CS 622 Distributed Networks

CS 622 Distributed Networks Access Network Design Dr. Xiaobo Zhou Department of Computer Science CS622 AccessNetwork.1 Review: Traffic Normalization Traffic Generators Uniform traffic Random traffic Realistic traffic (in relation with population and distance) Traffic Normalization Total normalization Row normalization Row & Column normalization Different applications have difference characteristics CS622 AccessNetwork.2

What is Access Network Backbone network Access network Backbone link Access link A Backbone network connects major sites Access networks connect small sites to the backbone network CS622 AccessNetwork.3 Access Network Design How to decide which sites should be in the backbone network? Traffic volume Close to multiple small sites Access network collect traffic from small sites into the high speed backbone network. Sharing high speed links, enjoy economic of scale benefit. Examples of local access networks Local subscriber loop connects users of a central office. Lottery network ATM network ISP s local access network. CS622 AccessNetwork.4

A Simple Access Design Example Consider a problem with 6 access locations and 1 backbone site N1 is the backbone site, the traffic is all from and to N1 Symmetric traffic CS622 AccessNetwork.5 The Cost Matrix for 56 Kbps links Linear Cost model: fixed cost = $400/month, and $3.00/km/month for the first 300km, and then a cost of $1.75/km/month after that Cost if distance-dependent. CS622 AccessNetwork.6

A Star Design Cost=$9650; Max. Utilization=23.2% CS622 AccessNetwork.7 A Cheaper Local-Access Design N2 serves as a concentrator for N6 and N7. Local link can use shorter less expensive link Cost $8666 CS622 AccessNetwork.8

A Even Cheaper Local-Access Design Two concentrators: N2 for N6 and N7; N4 for N3 Cost: $8158 CS622 AccessNetwork.9 Move to MST the cost is optimal Choose N7 as concentrator instead of N2 The design becomes an MST T2-1+T6-1+T7-1 = 26000 26000/56000=46.4% CS622 AccessNetwork.10

MSTs not always Optimal Access Designs The MST was the optimal, because the traffic volumes were moderate When the traffic grows 50%, the MST costs $10,616 and the links to concentrators N4 and N7, i.e, N1 - N4 and N1 - N7, must have two links to keep utilization below 50% CS622 AccessNetwork.11 An Optimal Design with Increased Traffic A Constraint MST Problem N3 connects directly to N1 since through N4 will violate the utilization constraint CS622 AccessNetwork.12

Frame Relay Design Frame Relay is a relatively new service Frame relay is accomplished by connecting each site into a frame relay cloud provided by the service carrier, just like plain old phone service is accomplished by attaching the phone into PSTN cloud. Packets exceed Committed Information Rate (CIR) will be discardable by having discard eligibility (DE) bit set Three classes of charges: access link costs, provider port costs (cost to frame relay), and CIR costs. It is volume dependent and not distance-bw-nodes dependent Port Charges CIR charges per PVC (permanent virtual circuits) CS622 AccessNetwork.13 Frame Relay Design Cost Model Each node is 20 km from the provider point of presence (POP) Access link cost is same for all 7 nodes: 7 * (400 + 3 * 20) N3 PVC port POP POP PVC port: 56/64 kbps N2 Frame Relay Cloud PVC port N4 POP POP PVC port: 128 kbps Σi T i ->1 = 59 bps; 50% N1 CS622 AccessNetwork.14

Frame Relay vs. Lease-Line Cost Let x be the distance from the site to the center Fixed cost=$400/month; $3.00/km/month; Leased-line Cost Model 6 * 400 + 6 * 3.00 * x Frame Relay Cost Model: Assume frame relay provider has point of presence (pop) at each site (20km away). Each site connects to the frame relay network N1 uses a 128 kbps link port (59 bps total traffic on way, 50%) Other nodes use 56kbps links - Port charges: 6 * 250 + 500 = 2000 Access charges: 7 * (400 + 3.0 * 20) = 7*460 = 3220 CIR charges: 4 * 30 + 2 * 25 = 170, if 4 PVCs with 16kbps CIR and 2PVCs with 8kbps Frame relay cost: 2000 + 3220 + 170 = $5390/mo Solve 2400 + 18 * x = 5390 x = 166.11 km, Break even point Most WAN are larger than this Frame Relay is a good candidate CS622 AccessNetwork.15 Choosing Backbone Nodes If the division between large sites and small sites is distinct, there is usually no problem in deciding backbone nodes Definition 5.1: Given a set of sites Ni and traffic matrix T(i,j), weight(ni) = Σ j(t(i,j)+t(j,i)) Sometimes, the weights of nodes indicate the choices of backbone nodes or traffic centers. Design 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 In airline networks, there are four kind of nodes Hubs Cities with enough traffic to have nonstop flights to cities other than hubs Cities with enough traffic to have nonstop flights to their hubs Little cities CS622 AccessNetwork.16

3 Types of Local Access Problems 1. Access node s traffic are considerably smaller than the smallest link. But occasionally, they may need to download huge file Use frame relay or access tree capacitated spanning tree building problem 2. Access node s traffic is comparable to the capacity of the smallest link Choice 1: connect them directly to the hub/center Choice 2: put a concentrator between hub and those nodes Concentrator placement problem, local access tree problem 3. Access node s traffic can fill several low-speed access lines Choice 1: multiple links to multiple backbone nodes Choice: a high speed link to a backbone node - Multiple low-speed links give better reliability - The high-speed link gives better performance and lower cost CS622 AccessNetwork.17 One-speed One-Center Design and Capacitated Trees Example: 19 nodes to be connected to a hub, N14 (total 20 nodes) Requirement: 4 sites can share a line Symmetric traffic: to and from each node Ni to N14 is 1200 bps Capacity of the one-speed link: 9600 bps Link utilization limitation: < 50% The problem becomes a capacitated access tree building problem Solutions: SPT by Dijkstra s algorithm MST by Prim s algorithm Intermediate trees by Prim-Dijkstra with 0<α<1 Exhaustive search for an optimal tree Other new algorithms? CS622 AccessNetwork.18

SPT(Star) High cost: $26358 Max_uitlization is 12.5% (12000 / 56000) How about aggregate traffic of nodes and connect to the center? CS622 AccessNetwork.19 MST Cost: $18,730 15 sites from N12 4 parallel links CS622 AccessNetwork.20

Prim-Dijkstra with α=0.3 Lower cost: $15930 Potential improvements: N11 can go through N4; Two clusters with N18 and N9 as concentrators ( a double link -> 2 single links). A double D96 link CS622 AccessNetwork.21 How Many Trees to Search for Optimal Designs? Exhaustive search for an optimal design is usually infeasible. Cayley s Theorem: Given n nodes, there are n n-2 different spanning tree For 20 nodes, there are 20 18 =2.621*10 23 trees. CS622 AccessNetwork.22

Constraint Minimum Spanning Tree Problem CMST problem: Given a central node N0 and a set of other nodes (N1,, Nn), 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 i T j w i, i> 0 min < W Trees l Links Cost ( end1, end2 ) l l CS622 AccessNetwork.23 A Greedy CMST Algorithm Sort the edges/links according to the cost take the lowest cost edge from sorted list; add it to the solution subtrees if the addition does not violated the constraint w < W; go to s1. Assume W=3, each node has wi = 1, and the following topology: i i T j, i> 0 T1 T2 CS622 AccessNetwork.24

Esau-William Algorithm Initially, each node starts off in a tree with itself Compute the tradeoff function: Tradeoff(Ni) = min j Cost(i, j) - Cost(Comp(N i ), Center) // attractive if 0 saving by linking Ni to Nj, rather than linking directly to Center (STAR) Cost(Comp(i),Center) is the cost of connecting the component with Node Ni to the Center. It is equivalent to the cost of the shortest path from the Center to any node in the component. Cost(i,j) is the link cost from Node Ni to Node Nj min j Cost(N i,n j ) suggests pick the closest neighboring Node Nj Maintain a sorted list of links based on the Tradeoff() value Tradeoff() is attractive if negative, smaller -> more attractive Actually, in each iteration, we only consider the shortest link out of a node to a neighbor that does not belong the component of the node L1: adds the top link (min Tradeoff) in the list to the solution if the weight constraint of the component is satisfied; otherwise, reject it update the tradeoffs in other links due to the newly added link and resort the list go to L1 CS622 AccessNetwork.25 Apply Esau-William Algorithm Assume W=3, each node has wi = 1, and the following topology: Tradeoff(1) = min j Cost(1, j) - Cost(Comp(1),Center) = Cost(1,3) - 7 //comp(1) contains Node 1 = 5 7 = -2 // pick closest neighbor, Node 3 Tradeoff(2,0) = 6-8 = -2 Tradeoff(3,1) = 5 11 = -6 Tradeoff(4,2) = 7 14 = -7 Tradeoff(5,3) = 8 17 = -9 Tradeoff(5) is lowest one Accept link(5,3) to the solution since weight constraint on component with nodes 5 and 3 are not violated. Σwi = w 5 + w 3 = 2 <= W=3 Effectively this picks the faraway node with short link to its neighbor and group them as component. CS622 AccessNetwork.26

Apply Esau-William Algorithm(2) Update the tradeoffs in other links due to the newly added link and resort the Tradeoff() list Tradeoff(5,4) = 9 11 = -2 // Next shortest link out of 5 is (5,4) // (Comp(5)=11,node 5 goes through node 3 to center) // 3 is already in the component, not considered Tradeoff(3,1) = 5 11 = -6 // not changed Tradeoff(1,3) = 5 7 = -2 Tradeoff(2,4) = 6 8 = -2 Tradeoff(4,2) = 7 14 = -7 Tradeoff(5,4) = 9 11 = -2 Pick Tradeoff(4,2) since it is smallest Accept link(4,2) since weight constraint on component with nodes 4 and 2 are not violated: Σwi = w 4 + w 2 = 2 <= W=3 CS622 AccessNetwork.27 Apply Esau-William Algorithm(3) Tradeoff(4,3) = 8 8 = 0 // Tradeoff(2,1)= -2 not changed Tradeoff(3,1) = 5 11 = -6, not changed Tradeoff(5,4) = 9 11 = -2 Tradeoff(1,3) = 5 7 = -2 Tradeoff(2,1) = 6-8 = -2 Tradeoff(4,3) = 8 8 = 0 Pick Tradeoff(3,1) Accept link (3,1) since weight constraint on component with nodes 1, 3 and 5 are not violated Σwi = w 1 + w 3 + w 5 = 3 <= W=3 CS622 AccessNetwork.28

Apply Esau-William Algorithm (4) and (5) Since nodes 5 and 3 now go through node 1 to the Center 0, Tradeoff(5,4) = 9 7 = 2 Tradeoff(3,4) = 8 7 = 1 Tradeoff(1,2) = 6 7 = -1 Tradeoff(2,1) = 6-8 = -2 Tradeoff(4,3) = 8-8 = 0 Tradeoff(2,1) is lowest but adding link(2,1) result a component with 5 nodes violate Σwi <= 3 Reject(2,1) recompute Tradeoff(2,0) = 8 8 = 0 Reject(1,2) due to the same reason Recompute Tradeoff(1,0) = 7 7 =0 Pick link(1,0) Pick link(2,0) completes the access network CS622 AccessNetwork.29 Creditability of Esau-Williams Algorithm The Esau-Williams Algorithm is heuristic, though works quite well Example: an Esau-Williams design with up to 7 sites per line CS622 AccessNetwork.30

Creditability of Esau-Williams Algorithm (Cont.) Given a set of sites N and a capacitated tree T, 1-exchange test: no cheaper link can be substituted for an existing link without violating the capacity constraints Example: for homogeneous traffic, up to 4 sites on a line For homogeneous traffic, the Esau-Williams does well on 1-change test CS622 AccessNetwork.31 Esau-Williams and InHomogenous Traffic One-speed link, but different sites have different traffic Link capacity is 9600 bps, 50% of sites have a requirement of 2400 bps, and the other 50% have a requirement of 4800 bps CS622 AccessNetwork.32

Line Crossing and Esau-Williams Are crossings an indication of a lack of creditability in capacitated trees? In tours, yes! CS622 AccessNetwork.33 Line Crossing in Access Designs: Sharma s Algorithm 1. Compute the angle θ s from each site S to the central site C. If S and C have the same coordinate, set θ s =0 2. Sort the angles θ 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 Σ 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 Sharma s algorithm builds CMSTs withour line crossings CS622 AccessNetwork.34

Sharma s Algorithm Result A better solution CS622 AccessNetwork.35 Creditability of Sharma Algorithm Much higher failure rate than Esau-Williams by 1-change test CS622 AccessNetwork.36

Sharma vs. Esau-Williams EW_Ratio = SharmaCost/EWCost; S_Ratio = 1/EW_Ratio CS622 AccessNetwork.37