1 Chapter 5 Access Network Design

2 Overview nA Backbone network connects major sites. nAccess networks connect “small” sites to the backbone network. nAccess networks are the “ends” and “tails” of networks that connect the smallest sites into the network. nAccess networks only function if they are attached to a backbone.

3 Access Network Example Visit to Grandma nYou live in Scarsdale, NY outside of New York City nGrandma lives in Framingham, MA, outside of Boston nThe trip involves 3 segments: n Travel from Scarsdale to the interstate by local access roads n Then traverse the Interstate backbone to the location closest to Framingham n Then you travel on local roads again to get to Grandma’s house.

4 Access Network Example cont’d nBackbone/access division is efficient for cars and it is efficient for telecommunications networks. nAccess network collect traffic from small sites into the high speed backbone network. nSharing high speed links, enjoy economic of scale benefit. nLocal access often represents most of the total network cost nExamples of local access networks n Local loop in the PSTN.. n Lottery network n ATM network n Insurance companies.

5 A Simple Access Design Problem nA problem with 6 access locations and 1 backbone site. Traffic is Symmetric and shown below. nUsing Leased Lines :Fixed cost=$400 $3.00/km/month for the first 300km and a cost of $1.75/km/month after 300km Cost Matrix for 56Kbps Lines

6 Star nCost=$9650; Maximum Utilization=23.2%

7 One Concentrator nN2 serves as a concentrator for N6 and N7. nShorter less expensive links are used. nCost=$8660; Maximum Utilization=46.4%

8 Two Concentrators nN2 for N6 and N7; N4 for N3. nCost=$8158; Maximum Utilization=46.4%

9 Final Design nChoose N7 as concentrator instead of N2. Is also MST nCost=$7659; Maximum Utilization=46.4%

10 MSTs Are Not Always Optimal Access Designs nWhen traffic grows 50%, MST costs $10,616 and the links to concentrators N4 and N7 must have two links to keep utilization below 50%.

11 Frame Relay nA frame relay network consists of endpoints, frame relay access equipment and network devices. nAccessing the frame relay network using a standard frame relay interface, the frame relay access equipment is responsible for delivering frames to the network in the prescribed format. nThe job of the network device is to switch or route the frame through the network to the proper destination user device.

12 Frame Relay Cont’d nA frame relay network will often be depicted as a network cloud, because the frame relay network is not a single physical connection between one endpoint and the other. nInstead, a logical path is defined within the network. This logical path is called a virtual circuit. No bandwidth is allocated to the path until actual data needs to be transmitted. Then, the bandwidth within the network is allocated on a packet-by-packet basis.

13 Frame Relay Design nWe will assume that only Permanent Virtual Circuits are available. There is also Switched Virtual Circuits. nPVC is fixed pipe. SVC is dialed pipe. nPackets exceed Committed Information Rate (CIR) will have discard eligibility (DE) bit set. nThree classes of charges: access link costs, provider port costs (cost to frame relay), and CIR costs. nIt is volume dependent and not distance dependent.

14 Frame Relay Design Port Charges CIR Charges

15 Frame Relay Design nLet x be the average distance from the sites to the center. nFixed cost=$400/month; $3.00/km/month. nLeased-line cost=6*400+6*3.00*x nN1 uses 128 kbps link, others use 56kbps links. nPort charges=6* =2000. nAccess charges=7*460=3220 nCIR charges=4*30+2*25=170 if 4 PVCs with 16kbps CIR and 2PVCs with 8kbps. nFrame relay cost= =$6390/month nSolve *x=6390  x= km. Break even point. nSince Square World is larger than this choose Frame Relay.

16 Backbone & Access Sites Definition 5.1: Given a set of sites Ni and traffic matrix T(i,j), weight(Ni)=  j(T(i,j)+T(j,i)). nDesign Principle 5.2 Compute the weight of all the nodes to determine if there are natural traffic centers or if the network is flat. nDesign Principle 5.3: It is acceptable for small nodes to route their traffic via big nodes, but generally we do not want to route the traffic between big nodes via the small nodes. NameTraffic N N … N N N N … N

17 Access Design and Traffic Scale 1.Traffic from access nodes is considerably smaller than the smallest link. But occasionally, we need to download 100MB files. 1. Use frame relay 2. Access trees that efficiently group sites together 2.Traffic from the access nodes is comparable to the capacity of the smallest link. 1. Connect them directly to hub 2. Put concentrator between hub and those nodes. 3.Access node’s traffic can fill several low-speed access lines. 1. Multiple links to multiple backbone nodes; 2. High speed link to a backbone node.

18 OR One-speed One-Center Design Problem: Connecting sites to one backbone node, all links with the same capacity

19 One-speed One-Center Example nProblem: Connect a large number of sites to a hub n 19 nodes that are to be connected to a hub n N14 is the hub location n 4 sites can share a line n Traffic to and from each node Ni is 1200bps n Capacity of the links is 9600bps n Limit the utilization to %50

20 SPT(Star) nCost= $26358 nVery low link utilization and expensive

21 MST nCost= $18,730 nMore cost effective but may have higher delays

22 Prim-Dijkstra with  =0.3 nCost= $ nN11 should connect to N4 nTwo clusters based at N18 and N9. nBetter results but higher complexity of calculation

23 Exhaustive Search nCayley’s Theorem: Given n nodes, there are n n-2 different spanning trees. nFor 20 nodes, there are =2.621*10 23 different trees.

24 Capacitated Minimum Spanning Tree Problem (CMST) nCMST problem: Given a central node N 0 and a set of other nodes (N 1, …, N n ), 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 T 1, …, T k such that each Ni belongs to exactly one T j and each T j contains N 0.

25 CMST Algorithm Sort the edges according to the cost. 1. Take the lowest cost edge from sorted list. 2.Add it to the solution subtrees if the addition does not exceed the capacity go to 1. Assume W=3, each node has w i =1. EdgeCostDecision (1,3)3Select (1,2)4Select (0,1)5Select (2,4)5 Reject  w i > 3 (0,2)6Already connected (3.4)6 Reject  w i > 3 (3,5)6 Reject  w i > 3 (4,5)7Select (2,3)8Already connected (1,4)8 Reject  w i > 3 (0,3)9Already connected (1,5)10 Reject  w i > 3 (0,4)12Select (2,5)12- (0,5)

26 The Esau-Williams Algorithm nHeuristic Algorithm but guarantees the tree meets the capacity constraint nEach node starts off in a tree with 1 node. nCompute the tradeoff function for each node: Tradeoff(N k )=min j Cost(N k, N j )-Cost(Comp(N k ),Center) nIf the tradeoff is negative, a merge is attractive nMerge is allowed if nTradeoff for merging components A and B computes the potential savings of going to a neighbor instead of going to the center node.

27 Esau-Williams Example nW=3, each node has wi=1 nTradeoff(1)=min j Cost(N1,NJ)-Cost(Comp(N1),Center) =min j Cost(N1,N3) -5 (Comp(N1) contains N1) =3-5= -2 (pick closest neighbor, N3) nTradeoff(2)=4-6= -2 nTradeoff(3)=3-9= -6 nTradeoff(4)=5-12= -7 nTradeoff(5)=6-15= -9 nTradeoff(5) is the lowest Accept link(5,3) to the solution since weight constraint on component with nodes 5 and 3 are not violated.  w i =w 5 +w 3 =2<=W=

28 Esau-Williams Example nUpdate Tradeoff(5)=7-9= -2 Next shortest link out of 5 is (5,4) (Comp(5)=11,node 5 goes through node 3 to center) nTradeoff(3)=3-9= -6 nTradeoff(1)=3-5= -2 nTradeoff(2)=4-6= -2 nTradeoff(4)=5-12= -7 nTradeoff(5)=7-9= -2 nPick Tradeoff(4) lowest Accept link(4,2) since weight constraint on component with nodes 4 and 2 are not violated.  w i =w 4 +w 2 =2<=W=

29 Esau-Williams Example nUpdate Tradeoff(4)=6-6= 0 nTradeoff(2)=4-6= -2 nTradeoff(3)=3-9= -6 nTradeoff(5)=7-9= -2 nTradeoff(1)=3-5= -2 nPick Tradeoff(3) Accept link (3,1) since weight constraint on component with nodes 1, 3 and 5 are not violated.  w i =w 1 +w 3 +w 5 =3<=W=

30 Esau-Williams Example nSince nodes 5 and 3 now go through node 1 to Center, update Tradeoff(5)=7-5=2 nTradeoff(3)=6-5= 1 nTradeoff(1)=4-5= -1 nTradeoff(2)=4-6= -2 nTradeoff(4)=6-6=0 Tradeoff(2) is lowest but adding link(2,1) result a component with 5 nodes violate  w i <=3. nReject(2,1) recompute Tradeoff(2)=6-6=0 nReject(1,2) similar reason. Recompute Tradeoff(1)=5-5=0 nThe access network is complete

31 The Creditability of Esau-Williams Algorithm n1-exchange test: Given a set of sites N and a capacitated tree T, we check that no cheaper link can be substituted for an existing link without violating the capacity constraints.

32 Esau-Williams and Inhomogeneous Traffic nAlgorithm does as well if the sites have a variety of different traffic. nLinks are 9600bps n50% of sites require 2400bps nOthers require 4800bps

33 Line Crossings in Access Designs nA 20 node Esau-Williams design

34 Sharma’s Algorithm 1.Compute the angle  s from each site S to the central site C. If S and C have the same coordinate, set  s = 0. 2.Sort the angles  s. 3.Beginning at a site S first, create a set of nodes clockwise (or counterclockwise) from S first. A set is complete when adding the next node would put  set w(site) > W. The next set starts with that node. 4.The design is completed by building a MST on each set with the addition of the central node C. Theorem 5.2: If the angles  s are distinct, then if the cost function is a linear or piecewise linear metric, Sharma’s algorithm builds CMSTs without crossings provided that all the central angles are less than π.

35 Sharma’s Algorithm Design Sorted Angles

36 Sharma’s Algorithm Design nCost= $16021, S first = N17

37 The Creditability of Sharma Designs nDesigns look nice but most of them fail the creditability test. n Much higher failure rate than Esau-Williams’.

38 Sharma vs. Esau-Williams nEW_Ratio=SharmaCost/EWCost; S_Ratio=EWCost/SharmaCost

39 Homework 5 n0 is the central node. The weight of each individual node is 1, except for nodes 4 and 5, which have a weight of 2. The cost function C(i,,j) is given by the physical distance between nodes i and j. W=3 nDesign a capacitated access tree using Esau-Williams algorithm. What is the total cost of your design?

40 Homework 6 nCompare the designs obtained with Esau-Williams’ and Sharma’s algorithms for the following set of nodes. Nodes 1 and 7 have weight 2, others have weight 1. W=3. nUse different colors to indicate parallel lines. n0 is the central node. For Sharma pick S first to be Node