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TCOM 541

TCOM 541. Session 2. Mesh Network Design. Algorithms for access are not suitable for backbone design Access designs generally are trees – sites connect to center Diverse access (redundancy) is another question, and only needed for special situations

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TCOM 541

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  1. TCOM 541 Session 2

  2. Mesh Network Design • Algorithms for access are not suitable for backbone design • Access designs generally are trees – sites connect to center • Diverse access (redundancy) is another question, and only needed for special situations • Backbone designs require many-many connectivity

  3. MENTOR Algorithm • “High quality, low complexity” algorithm • Originally developed for time division multiplexing • Works with other technologies

  4. MENTOR Algorithm (2) • Assume initially only a single link type of capacity C • Divide sites into backbone sites and end sites • Backbone sites are aggregation points • Several algorithms to do this • Threshold clustering is used

  5. Threshold Clustering • Weight of a site is sum of all traffic into and out of the site • Normalized weight of site i is NW(i) = W(i)/C • Sites with NW(i) > W are made into backbone sites • Where W is a parameter

  6. Threshold Clustering (2) • All sites that do not meet the weight criterion and are close to a backbone site are made into end sites • “Close” is defined as when the link cost from the end site e to the backbone site is less than a predefined fraction of the maximum link cost MAXCOST = maxi,jcost(Ni,Nj): cost(e,Ni) < MAXCOST*RPARM

  7. Threshold Clustering (3) • If all sites that pass the weight limit as backbone sites have been chosen and there are still edge sites “too far” from any backbone site, we assign a “merit” to each site • Assign coordinates to each site (e.g., V&H) • Compute center of gravity of sites

  8. Center of Gravity (CG) • Defined as (xctr, yctr) where xctr = SnxnWn/SWn yctr = SnynWn/SWn Note: These coordinates need not correspond to any actual site

  9. Distances to CG • Define dcn = [(xn-xctr)2 + (yn-yctr)2]0.5 maxdc = max(dcn) maxW = max(Wn) • Then meritn= 0.5(maxdc–dcn)/maxdc + 0.5(Wn/maxW) • That is, “merit” gives equal value to a node’s proximity to the center and to its weight

  10. MENTOR Algorithm (3) • From among remaining nodes, choose the one with the highest merit as a backbone node • Continue until all nodes are either backbone nodes or within RPARM*MAXCOST of a backbone node • Select backbone node with smallest moment to be center • Moment(n) = Sdist(n,n*)Wn* • Construct a Prim-Dijkstra tree, parameter a

  11. MENTOR Example Radius = RPARM*MAXCOST C*G Edge node Backbone node

  12. MENTOR Example (2) Radius = RPARM*MAXCOST C*G Edge node Backbone node

  13. MENTOR Example (3) Radius = RPARM*MAXCOST C*G Edge node Backbone node

  14. MENTOR Example (4) Radius = RPARM*MAXCOST C*G Edge node Backbone node

  15. MENTOR Example (5) Radius = RPARM*MAXCOST C*G Edge node Backbone node

  16. Need for Improvement • As we know, tree designs have several drawbacks, especially for large networks • Lack of redundancy increases probability of failure • Chain-like network (low a) • Aggregation of traffic in “central” links raises costs • Large average hops in large networks • Star-like network network (high a) • May have low link utilization

  17. Refining the Design in MENTOR • We introduce the concepts of sequencing and homing to add links so as to make a better design by adding direct links where the traffic justifies it • Use the Prim-Dijkstra tree to define a sequencing of the sites • A sequencing is an outside-in ordering • Do not sequence the pair (N1,N2) until all pairs (N1*,N2*) have been sequenced where N1 and N2 lie on the path between N1* and N2* • Roughly, the longest paths get sequenced first

  18. Example of Sequencing Sequence AE AF BE BF CE CF DA DB AC BC … DF F A C 3 hops D E B 2 hops 1 hop

  19. Comments on Sequences • Sequences are not unique • Different (valid) sequences do not influence the design greatly

  20. Homing • For each pair of nodes (N1, N2) that are not adjacent we select a home • If 2 hops separate N1 and N2, the home is the node between them • If they are more than 2 hops apart there are multiple candidates for their home

  21. Homing (2) N4 N1 N3 N2 Candidate for home (N1,N2) Candidate for home (N1,N2) Choose N3 as home(N1,N2) if: Cost(N1,N3) + Cost(N3,N2) < Cost(N1,N4) + Cost(N4,N2) Otherwise choose N4

  22. Last Step • Consider each node pair only once, add a link if it will carry enough traffic to justify itself • Consider the traffic matrix T(Ni,Nj) • Assume it is symmetric • Recall that MENTOR was developed to design TDM networks, and muxes are bi-directional (usually)

  23. Last Step (2) • For each pair (N1,N2), execute the following algorithm: • If capacity of a link is C, compute • n = ceil[T(N1,N2)/C] • Compute utilization • u = T(N1,N2)/(n*C) • Add link if u > umin, otherwise move traffic 1 hop through the network • I.e., add T(N1,N2) to both T(N1,H) and T(H,N2) • And do same for T(N2,N1) • Note – there is a special case when (N1,N2) belongs to the original tree • In this case just add the link (N1,N2) to the design

  24. Comments • The link-adding algorithm aggregates traffic to justify links between nodes that are multiple hops apart • If traffic between N1 and N2 cannot justify a direct link, it is routed through their home node H • Eventually, in large networks, enough traffic is aggregated to justify a direct link

  25. Comments (2) • Performance of MENTOR is governed by utilization parameter umin and the Prim-Dijkstra tree-building parameter a • How easy it is to add new links is controlled by umin • The shape of the initial tree is controlled by a • High a will build a star-like tree – then links will be added only between site pairs that have enough traffic without help from other nodes • Low a will build a more chain-like tree, so there will be more aggregation of traffic and likely addition of links

  26. Performance of MENTOR • Low-cost algorithm • Three main steps • Backbone selection • Tree building • Link addition • All of O(n2) • Possible to re-run many times, varying parameters

  27. MENTOR Example Based on mux1.inp on Cahn’s FTP site 15 sites, 60 256 kbps circuits 13 6 2 7 15 14 10 9 1 5 12 4 8 11 3

  28. Initial Choice of Backbone Nodes (5) 13 6 2 7 15 Backbone node Backbone node 14 10 9 1 Backbone node 5 12 Backbone node 4 8 Backbone node 11 3

  29. Initial Design a = 0 Cost = $269,785/month 13 6 2 7 15 5 x T1 2 x T1 14 10 9 1 5 5 x T1 12 5 x T1 4 8 11 3

  30. Review of Initial Design • Backbone links have multiple (5) T1 links • Probably not a good thing • Design Principle: • If a design has multiple parallel high-speed links there is usually a better, meshier design • Lower cost, greater diversity (= reliability) • Note this is not mathematically provable

  31. Revised Design umin = 0.7 Cost = $221,590 13 6 2 7 15 3 1 2 14 10 9 1 1 2 5 12 1 4 8 1 11 3

  32. “Best” 5-Node Backbone Design a = 0.1 umin = 0.9 Cost = 209,220 13 6 2 7 15 2 2 14 10 9 1 2 5 2 12 1 4 1 8 11 3

  33. Comments • Note that we produced multiple designs by varying some parameters and picking the best • Of course, there is no guarantee that this design really is “best” • In fact, changing number of backbone nodes yields much better designs • 13-node backbone yields design costing only $191,395 • 12-node backbone costs $198,975

  34. Routing • Now we have designed a good network, we consider how the traffic will actually flow across it • This introduces a whole new class of problems that center on the performance of the routing algorithms

  35. Feasibility Considerations • For any pair of nodes N0 and N1, define a route by (N0, N1, h,n) Where n = 0 if h is adjacent to N0 and n = 1 if h is adjacent to N1 • If N0 and N1 are adjacent, we have a direct route • Else the route is the link (Nn,h) and the route (N1-n,h,n*,n*) • Continue until the full route is established

  36. Feasibility Considerations • This process establishes a feasible routing pattern for the network • However, the muxes may not be smart enough to find this pattern • As an example, consider single-route, minimum-hop (SRMH) routing

  37. An SRMH Disaster A H • Assume MENTOR adds link BF to carry traffic from B to F, G, H, I – but not traffic from F to ABC • SRMH insists on carrying all traffic from A, B, C to F, G, H, I – result is overload on BF B G F C E I D

  38. Feasibility and Routing • In reality, few network-loading algorithms are as bad as SRMH • However, network-loading algorithms do add to the design constraints • In particular, minimum-hop routing algorithms are fragile with respect to network capacity changes • Effective algorithms for redesign are not available

  39. A More Realistic Loading Algorithm • Flow-Sensitive, Minimum-Hop (FSMH) loader loads traffic onto a minimum-hop path, subject to using only links with enough free capacity to carry it • Allows overflow onto longer paths • If no path exists, traffic is blocked • However, there is no guarantee that FSMH will do better than SRMH!

  40. FSMH Failure Example A B Each link has capacity 1 C D Traffic: SRMH will block the second AB traffic and load 4 out of 5 requirements FSMH will load load both AB requirements, but block all the rest Note: order of loading traffic is significant!

  41. Comments on FSMH • In the earlier example (15 sites), FSMH fails on the best designs • 13-node, $191k design blocks 3.3% of traffic • 12-node, $199k design blocks 6.7% of traffic • Best design where FSMH does not block is 11-node, $201k

  42. Approaches • We cannot guarantee that a highly-optimized network design will work with a given routing algorithm • Approaches • Test the loading algorithm against best designs • Routing takes more computation than design Raises complexity to between O(n3) and O(n4) • Limit maximum link utilization to <100% • Also increases reliability, allows for growth

  43. Router Network Design • Common routing algorithm for IP is OSPF (Open Shortest Path First) • Implicit problem is design for minimum distance • Single-route, minimum distance loader (SRMD) • Computes single shortest path between site pairs • If traffic saturates the route, it’s discarded • Designer chooses link lengths appropriately

  44. SRMD Characteristics • Traffic not forced onto illogical paths if link lengths are chosen properly • Problems can still arise • Not dynamic • Cannot split traffic between different routes

  45. OSPF Example This link intended to carry traffic between A and H, and B to H but not traffic between A and G A 395 H 90 100 B 100 G 100 F 100 C E I 100 D A-H traffic will take 1-hop path length 395 B-H traffic will take 2-hop path length 485 A-G traffic will take 5-hop path length 490

  46. Important Difference • Mux networks are designed for high utilization • Router networks are not designed for high utilization • Allows some margin for error by the routing algorithm

  47. Comments • Can encourage the traffic to use the MENTOR routing as we add edges by setting the length of each tree edge to 100, and the length of a direct edge between N1 and N2 to: 100 + 90*hops(N1,N2)

  48. Comments (2) • Any routing algorithm should work for a tree • Problems arise when design becomes more highly meshed • Can manipulate solution by • Increasing length of overloaded links • Shortening under-utilized links • Adding or deleting capacity

  49. Homework Assignment • Cahn Exercises 8.2, 8.6 • Read Cahn Chapter 9

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