1. TCOM 540/11 TCOM 540 Session 5

2. TCOM 540/12 Agenda Quiz Review Session 3 assignments Access and backbone design

3. TCOM 540/13 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

4. TCOM 540/14 Access and Backbone (2) Access Backbone

5. TCOM 540/15 Access and Backbone (3) IXC1 POP IXC2 POP LEC Central Office Local Loops IXC1 Backbone IXC2 Backbone Access lines to IXCs To other LEC COs

6. TCOM 540/16 Local Access Costs Are Significant Relative cost of local access has been increasing Source: Bureau of Labor Statistics

7. TCOM 540/17 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

8. TCOM 540/18 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)

9. TCOM 540/19 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?

10. TCOM 540/110 Local Access Design Example BW 1212000 1311000 149000 1513000 168000 176000 1234567 140019291985132866721121629 240028142168203115261225 34001483204432432714 4400142725512024 540021361689 64001327 7400 Traffic (symmetric)Costs (symmetric)

11. TCOM 540/111 Local Access Design Example (2) Use some nodes as concentrators $1929 $1985 $1328 $667 $2112 $1629 1526 1225 1929 667 1328 1985 1225 1327 1629 1328 1483 667 965086607659 (OPTIMAL) 1 2 7 6 5 4 3 1 2 7 6 5 4 3 1 2 7 6 5 4 3

12. TCOM 540/112 Local Access Design Example (3) If traffic grows by 50%, links (1,4) and (1,7) must be doubled 1225 1327 3258 2656 1483 667 10616 1 2 7 5 4 3 1327 1629 1328 667 8865 (OPTIMAL) 1 2 7 6 5 4 3 6 1929 1985 IMPROVEMENT

13. TCOM 540/113 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

14. TCOM 540/114 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)

15. TCOM 540/115 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

16. TCOM 540/116 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

17. TCOM 540/117 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

18. TCOM 540/118 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??

19. TCOM 540/119 Traffic Scale Depends on relationship of node size to smallest desired link size –Smallest link size determined by factors such as packet size/delay 1.Traffic from access node much smaller than smallest link we wish to use - Create access trees to group sites efficiently - Capacitated spanning trees

20. TCOM 540/120 Traffic Scale (2) 2.Traffic from access node comparable to smallest link - Low speed link to hub vs. concentrator part way to hub - Concentrator placement problem 3.Traffic from access node significantly larger than smallest link - Multiple lower speed links vs. single higher speed link

21. TCOM 540/121 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?

22. TCOM 540/122 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  = 0.3 –Hundreds of designs tested

23. TCOM 540/123 One Speed, One Center (3) For n nodes, there are n n-2 different spanning trees –20 18 = 2.621 * 10 23 –This is a rather large number … –And partitioning does not help much Groups of 4 can be done in 2.546 * 10 10 ways Not to mention groups of 3 etc., etc., etc.

24. TCOM 540/124 Esau-Williams Algorithm Esau-Williams creates a Capacitated Minimum Spanning Tree (CMST) Given a central node N 0 and a set of other nodes (N 1, N 2, … N n ), and a set of weights (w 1, …, w n ) 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 N i belongs to exactly one Tj and each Tj contains N 0 and  i   Tj w i < W  trees  l   Links Cost(end1 l, end2 l ) is a minimum

25. TCOM 540/125 Esau-Williams Algorithm (2) Central concept is tradeoff function Build “good” trees Each tree starts off as one node –Component (graph theory meaning) Comp(N i ) 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

26. TCOM 540/126 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(N i )) +W(Comp(N j )) < W –Algorithm limitation – often desirable to increase link capacities in real life

27. TCOM 540/127 Esau-Williams Algorithm (3) N4 N3 N1 N2 N0 Scanning node N3: 1. Examine costs of these links 2. Compare with cost of this link

28. TCOM 540/128 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

29. TCOM 540/129 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

30. TCOM 540/130 Heaps (3) -100-200 -700-400 -1000 0

31. TCOM 540/131 Heaps (3) -400-200 -700-100 -1000 0-100-200 -700-400 -1000 0

32. TCOM 540/132 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

33. TCOM 540/133 E-W Implementation (2) Let’s say top of heap for a node is –1000 -100-200 -700-400 -1000 inf

34. TCOM 540/134 E-W Implementation (3) Say this is infeasible – change value to inf -100-200 -700-400 inf But now this is not a heap any more - “bubble down” offending node

35. TCOM 540/135 E-W Implementation (4) Swap with best child -100-200 inf-400 -700 inf-100inf -200-400 -700 inf

36. TCOM 540/136 E-W Implementation (5) Heaps are efficient Number of levels in the heap grows as the order of log 2 (n) –Where n is total number of elements in the heap –On average, each level is twice the size of the level above

37. TCOM 540/137 E-W Implementation (6) Algorithm 1.Top of global heap is node n1, which has the best tradeoff 2.Go to heap of N1 and find partner n2 which appears to have best tradeoff 3.Remove n2 from node heap 4.Find components of n1 and n2 5.Tricky bit: When we start this loop, all tradeoffs are correct, but we do not update all tradeoffs as we go along 1.Wait until an n1, n2 pair appears, then check tradeoff 2.If tradeoff is incorrect, reset and push pair back into heap 6.If tradeoff is correct, check if merge of components is feasible 1.If feasible, merge 7.Update global heap with new n1 tradeoff

38. TCOM 540/138 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

39. TCOM 540/139 Esau-Williams Failure Rate Four sites per line

40. TCOM 540/140 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

41. TCOM 540/141 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  set w(node) > W –Start next set with that node

42. TCOM 540/142 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.,  However, Sharma is generally inferior to E- W –Poorer creditability –Higher cost

43. TCOM 540/143 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.

44. TCOM 540/144 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

45. TCOM 540/145 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 pred n (N) = Root

46. TCOM 540/146 Ancestors Given a tree T and the associated predecessor function, the ancestors of N are all the nodes N* where pred n (N*) = N for some n > 0

47. TCOM 540/147 Multispeed CMST Definition Given: –A set of nodes N 0, N 1, …, N n –A set of weights (w 1, …, wn) for each node –A set of link types L 1, L 2, …, L m –Capacities W 1, W 2, …, W m –A cost matrix C(i,j,k) for the cost of link type L k between N i and N j

48. TCOM 540/148 Multispeed CMST Definition (2) Then the multispeed CMST problem is to find the tree rooted at N 0 with link assignments such that  ancestors(N) w(i) < W Link(N, pred(N)) And  Links c(end1 L, end2 L, type L ) is minimized

49. TCOM 540/149 MSLA Algorithm for Multispeed CMSTs 1.Assign each node n the smallest link l to connect it to root. Compute spare_capacity(n) = W l – w n 2.Create tradeoff heap for n (similar to E-W) – tradeoffs represent savings by connecting site n to site i rather than to the root Tradeoff n (i) = c(n,i,L) + Upgrade (i, w n ) – c(n,0,L) The function Upgrade() computes the cost of adding w n units to the links that connect i and 0 by following back the predecessors 3.Add edges as long as tradeoffs are less than or equal to 0

50. TCOM 540/150 Session 5 Assignment Read Cahn, Chapter 7 Do Exercises 5.3 and 6.1