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TCOM 540

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  1. TCOM 540 Session 5 TCOM 540/1

  2. Agenda • Quiz • Review Session 3 assignments • Access and backbone design TCOM 540/1

  3. Access and Backbone • We already encountered access and backbone in the first session • To over-simplify, access lines provide local connectivity, backbone provides long-distance transport • Balance between access and backbone costs can vary widely TCOM 540/1

  4. Access and Backbone (2) Backbone Access TCOM 540/1

  5. Access and Backbone (3) IXC1 Backbone IXC1 POP LEC Central Office IXC2 Backbone Access lines to IXCs IXC2 POP Local Loops To other LEC COs TCOM 540/1

  6. Local Access Costs Are Significant • Relative cost of local access has been increasing Source: Bureau of Labor Statistics TCOM 540/1

  7. Local Access Costs Are Significant (2) • Situation regarding dedicated local access is less clear • Accurate information regarding real prices paid for dedicated access circuits is not easy to find • Probably has been some decrease, at least in areas where there is local access competition TCOM 540/1

  8. Local Access Costs Are Significant (3) • The Telecommunications Reform Act of 1996 was supposed (among other things) to foster local competition • Appears to have been relatively unsuccessful • Competitive Local Access Carriers (CLECs) have been decimated by collapse of high-tech stocks • Relatively little facilities-based local competition (< 5% of market) TCOM 540/1

  9. Local Access Costs Are Significant (4) • Appears that whatever competition there is for at least residential local access (high speed) is coming from satellite and cable, not CLECs • Legislative action – Tauzin-Dingell bill? TCOM 540/1

  10. Local Access Design Example Traffic (symmetric) Costs (symmetric) TCOM 540/1

  11. Local Access Design Example (2) • Use some nodes as concentrators 6 6 6 1526 2 2 2 1225 1327 $1629 1225 7 7 7 $2112 $1929 1929 1629 1 1 1 5 5 5 667 $667 667 $1328 1328 1328 4 4 4 $1985 1985 1483 3 3 3 9650 8660 7659 (OPTIMAL) TCOM 540/1

  12. Local Access Design Example (3) • If traffic grows by 50%, links (1,4) and (1,7) must be doubled 6 6 2 1327 2 1225 1327 7 1929 7 1629 IMPROVEMENT 3258 1 5 1 667 5 1328 667 2656 4 4 1985 1483 3 8865 (OPTIMAL) 3 10616 TCOM 540/1

  13. Frame Relay (FR) • Frame Relay Permanent Virtual Circuits (PVCs) use concepts of Committed Information Rate (CIR) and Port Speed • Charges for • Access • Port (connection to network) • CIR of PVC – does not vary with distance TCOM 540/1

  14. Asynchronous Transfer Mode (ATM) • ATM uses similar concepts to FR • Constant Bit Rate (CBR) • Variable Bit Rate non-real-time (VBR-nrt) • Variable Bit Rate real-time (VBR-rt) • Available Bit Rate (ABR) • Unspecified Bit Rate (UBR) TCOM 540/1

  15. ATM Definitions Constant Bit Rate (CBR) - fixed bit rate in which bits are sent in a steady stream. A CBR is useful for applications requiring small but near constant transmission, for example, remote-site monitoring. Variable Bit Rate (VBR) - while overall transmission capacity (bits per second) is guaranteed, the rate at any given second may not equal the stated capacity. A VBR of 28 Kb/s, for example, may have periods where the transmission rate ranges from 23 to 33 Kb/s. VBR(rt) means a variable bit rate in real time transmission; VBR(nrt) means a variable bit rate transmission in near-real-time conditions. Both are used in voice and videoconferencing, where a quality channel is reserved but over which data does not flow evenly. Unspecified Bit Rate (UBR) - a transmission service which does not guarantee a fixed transmission capacity. Any application that can tolerate delays is ideally satisfied by an UBR. Source: BCE Teleglobe TCOM 540/1

  16. ATM Definitions (2) Available Bit Rate (ABR) -The bit rate left after the predictive and guaranteed service traffic (CBR/VBR) is served. In essence, it is simply a fair share of the remaining bandwidth amongst the VPs and VCs that have asked for this service. Source: cell-relay.indiana.edu TCOM 540/1

  17. Rules of Thumb • Cannot choose between a leased line and a FR/ATM design until both are done and costs compared • Availability of FR and ATM just complicates life … • Note that leased lines may have security advantages TCOM 540/1

  18. Rules of Thumb (2) • If sites vary widely in size (traffic originated/terminated), choose the bigger sites as aggregation points • Define weight of a node as sum of all traffic flowing into and out of it • Design problem then has two parts • Access – gets traffic from small sites to backbone • Backbone – carries traffic between backbone nodes • Which comes first?? TCOM 540/1

  19. Traffic Scale • Depends on relationship of node size to smallest desired link size • Smallest link size determined by factors such as packet size/delay • Traffic from access node much smaller than smallest link we wish to use - Create access trees to group sites efficiently - Capacitated spanning trees TCOM 540/1

  20. Traffic Scale (2) • Traffic from access node comparable to smallest link - Low speed link to hub vs. concentrator part way to hub - Concentrator placement problem • Traffic from access node significantly larger than smallest link - Multiple lower speed links vs. single higher speed link TCOM 540/1

  21. One Speed, One Center • Example problem with 20 nodes – one of which is the hub • 1200 bps/node, 9600 bps links, utilization 50% • What algorithm to use? TCOM 540/1

  22. One Speed, One Center (2) • Star design costs $26,358 • Link utilization 12.5% • MST cost $18,730 • Uses multiple (up to 4) links on some legs • Prim-Dijkstra tree cost $15,930 • Using a = 0.3 • Hundreds of designs tested TCOM 540/1

  23. One Speed, One Center (3) • For n nodes, there are nn-2 different spanning trees • 2018 = 2.621 * 1023 • This is a rather large number … • And partitioning does not help much • Groups of 4 can be done in 2.546 * 1010 ways • Not to mention groups of 3 etc., etc., etc. TCOM 540/1

  24. Esau-Williams Algorithm • Esau-Williams creates a Capacitated Minimum Spanning Tree (CMST) • Given a central node N0 and a set of other nodes (N1, N2, … Nn), and a set of weights (w1, …, wn) for each node, the capacity of a link W, and a cost matrix Cost(i,j) find a set of trees T1, …, Tk such that each Ni belongs to exactly one Tj and each Tj contains N0 and Si eTj wi < W StreesS l eLinks Cost(end1l, end2l) is a minimum TCOM 540/1

  25. Esau-Williams Algorithm (2) • Central concept is tradeoff function • Build “good” trees • Each tree starts off as one node • Component (graph theory meaning) Comp(Ni) • 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 TCOM 540/1

  26. Esau-Williams Algorithm (2) • Negative value of Tr means it is preferable to link to neighbor tree rather than running a link to the center • Must check that the design is feasible – i.e., does not exceed link capacity: W(Comp(Ni)) +W(Comp(Nj)) < W • Algorithm limitation – often desirable to increase link capacities in real life TCOM 540/1

  27. Esau-Williams Algorithm (3) N4 N2 N3 N1 Scanning node N3: 1. Examine costs of these links 2. Compare with cost of this link N0 TCOM 540/1

  28. Heaps • Code for implementing Esau-Williams in Cahn uses heaps (not essential, but interesting) • A heap is a special type of binary tree • Binary tree: each node has at most 3 edges • Parent • Left child • Right child TCOM 540/1

  29. Heaps (2) • Heap • Root at level 0 – smallest element • Any node has a value no larger than either of its children • Heaps are not unique TCOM 540/1

  30. Heaps (3) -1000 -700 -400 -200 -100 0 TCOM 540/1

  31. Heaps (3) -1000 -1000 -700 -400 -700 -100 -200 -100 0 -200 -400 0 TCOM 540/1

  32. Esau-Williams Implementation • Uses a heap for each node nHeap(i) and a global heap tHeap • Heap for a node has tradeoff values with respect to neighbors • Subject to feasibility TCOM 540/1

  33. E-W Implementation (2) • Let’s say top of heap for a node is –1000 -1000 -700 -400 -200 -100 inf TCOM 540/1

  34. E-W Implementation (3) • Say this is infeasible – change value to inf inf But now this is not a heap any more - “bubble down” offending node -700 -400 -200 -100 inf TCOM 540/1

  35. E-W Implementation (4) • Swap with best child -700 -700 inf -400 -200 -400 -200 -100 inf inf -100 inf TCOM 540/1

  36. E-W Implementation (5) • Heaps are efficient • Number of levels in the heap grows as the order of log2(n) • Where n is total number of elements in the heap • On average, each level is twice the size of the level above TCOM 540/1

  37. E-W Implementation (6) • Algorithm • Top of global heap is node n1, which has the best tradeoff • Go to heap of N1 and find partner n2 which appears to have best tradeoff • Remove n2 from node heap • Find components of n1 and n2 • Tricky bit: When we start this loop, all tradeoffs are correct, but we do not update all tradeoffs as we go along • Wait until an n1, n2 pair appears, then check tradeoff • If tradeoff is incorrect, reset and push pair back into heap • If tradeoff is correct, check if merge of components is feasible • If feasible, merge • Update global heap with new n1 tradeoff TCOM 540/1

  38. Creditability of E-W • E-W is heuristic • Guarantees resulting design is feasible • Does not guarantee that design is optimal • Poorer performance as number of sites increases • Works well for both homogenous and inhomogeneous traffic TCOM 540/1

  39. Esau-Williams Failure Rate Four sites per line TCOM 540/1

  40. Sharma’s Algorithm • E-W sometimes introduces crossings • We know the design can be improved if crossings are removed • Sharma’s algorithm builds MSTs in “wedges” from the central node TCOM 540/1

  41. Sharma’s Algorithm (2) • Compute the angle from the central node to each other node • Sort the angles • Move clockwise from node with smallest angle • Create sets of nodes such that adding another node would put Ssetw(node) > W • Start next set with that node TCOM 540/1

  42. Sharma’s Algorithm (3) • Sharma’s algorithm builds Capacitated Minimum Spanning Trees without crossings • So long as no set has more than half the pie (i.e., q > p) • However, Sharma is generally inferior to E-W • Poorer creditability • Higher cost TCOM 540/1

  43. Multiple Link Speeds • In real problems, almost always have a variety of link speeds to choose from • DS0 @ 64kbps • N x DS0 • T1 @1.5 Mbps • T3 @ 45 Mbps • Etc. TCOM 540/1

  44. Multiple Link Speeds (2) • Intuitively, we’d like the access tree to use higher speeds closer to the root, and lower speeds out towards the edges TCOM 540/1

  45. Predecessor Function • A tree T rooted at node Root can be represented uniquely by a predecessor function pred:V V on the set of vertices: • pred(Root) = Root • No other node is its own predecessor • For any node N there is an n>0 such that predn(N) = Root TCOM 540/1

  46. Ancestors • Given a tree T and the associated predecessor function, the ancestors of N are all the nodes N* where predn(N*) = N for some n > 0 TCOM 540/1

  47. Multispeed CMST Definition • Given: • A set of nodes N0, N1, …, Nn • A set of weights (w1, …, wn) for each node • A set of link types L1, L2, …, Lm • Capacities W1, W2, …, Wm • A cost matrix C(i,j,k) for the cost of link type Lk between Ni and Nj TCOM 540/1

  48. Multispeed CMST Definition (2) • Then the multispeed CMST problem is to find the tree rooted at N0 with link assignments such that Sancestors(N) w(i) < WLink(N, pred(N)) And SLinksc(end1L, end2L, typeL) is minimized TCOM 540/1

  49. MSLA Algorithm for Multispeed CMSTs • Assign each node n the smallest link l to connect it to root. Compute spare_capacity(n) = Wl – wn • Create tradeoff heap for n (similar to E-W) – tradeoffs represent savings by connecting site n to site i rather than to the root Tradeoffn(i) = c(n,i,L) + Upgrade (i, wn) – c(n,0,L) The function Upgrade() computes the cost of adding wn units to the links that connect i and 0 by following back the predecessors • Add edges as long as tradeoffs are less than or equal to 0 TCOM 540/1

  50. Session 5 Assignment • Read Cahn, Chapter 7 • Do Exercises 5.3 and 6.1 TCOM 540/1