Transcript Document 7565752

Chapter 5
Access Network Design
1
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.
2
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.
4
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/month
for the first 300km and a cost of
$1.75/km/month after 300km
Cost Matrix for 56Kbps Lines
5
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%
8
Final Design
 Choose N7 as concentrator instead of N2. Is also MST
 Cost=$7659; Maximum Utilization=46.4%
9
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%.
10
Frame Relay
A 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.
11
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.
12
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.
13
Frame Relay Design
CIR Charges
Port Charges
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Frame Relay Design

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
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


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)=Sj(T(i,j)+T(j,i)).
Name
Traffic
N1
324500
N2
296000
…
N6
221000
N7
38600
N8
38200
N9
37600
…
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.
N24
18700
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.
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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 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.
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One-speed One-Center Design
Problem: Connecting sites to one backbone node, all links with the same capacity
OR
OR
18
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
19
SPT(Star)
 Cost= $26358
 Very low link utilization and expensive
20
MST
 Cost= $18,730
 More cost effective but may have higher delays
21
Prim-Dijkstra with a=0.3




Cost= $15930.
N11 should connect to N4
Two clusters based at N18 and N9.
Better results but higher complexity of calculation
22
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.
w W
iT j ,i  0
min
i
  Cost (end1 , end 2 )
Trees lLinks
l
l
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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
wi =1.
2
6
4
8
12
5
4
7
12
15
0
6
5
9
Edge
(1,3)
(1,2)
(0,1)
(2,4)
(0,2)
(3.4)
(3,5)
(4,5)
(2,3)
(1,4)
(0,3)
(1,5)
(0,4)
(2,5)
(0,5)
Cost
3
4
5
5
6
6
6
7
8
8
9
10
12
12
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Decision
Select
Select
Select
Reject Swi > 3
Already connected
Reject Swi > 3
Reject Swi > 3
Select
Already connected
Reject Swi > 3
Already connected
Reject Swi > 3
Select
-
6
10
5
3
8
3
1
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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
weight(Com p(N K ))  weight(Com p(N J ))  W
 Tradeoff for merging components A and B computes the
potential savings of going to a neighbor instead of going to
the center node.
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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)
2
=3-5= -2 (pick closest neighbor, N3)
8
 Tradeoff(2)=4-6= -2
6
4
12
 Tradeoff(3)=3-9= -6
12
 Tradeoff(4)=5-12= -7
15
0
 Tradeoff(5)=6-15= -9
9
 Tradeoff(5) is the lowest
10
5
 Accept link(5,3) to the solution
since weight constraint on component
1
with nodes 5 and 3 are not violated.
Swi =w5+w3=2<=W=3
5
4
7
6
5
6
3
8
3
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Esau-Williams Example
 Update 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)
 Tradeoff(3)=3-9= -6
 Tradeoff(1)=3-5= -2
 Tradeoff(2)=4-6= -2
0
 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.
Swi =w4+w2=2<=W=3
2
6
4
8
12
5
4
7
12
15
6
5
9
6
10
5
3
8
3
1
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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
0
Pick Tradeoff(3)
Accept link (3,1) since
weight constraint on component
with nodes 1, 3 and 5 are not violated.
Swi =w1+w3 +w5 =3<=W=3
2
6
4
8
12
5
4
7
12
15
6
5
9
6
10
5
3
8
3
1
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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
2
 Tradeoff(3)=6-5= 1
 Tradeoff(1)=4-5= -1
8
6
4
12
 Tradeoff(2)=4-6= -2
12
 Tradeoff(4)=6-6=0
15
0
 Tradeoff(2) is lowest but
9
adding link(2,1) result a component
10
5
with 5 nodes violate Swi<=3.
 Reject(2,1)
1
recompute Tradeoff(2)=6-6=0
 Reject(1,2) similar reason.
Recompute Tradeoff(1)=5-5=0
 The access network is complete
5
4
7
6
5
6
3
8
3
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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 9600bps
50% of sites require 2400bps
Others require 4800bps
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Line Crossings in Access Designs
 A 20 node Esau-Williams design
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Sharma’s Algorithm
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 Ssetw(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.
1.
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Sharma’s Algorithm Design
19
12
5
1
6
14
18
13
9
17
8
11
15
16
0
3
10
7
2
4
Sorted Angles
17
13
18
6
5
8
1
19
14
12
9
15
7
2
10
3
4
11
0
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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’.
37
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?
0
1
2
1
4
3
5
1
6
7
1
8
1
39
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
1
0
4
2
1
5
3
6
1
1
7
1
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