1. TCOM 540/11 TCOM 540 Session 6

2. TCOM 540/12 Agenda Review Session 4 and 5 assignments Multicenter local access design

3. TCOM 540/13 Another Definition A Forest, F = (V,E) is a simple graph without cycles –Note it doesn’t say connected

4. TCOM 540/14 Multicenter Local Access (MCLA) Problem Given –A set of backbone sites (B 0, …, B m ) = B –A set of access nodes (N 1, …, N n ) = N –A set of weights (w 1, …, w n ) for each access node –A cost matrix Cost(i,j) giving the costs between each backbone/access pair of sites

5. TCOM 540/15 Multicenter Local Access (MCLA) Problem (2) MCLA is to find a set of trees T 1, …, T k such that –Exactly one backbone site belongs to each tree –  Ni  Tj w i < W –  Trees  L  Links Cost(end L 1, endL 2 ) is minimum

6. TCOM 540/16 Example X Y Z A B D C 3 backbone nodes 17 access locations

7. TCOM 540/17 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  ( ) 2 17-k partitions ….. Computationally very large … 17 k k = 0,…, 17

8. TCOM 540/18 A Simple Approach … Use nearest neighbor approach –For each backbone node B, let S B be the set of access nodes that are closer to B than any other backbone node –Run Esau-Williams on each S B –Call this Nearest-Neighbor Esau-Williams (NNEW)

9. TCOM 540/19 … 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

10. TCOM 540/110 An Example of How NNEW Fails 2 1 10 6 9 7 5 4 3 8 Node 8 is closer to 1 than 2 But it’s cheaper to home it to 2 via 9 Lesson: Locations of other access nodes cannot be ignored!

11. TCOM 540/111 Multicenter Esau-Williams (MCEW) Developed by Kerschenbaum and Chou (1974) Changes the tradeoff function

12. TCOM 540/112 MCEW (2) EW Tradeoff function is Tr() where Tr(N i ) = min j [Cost(N i,N j )] –Cost (Comp(N i ),N 0 ) Computes cost of linking to neighbor vs. cost of going to center MCEW Tradeoff function is Tr(N i ) = min j Cost(N i,N j ) – dist(Comp(N i ), Center(N j ))

13. TCOM 540/113 MCEW (3) Initially, set Center(N i ) to be closest center If merge N i with N j, update Center(N i ) = Center(N j ) Note: Tradeoff function merges cost and distance functions

14. TCOM 540/114 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

15. TCOM 540/115 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

16. TCOM 540/116 More Highly-Connected Networks Best topology is not limited to a tree design –E.g., Four sites, full-duplex 64k lines, with traffic matrix: From/ToABCD A32 B C D

17. TCOM 540/117 Mesh Example AB CD 32

18. TCOM 540/118 Example – Tree Design AB CD 64 Requires 6 x 64kbps links at 50% utilization

19. TCOM 540/119 Example – Ring Design AB CD 32 Requires 4 x 64 kbps links

20. TCOM 540/120 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

21. TCOM 540/121 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 ….

22. TCOM 540/122 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

23. TCOM 540/123 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

24. TCOM 540/124 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

25. TCOM 540/125 Two Indicators of Possible Problems (2) High average number of hops –Hops act as traffic magnifiers –Introduce latency, reliability issues

26. TCOM 540/126 Routing Considerations Routing is generally irrelevant for access designs Can be important for backbone (mesh) designs Many algorithms

27. TCOM 540/127 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

28. TCOM 540/128 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

29. TCOM 540/129 Assignment and Schedule (2) No class following week (March 9) TCOM 541 starts following week