1. Mesh Network Design Backbone network design goals:
Direct path between source and destination.
Well-utilized components
Use high speed lines to achieve economy of scale.
These goals are self-contradictory.
2/19/2019
C. Edward Chow

2. Examples of Bad Design Too Many Direct Links; Nodes with High Degree
45 node network with cost=$264,411/month
2/19/2019
C. Edward Chow

3. Design with Only High Speed Links
Warning sign: high average number of hops
2/19/2019
C. Edward Chow

4. 2-Level Design ($96,777)
Pick heavy traffic nodes as interior nodes of the tree.
2/19/2019
C. Edward Chow

5. More Reliable Design
Instead of tree, interior nodes form a 2-connected graph.
2/19/2019
C. Edward Chow

6. A Different Interior Topology
Reduce cost from $112,587$108,724
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C. Edward Chow

7. Add More Backbone Nodes
$103,107 cost reduced.
2/19/2019
C. Edward Chow

8. Even Lower Cost Design
$101,806
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C. Edward Chow

9. Algorithm Complexity and Design Space Size
Even if a subset of designs can be identified we are still dealing with big design space.
Here the number in D is based on 2 c(45,2)
2/19/2019
C. Edward Chow

10. Mentor Algorithm [KKG91]
Assume single link type with capacity C.
Choose backbone sites. (Also called Threshold Cluster Algorithm)
Calculate the normalized weight NW(Ni)=W(Ni)/C
Choose sites with NW(Ni) > WPARM (threshold)
Group end sites around a backbone site, x, based on Cost(x, Ni)/MAXCOST < RPARM. Where MAXCOST=Max i,j Cost(Ni, Nj)
If there are sites not covered in groups, compute merit(n)=1/2*(MaxDistCtr-distCtrn)/MaxDistCtr /2*(Weightn/WeightMax) Here and Center of Mass (xctr, yctr) defined by
Sort the merit functions. The node with largest merit get picked as backbone node. Group end node around it. Repeat until all nodes are covered in groups.
2/19/2019
C. Edward Chow

11. Mid Stage of Threshold Cluster Algorithm
Big Squares are Backbone nodes.
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C. Edward Chow

12. Final Stage of Threshold Clustering
Based on merit(), three backbone nodes are picked.
2/19/2019
C. Edward Chow

13. Mentor Algorithm Steps 2-3
Pick median node (root node of the network) with smallest Moment():
Build a restricted Prim-Dijkstra tree rooted at median. Here only backbone nodes can be the interior nodes of the tree.
Sequencing Node Pair: Prepare adding additional direct links to the tree.
Use the tree to list node pair in “sequence” The node pair with longer path will list first
Choose home node H for each node pair (Ni,Nj) (H and Nx are intermediate nodes along the path) that satisfies Cost(Ni, H)+Cost(H,Nj)<= Cost(Ni, Nx)+Cost(Nx,Nj).
2/19/2019
C. Edward Chow

14. Restricted Prim-Dijkstra Tree
Note that there is an end node that violate the constraint.
2/19/2019
C. Edward Chow

15. Sequencing Node Pairs
2/19/2019
C. Edward Chow

16. Mentor Algorithm Step 5 Decide which node pairs deserve direct links.
Start with the top node pair (N1,N2) in the sequence.
Calculate the utilization u=Traf(N1,N2)/(n*C) where n=ceil(Traf(N1,N2)/C).
If u>utilmin, add direct link between N1 and N2.
If u< utilmin, add Traf(N1,N2) to Traf(N1,H) and Traf(H,N2). Here H is the home of (N1,N2).
Remove (N1,N2) from the sequence and repeat Step 5 again until all node pairs are processed.
2/19/2019
C. Edward Chow

17. Complexity of Mentor Algorithm
The three basic steps: backbone selection, tree building, and direct link addition are all O(n2).
It can be executed pretty fast.
Typically we will generate a set of designs based on the same threshold parameter, e.g., different a in the restricted Prim-Dijkstra tree, or different node pair sequence (note that the sequence are not unique).
We then pick the best design from the set.
2/19/2019
C. Edward Chow

18. Example of Mentor Algorithm Result
15 sites, 5 backbone nodes
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C. Edward Chow

19. Mentor Algorithm Design 2
$221,590, same 5 backbone nodes, with lower utilmin=0.7
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C. Edward Chow

20. Mentor Algorithm Design 3
Same 5 backbone nodes but with different tree. $209,220.
2/19/2019
C. Edward Chow

21. Cost of Designs vs. a and utilmin
A=0.1 and 1-utilmin=0.1 is the best value.
2/19/2019
C. Edward Chow

22. Cost vs. Size of Backbone
2/19/2019
C. Edward Chow