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TCOM 540

TCOM 540. Session 6. Agenda. Review Session 4 and 5 assignments Multicenter local access design. Another Definition. A Forest, F = (V,E) is a simple graph without cycles Note it doesn’t say connected. Multicenter Local Access (MCLA) Problem. Given

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TCOM 540

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  1. TCOM 540 Session 6 TCOM 540/1

  2. Agenda • Review Session 4 and 5 assignments • Multicenter local access design TCOM 540/1

  3. Another Definition • A Forest, F = (V,E) is a simple graph without cycles • Note it doesn’t say connected TCOM 540/1

  4. Multicenter Local Access (MCLA) Problem • Given • A set of backbone sites (B0, …, Bm) = B • A set of access nodes (N1, …, Nn) = N • A set of weights (w1, …, wn) for each access node • A cost matrix Cost(i,j) giving the costs between each backbone/access pair of sites TCOM 540/1

  5. Multicenter Local Access (MCLA) Problem (2) • MCLA is to find a set of trees T1, …, Tk such that • Exactly one backbone site belongs to each tree • SNie Tj wi < W • STreesSL e LinksCost(end L1, endL2) is minimum TCOM 540/1

  6. Example A B Y X C D 3 backbone nodes 17 access locations Z TCOM 540/1

  7. Solve by Enumeration? • Each solution divides the 17 access locations into 3 sets (one to each backbone node) = 3 capacitated MST problems • We can use E-W to solve these! • But there are S() 217-k partitions ….. • Computationally very large … 17 k k = 0,…, 17 TCOM 540/1

  8. A Simple Approach … • Use nearest neighbor approach • For each backbone node B, let SB be the set of access nodes that are closer to B than any other backbone node • Run Esau-Williams on each SB • Call this Nearest-Neighbor Esau-Williams (NNEW) TCOM 540/1

  9. … That is Not Very Good • NNEW algorithm shows a failure rate of 30 to 60% on random problems with 2 or 3 backbone nodes and 10 to 150 total nodes TCOM 540/1

  10. Lesson: Locations of other access nodes cannot be ignored! An Example of How NNEW Fails 6 2 7 1 5 4 10 9 8 3 Node 8 is closer to 1 than 2 But it’s cheaper to home it to 2 via 9 TCOM 540/1

  11. Multicenter Esau-Williams (MCEW) • Developed by Kerschenbaum and Chou (1974) • Changes the tradeoff function TCOM 540/1

  12. MCEW (2) • EW Tradeoff function is Tr() where Tr(Ni) = minj[Cost(Ni,Nj)] –Cost (Comp(Ni),N0) • Computes cost of linking to neighbor vs. cost of going to center • MCEW Tradeoff function is Tr(Ni) = minjCost(Ni,Nj) – dist(Comp(Ni), Center(Nj)) TCOM 540/1

  13. MCEW (3) • Initially, set Center(Ni) to be closest center • If merge Ni with Nj, update Center(Ni) = Center(Nj) • Note: Tradeoff function merges cost and distance functions TCOM 540/1

  14. MCEW (4) • MCEW produces more creditable results than NNEW • Produces a better solution much more often • But cost advantage is surprisingly small • < 1% for large numbers of sites TCOM 540/1

  15. Practical Issues • Real problems often involve additional, sometimes quirky, constraints, such as • Limit on number of nodes in an access tree • Limit on number of hops • Limit on number of connections at a site • Unreliable links or sites TCOM 540/1

  16. More Highly-Connected Networks • Best topology is not limited to a tree design • E.g., Four sites, full-duplex 64k lines, with traffic matrix: TCOM 540/1

  17. Mesh Example 32 A B 32 32 32 32 32 32 D C 32 TCOM 540/1

  18. Example – Tree Design 64 A B 64 64 64 64 64 D C Requires 6 x 64kbps links at 50% utilization TCOM 540/1

  19. Example – Ring Design 32 A B 32 32 32 32 32 32 D C 32 Requires 4 x 64 kbps links TCOM 540/1

  20. Full vs. Partial Mesh • Full mesh requires n(n-1)/2 links • Require n-1 connections at each site, imposes heavily on site equipment • Likely to have many lower-speed links which should be aggregated • Partial mesh generally preferable • Increased number of hops TCOM 540/1

  21. Design Principles • Have direct paths between origin and destination • Have well-utilized (but not overloaded) components • Have efficient high-speed links where possible • Of course, these principles contradict each other …. TCOM 540/1

  22. How to Recognize a Good Design? • For most designs, there is no known math that will prove they are optimal, or even close to optimal • Most real designs will be produced by a computer program • Good algorithms can yield bad designs • And vice-versa TCOM 540/1

  23. How to Recognize a Good Design? (2) • Look for obvious problems • Look for ways of changing a few links and saving costs • Change design parameters (a little) and rerun algorithm TCOM 540/1

  24. Two Indicators of Possible Problems (1) • High average nodal degree • I.e., lots of connections at each node • May indicate over-use of low-speed links • Unless most links are highest capacity available • Or there are stringent hop limitations TCOM 540/1

  25. Two Indicators of Possible Problems (2) • High average number of hops • Hops act as traffic magnifiers • Introduce latency, reliability issues TCOM 540/1

  26. Routing Considerations • Routing is generally irrelevant for access designs • Can be important for backbone (mesh) designs • Many algorithms TCOM 540/1

  27. Some Examples of Routing Algorithms • Open Shortest Path First (OSPF) • Minimum distance routing • Hierarchical (telephony) • Open alternate path when primary is busy (bifurcated) • Systems Network Architecture (SNA) • Static, arbitrary, multiple, bifurcated • Black box – e.g., PVCs • User generally has no information as to physical route used TCOM 540/1

  28. Assignment and Schedule • No homework this week • Next session • TCOM540 papers due (where appropriate) • Interim TCOM540/541 annotated outlines due • Must contain significant amount of information • Finals for TCOM540 • Open book exam, may deal with any topics covered to date TCOM 540/1

  29. Assignment and Schedule (2) • No class following week (March 9) • TCOM 541 starts following week TCOM 540/1

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