation guarantee (can’t handle crowds)
In addition to cost, in the distributed case we are interested about locality.

7. Workload-Sensitive Locality
Workload-Sensitive Locality
The cost function is distance-sensitive
Most assignments can go to the near servers
… except for dissipating congestion peaks
Distributed solution structure
Start from the nearest-server assignment
Offload congestion to near servers
Workload-sensitive locality
Go as far as needed …
… to achieve the desired approximation α

8. Example: Light Uniform Workload
Example: Light Uniform Workload

9. Example: Peaky Workload
Example: Peaky Workload
LDB-approximation
LDB-approximation
LDB-approximation

10. Iterative Clustering Partition servers into clusters
Iterative Clustering
Partition servers into clusters
Assign each user within its cluster
Choose one leader per cluster
Leader collects local data
Computes within-cluster assignments
Clusters may merge
A cluster tries to merge as long as its cost is ε-improvable
Can be decreased by ≥ 1+ε if all servers are harnessed
No ε-improvable cluster 
desired approximation achieved (α =2(1+ε))
slack factor

11. Tree (Structured) Clustering
Tree (Structured) Clustering
Maintain a hierarchy of clusters
Employ clusters of size 2i
While some cluster ε-improvable
Double it (merge with hierarchy neighbor)
Simple, O(log N) convergence
Requires hierarchy maintenance
May not adapt well
Miss cross-boundary optimization

12. Ripple (Unstructured) Clustering
Ripple (Unstructured) Clustering
Define linear order among servers
While cluster improvable
Merge with smaller-cost L/R neighbor
Adaptive merging
Conflicts possible
A BC, ABC
Randomized tie-breaking to resolve
Many race conditions (we love it )

13. Ripple Example: Merging Without Conflicts
Ripple Example: Merging Without Conflicts
Propose merge
High cost, improvable
Low cost
Accept proposal

14. Example Ripple Conflict Resolution ABC
Example Ripple Conflict Resolution ABC
Propose
Propose
Accept

15. Ripple’s Properties Near-Optimal Cost Convergence Locality
Ripple’s Properties
Near-Optimal Cost
α-approximation of the optimal cost
Convergence
Communication quiescence + stability of assignment
N rounds in the worst case (despite coin-tossing)
Much faster in practice
Locality
For isolated load peaks, final clusters are at most twice as large as minimum required to obtain cost

16. Sensitivity to Required Approximation: Cost
Sensitivity to Required Approximation: Cost
Urban WMN
64 servers (grid)
Internet gateways
12800 users
Mixed distribution (50%uniform / % peaky)
2-approximation algorithm applied within each cluster
Nearest Server
Theoretical Worst-Case Bound
Tree
Ripple
Tree and Ripple outperform NS
Beyond upper bound
Ripple s better
α =2(1+ε)

17. Sensitivity to Required Approximation: Locality
Sensitivity to Required Approximation: Locality
Urban WMN
64 servers
Internet gateways
12800 users
Mixed distribution (50%uniform / % peaky)
Ripple: max cluster size
Most clusters built by Ripple are smaller
Ripple: avg cluster size

18. Scalability with Network Size: Cost
Scalability with Network Size: Cost
Urban WMN
64 to 1024 servers
12800 to users
Nearest Server
Tree
Ripple

19. Scalability with Network Size: Locality
Scalability with Network Size: Locality
Urban WMN
64 to 1024 servers
12800 to users
Tree
Ripple

20. Summary LD Balancing: novel optimization problem
Summary
LD Balancing: novel optimization problem
Distributed workload-sensitive solutions
Tree and Ripple algorithms
Ripple is more complex but performs better
No infrastructure
Scales better in practice
Achieves lower costs in practice

21. Thank you