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Chapter 5Access Network Design

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Overview

A Backbone network connects major sites. Access networks connect “small” sites to the backbone

network. Access networks are the “ends” and “tails” of networks that

connect the smallest sites into the network. Access networks only function if they are attached to a

backbone.

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Access Network Example

Visit to Grandma You live in Scarsdale, NY outside of New York City Grandma lives in Framingham, MA, outside of Boston The trip involves 3 segments:

Travel from Scarsdale to the interstate by local access roads

Then traverse the Interstate backbone to the location closest to Framingham

Then you travel on local roads again to get to Grandma’s house.

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Access Network Example cont’d

Backbone/access division is efficient for cars and it is efficient for telecommunications networks.

Access network collect traffic from small sites into the high speed backbone network.

Sharing high speed links, enjoy economic of scale benefit. Local access often represents most of the total network

cost Examples of local access networks

Local loop in the PSTN.. Lottery network ATM network Insurance companies.

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A Simple Access Design Problem A problem with 6 access locations

and 1 backbone site. Traffic is Symmetric and shown below.

Using Leased Lines :Fixed cost=$400 $3.00/km/monthfor the first 300km and a cost of $1.75/km/month after 300km

Cost Matrix for 56Kbps Lines

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Star Cost=$9650; Maximum Utilization=23.2%

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One Concentrator N2 serves as a concentrator for N6 and N7. Shorter less expensive links are used. Cost=$8660; Maximum Utilization=46.4%

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Two Concentrators N2 for N6 and N7; N4 for N3. Cost=$8158; Maximum Utilization=46.4%

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

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MSTs Are Not Always Optimal Access Designs

When traffic grows 50%, MST costs $10,616 and the links to concentrators N4 and N7 must have two links to keep utilization below 50%.

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Frame RelayA frame relay network consists of endpoints, frame relay access equipment and network devices.

Accessing 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.

The job of the network device is to switch or route the frame through the network to the proper destination user device.

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Frame Relay Cont’d

A 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.

Instead, 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.

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Frame Relay Design

We will assume that only Permanent Virtual Circuits are available. There is also Switched Virtual Circuits.PVC is fixed pipe. SVC is dialed pipe.Packets exceed Committed Information Rate (CIR) will have 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 dependent.

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Frame Relay Design

Port Charges

CIR Charges

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Frame Relay Design

Let x be the average distance from the sites to the center. Fixed cost=$400/month; $3.00/km/month. Leased-line cost=6*400+6*3.00*x N1 uses 128 kbps link, others use 56kbps links. Port charges=6*250+500=2000. Access charges=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=$6390/month Solve 2400+18*x=6390 x=221.66 km. Break even point. Since Square World is larger than this choose Frame

Relay.

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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)).

Design Principle 5.2 Compute the weight of all the nodes to determine if there are natural traffic centers or if the network is flat.

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.

Name Traffic

N1 324500

N2 296000

…

N6 221000

N7 38600

N8 38200

N9 37600

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N24 18700

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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 relay2. 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.

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OR OR

One-speed One-Center Design

Problem: Connecting sites to one backbone node, all links with the same capacity

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One-speed One-Center Example

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

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SPT(Star) Cost= $26358 Very low link utilization and expensive

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MST Cost= $18,730 More cost effective but may have higher delays

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Prim-Dijkstra with =0.3 Cost= $15930. N11 should connect to N4 Two clusters based at N18 and N9. Better results but higher complexity of calculation

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Exhaustive Search

Cayley’s Theorem: Given n nodes, there are nn-2 different spanning trees.

For 20 nodes, there are 2018=2.621*1023 different trees.

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Capacitated Minimum Spanning Tree Problem(CMST)

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.

0,iTii

j

Ww

Trees Linksl

ll endendCost )2,1(min

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CMST AlgorithmSort 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

wi =1.

Edge Cost Decision(1,3) 3 Select(1,2) 4 Select(0,1) 5 Select(2,4) 5 Reject wi > 3(0,2) 6 Already connected(3.4) 6 Reject wi > 3(3,5) 6 Reject wi > 3(4,5) 7 Select(2,3) 8 Already connected(1,4) 8 Reject wi > 3(0,3) 9 Already connected(1,5) 10 Reject wi > 3(0,4) 12 Select(2,5) 12 -(0,5) 15 -0

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The Esau-Williams Algorithm

Heuristic Algorithm but guarantees the tree meets the capacity constraint

Each node starts off in a tree with 1 node. Compute the tradeoff function for each node:

Tradeoff(Nk)=minj Cost(Nk, Nj)-Cost(Comp(Nk),Center)

If the tradeoff is negative, a merge is attractive Merge is allowed if

Tradeoff for merging components A and B computes the potential savings of going to a neighbor instead of going to the center node.

W))p(Nweight(Com))p(Nweight(Com JK

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Esau-Williams Example

W=3, each node has wi=1 Tradeoff(1)=minj Cost(N1,NJ)-Cost(Comp(N1),Center)

=minj Cost(N1,N3) -5 (Comp(N1) contains N1)=3-5= -2 (pick closest neighbor, N3)

Tradeoff(2)=4-6= -2 Tradeoff(3)=3-9= -6 Tradeoff(4)=5-12= -7 Tradeoff(5)=6-15= -9 Tradeoff(5) is the lowest Accept link(5,3) to the solution

since weight constraint on component with nodes 5 and 3 are not violated. wi =w5+w3=2<=W=3

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Esau-Williams Example

Update Tradeoff(5)=7-9= -2Next shortest link out of 5 is (5,4)(Comp(5)=11,node 5 goes through node 3 to center)

Tradeoff(3)=3-9= -6 Tradeoff(1)=3-5= -2 Tradeoff(2)=4-6= -2 Tradeoff(4)=5-12= -7 Tradeoff(5)=7-9= -2 Pick Tradeoff(4) lowest Accept link(4,2) since

weight constraint on component with nodes 4 and 2 are not violated. wi =w4+w2=2<=W=3

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Esau-Williams Example Update Tradeoff(4)=6-6= 0 Tradeoff(2)=4-6= -2 Tradeoff(3)=3-9= -6 Tradeoff(5)=7-9= -2 Tradeoff(1)=3-5= -2 Pick Tradeoff(3) Accept link (3,1) since

weight constraint on component with nodes 1, 3 and 5 are not violated. wi =w1+w3 +w5 =3<=W=3

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Esau-Williams Example Since nodes 5 and 3 now go through node 1 to Center,

update Tradeoff(5)=7-5=2 Tradeoff(3)=6-5= 1 Tradeoff(1)=4-5= -1 Tradeoff(2)=4-6= -2 Tradeoff(4)=6-6=0 Tradeoff(2) is lowest but

adding link(2,1) result a componentwith 5 nodes violate wi<=3.

Reject(2,1) recompute Tradeoff(2)=6-6=0

Reject(1,2) similar reason. Recompute Tradeoff(1)=5-5=0

The access network is complete

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The Creditability of Esau-Williams Algorithm

1-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.

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Esau-Williams and Inhomogeneous Traffic

Algorithm does as well if the sites have a variety of different traffic.Links are 9600bps50% of sites require 2400bpsOthers require 4800bps

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Line Crossings in Access Designs

A 20 node Esau-Williams design

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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 Sfirst, create a set of nodes clockwise (or counterclockwise) from Sfirst. A set is complete when adding the next node would put setw(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.

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Sharma’s Algorithm Design

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Sharma’s Algorithm Design Cost= $16021, Sfirst = N17

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

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

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Homework 5

0 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

Design a capacitated access tree using Esau-Williams algorithm. What is the total cost of your design?

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Homework 6 Compare 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.

Use different colors to indicate parallel lines. 0 is the central node. For Sharma pick Sfirst to be Node 1

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