1. 1 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 3 Warsaw University of Technology, Poland & Lund University, Sweden October 2007 Routing, Flow, and Capacity Design in Communication and Computer Networks Chapter 6: Location and Topological Design

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

3. 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. 4 NLD: Formulation

5. 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. 6 Add Heuristic: the algorithm  Complexity: O(NM 2 ), N--number of areas, M--number of locations

7. 7 Add Heuristic: example  6 areas, 4 locations  connectivity cost 12 3 4 5 6

8. 8 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 design access node locations and core node locations are different: IP/MPLS IP

9. 9 One-level Formulation

10. 10 Two-level Formulation

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

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

13. 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. 14 Design with Budget Constraint: optimal network problem  access/core locations given  link cost  capital cost (installation) must under budget  maintenance/opera tional (capacity dependent) cost to be minimized  enforce path diversity?

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

16. 16 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) X

17. 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. 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. 19 Link-Path Formulation (cont.d)

20. 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. 21 REF: Node-Link Formulation II

22. 22 Node-Link Formulation

23. 23 Node-Link Formulation

24. 24 Node-Link Formulation