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

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

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

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

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

A Different Interior Topology Reduce cost from $112,587$108,724 2/19/2019 C. Edward Chow

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

Even Lower Cost Design $101,806 2/19/2019 C. Edward Chow

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

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 + 1/2*(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

Mid Stage of Threshold Cluster Algorithm Big Squares are Backbone nodes. 2/19/2019 C. Edward Chow

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

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

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

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

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

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

Example of Mentor Algorithm Result 15 sites, 5 backbone nodes 2/19/2019 C. Edward Chow

Mentor Algorithm Design 2 $221,590, same 5 backbone nodes, with lower utilmin=0.7 2/19/2019 C. Edward Chow

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

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

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