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Slides by Yong Liu 1 , Deep Medhi 2 , and Michał Pióro 3 1 Polytechnic University, New York, USA

Routing, Flow, and Capacity Design in Communication and Computer Networks Chapter 6: Location and Topological Design. Slides by Yong Liu 1 , Deep Medhi 2 , and Michał Pióro 3 1 Polytechnic University, New York, USA 2 University of Missouri-Kansas City, USA

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Slides by Yong Liu 1 , Deep Medhi 2 , and Michał Pióro 3 1 Polytechnic University, New York, USA

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  1. Routing, Flow, and Capacity Design in Communication and Computer NetworksChapter 6: Location and Topological Design Slides by Yong Liu1, Deep Medhi2, and Michał Pióro3 1Polytechnic University, New York, USA 2University of Missouri-Kansas City, USA 3Warsaw University of Technology, Poland & Lund University, Sweden October 2007

  2. Outline • Topological Design Modeling • location • connectivity • demand/capacity allocation • Solution • heuristic algorithms

  3. Node Location Problem • connect N areas through M possible locations • one access link per location • maximal connection per location • maximum number of ports per router • cost of open each location • cost of connecting each area to each location • always connect to the cheapest/closest station?

  4. NLD: Formulation

  5. Add Heuristic • Local Search Algorithm • Start with a random location • all sources connect to that location • Iteratively add new locations, one each time • to reduce the opening and connection cost • choose the candidate with largest reduction • Stop if cost reduction is not possible

  6. Add Heuristic: the algorithm • Complexity: O(NM2), N--number of areas, M--number of locations

  7. Add Heuristic: example • 6 areas, 4 locations • connectivity cost 2 1 3 6 5 4

  8. IP MPLS Joint Node Location and Link Connectivity • connectivity cost • from access nodes to core nodes • between core nodes • fully connected core • two models • one-level all nodes same type, each site can be possibly a core node site (same node for access and core): IP routers with different capacities • overlay-underlay designaccess node locations and core node locations are different: IP/MPLS

  9. One-level Formulation

  10. Two-level Formulation

  11. Illustration: Distance-based/Skewed-Distance-based

  12. Non-Fully Connected Core • Non-fully connected in practice • Avoid disconnecting network • Delete core link heuristic

  13. Topological Design • traffic demand has big impact on node and link location • jointly design location/dimesnion/flow • given access/core locations, determine link locations, flow and capacity allocation • given access locations only, determine core locations, link locations, flow and capacity allocation • traffic demand between access nodes, to be realized; pure access nodes cannot transit traffic; pure core nodes don’t generate traffic • cost • link/node opening • Capacity cost access node Core/transit node

  14. Design with Budget Constraint: optimal network problem • access/core locations given • link cost • capital cost (installation) must under budget • maintenance/operational (capacity dependent) cost to be minimized • enforce path diversity?

  15. Optimal Network Problem: extended objective • what if budget too tight? • network cost = capital cost + maintenance cost

  16. X Optimal Network Problem:Heuristic Algorithm • start with all links installed • iteratively remove links, one each iteration • saving from link removal: capital + operational • cost from link removal: • traffic on the removed link have to be rerouted: local rerouting v.s. global rerouting • capacity cost incurred on new paths • Net gain of remove link e • gain(e)=saving(e)-cost(e) • Remove the link maximizing gain(e)

  17. Core Nodes and Links Location • both core nodes and links locations to be determined • new constraints • if a node v not installed, all links attached to v won’t be installed • bound on core node degree • Link-path formulation or node-link formulation

  18. Link-Path Formulation • how to pre-set paths without knowing the locations of core nodes and links? • bad set of candidate paths might lead to expensive or infeasible solutions

  19. Link-Path Formulation (cont.d)

  20. Node-Link Formulation • distinguish access and transit links • directed access links: between access and transit nodes • directed transit links: between transit nodes • use source-based link-flow variable

  21. REF: Node-Link Formulation II

  22. Node-Link Formulation

  23. Node-Link Formulation

  24. Node-Link Formulation

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