Mesh Network Design

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
Examples of Bad DesignToo Many Direct Links
Nodes with High Degree

• 45 node network with cost264,411/month

3
Design with Only High Speed Links

• Warning sign high average number of hops

4
2-Level Design (96,777)

• Pick heavy traffic nodes as interior nodes of
  the tree.

5
More Reliable Design

• Instead of tree, interior nodes form a
  2-connected graph
• 2-connected at least two edges must be removed
  to make the graph disconnected

6
Even Lower Cost Design

• 101,806

7

• Fact
• For most designs, there is no known mathematics
  that can prove that they are optimal.

8
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)

9
Design Alternatives

• Fact
• To be able to have confidence in a design, it is
  necessary to have created hundreds of alternate
  designs that examine the alternatives. In other
  words, a given design looks good only if you have
  looked at lots of uglier alternatives.

10
Routing in Backbone Design

• Mesh network in backbone versus tree in access
  network
• Capacity (bi-directional)
• 10, min. hop routing
• 6, AH A-E-F-G-H ED E-A-B-C-D
• 4 dividing AH flow to 1 (ABCDH) and 3 (AEFGH)
  (bifurcated routing)
• Routing strategies
• 1 route vs. multiple routes
• Fixed vs. dynamic routing
• Minimum hop arbitrary routing
• Bifurcated vs. nonbifurcated routing

X flow
1
A
B
C
D
4
1
E
F
G
H
11
Mentor Algorithm (mesh network topological
optimization and routing)

• Assume single link type with capacity C.
• Choose backbone sites. (Also called Threshold
  Cluster Algorithm)
• Calculate the normalized weight NW(Ni)W(Ni)/C
  (W(Ni)sum in and out traffic)
• Choose sites with NW(Ni) gt WPARM (threshold)
• Group end sites around a backbone site, x, based
  onCost(x, Ni)/MAXCOST lt RPARM where MAXCOSTMax
  i,j Cost(Ni, Nj)
• If there are sites not covered in groups, compute
  merit(n)1/2(MaxDistCtr-distCtrn)/MaxDistCtr
  1/2(Weightn/WeightMax)Here
  andCenter of Mass (xctr, yctr) defined by

12
Mentor Algorithm (cont.)

• xn and yn are some coordinates
• Sort the merit functions. The node with largest
  merit get picked asbackbone node. Group end
  node around it. Repeat until all nodes are
  covered in groups.

13
Mid Stage of Threshold Cluster Algorithm

• Big Squares are Backbone nodes.

14
Final Stage of Threshold Clustering

• Based on merit(), three backbone nodes are picked.

15
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 sequenceThe
  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)lt Cost(Ni,
  Nx)Cost(Nx,Nj).

16
Restricted Prim-Dijkstra Tree

• Note that there is an end node that violate the
  constraint.

17
Sequencing Node Pairs
18
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 uTraf(N1,N2)/(nC)wher
  e nceil(Traf(N1,N2)/C).
• If ugtutilmin, add direct link between N1 and N2.
• If ult 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.

19
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.

20
Example of Mentor Algorithm Result

• 15 sites, 5 backbone nodes

21
Mentor Algorithm Design 2

• 221,590, same 5 backbone nodes, with lower
  utilmin0.7

22
Mentor Algorithm Design 3

• Same 5 backbone nodes but with different tree.
  209,220.

23
Cost of Designs vs. a and utilmin

• a 0.1 and 1-utilmin0.1 is the best value.

24
Cost vs. Size of Backbone