Access Network Design

1
Access Network Design

• A Backbone network connects major sites.
• Access networks connect small sites to the
  backbone network.
• 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
• ISPs local access network.

2
A Simple Access Design

• 7 nodes. N1 is the backbone site. Symmetric
  traffic.

Piecewise linear cost (56Kbps) Fixed
cost4003.00/km/mofirst 300km 1.75/km/moafter
300km
3
Star

• Cost9650 Max. Utilization23.2

4
Cheaper Local-Access Design

• N2 serves as a concentrator for N6 and N7.
• Local link can use shorter less expensive link.

5
Two concentrators

• N2 for N6 and N7 N4 for N3.

6
Move to MST

• Choose N7 as concentrator instead of N2. Become
  MST

7
MSTs 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.

8
An Optimal Design

• Constraint MST problem. Note that N3 connect
  directly to N1 since through N4 will violate the
  utilization constraint.

9
Choosing Backbone Nodes

• Definition 5.1 Given a set of sites Ni and
  traffic matrix T(i,j), weight(Ni)Sj(T(i,j)T(j,i)
  ).
• Sometimes, the weights of nodes indicate the
  choices of backbone nodes or traffic centers.
• 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.

10
3 Types of Local Access Problems

• Access nodes traffic are considerably smaller
  than the smallest link. But occasionally, they
  may need to download huge file? capacitated
  spanning tree building problem.
• Access nodes traffic is comparable to the
  capacity of the smallest link. Concentrator
  placement problem, local access tree problem.
• Access nodes traffic can fill several low-speed
  access lines. Choices multiple links to multiple
  backbone nodes or high speed link to a backbone
  node. They are nature choices for concentrator
  locations.

11
One-speed One-Center Design

• Example 19 nodes to a hub, N14.
• 4 sites can share a line. Each link is 1200 bps.
• 4800 bps ? Use 9600 bps link. 50 utilization.
• The problem becomes a tree building problem.
• Solution
• SPT
• MST
• Prim-Dijkstra with 0ltalt1.
• Other algorithm

12
SPT(Star) and MST

• SPT, Cost26358

• MST, 18,730

13
Prim-Dijkstra with a0.3

• 15930. N11 can go through N4 Two clusters with
  N18 and N9 as concentrators.
• Cheaper than MST since multiple lines are used

14
Constraint Minimum Spanning Tree Problem

• It solves the problem of creating capacitated
  (constraint) minimum spanning tree (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, and

15
Greedy CMST Algorithm

• Sort the edges according to the cost.
• s1 Take the lowest cost edge from sorted
  list.Add it to the solution subtrees if the
  addition does not violated the constraint and it
  does not form a loop, go to s1.
• Example Node 0 is the center (sink). Other nodes
  are sources. Assume link capacity W3, each node
  has a flow to the center wi 1, and the following
  topology, link costs are given along the edges

16
Esau-William Algorithm

• Initially, each node starts off in a tree with
  itself.
• Compute the tradeoff functionTradeoff(i,j)minj
  Cost(i, j)-Cost(Comp(ii),Center)where
  Cost(Comp(i),Center) is the cost of connecting
  the component with Node i 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 i to Node j.
  minj Cost(Ni,Nj) suggests pick the closest
  neighboring Node j.
• Maintain a sorted list of links based on the
  Tradeoff() value.
• 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 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.
• stop if all tradeoffs are nonnegative otherwise
  got to L1.

17
Apply Esau-William Algorithm

• Assume W3, each node has wi1, and the following
  topology
• Tradeoff(1,3)minj Cost(1,3)-Cost(Comp(1),Center)
  minj Cost(1,3)-7 //comp(1) contains N15-7-2
  // pick closest neighbor, Node 3
• Tradeoff(2,1)6-8-2
• Tradeoff(3,1)5-11 -6
• Tradeoff(4,2)7-14 -7
• Tradeoff(5,3)8-17 -9
• Tradeoff(5,3) is lowest one.
• Accept link(5,3) to the solutionsince weight
  constraint on component with nodes 5 and 3 are
  not violated.SWiW5W32ltW3
• Effectively this picks the faraway nodewith
  short link to its neighbor and group them as
  component.

18
Apply Esau-William Algorithm(2)

• Update Tradeoff(5,4)9-11 -2Next shortest link
  out of 5 is (5,4)(Comp(5)11,node 5 goes through
  node 3 to center)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) lowest
• Accept link(4,2) sinceweight constraint on
  component with nodes 4 and 2 are not
  violated.SWiW4W22ltW3

19
Apply Esau-William Algorithm(3)

• Update Tradeoff(4,3)8-8 0Tradeoff(2,1) -2 not
  changed.
• Tradeoff(3,1)5-11 -6
• 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) sinceweight constraint on
  component with nodes 1, 3 and 5 are not
  violated.SWiW1W3 W5 3ltW3
• Since nodes 5 and 3 now go through node 1 to
  Center,update Tradeoff(5,4)9-72Tradeoff(3,4)8
  -7 1Tradeoff(1,2)6-7 -1

20
Apply Esau-William Algorithm(4)

• Tradeoff(5,4)9-72
• Tradeoff(3,4)8-71
• Tradeoff(1,2)6-7 -1
• Tradeoff(2,1)6-8 -2
• Tradeoff(4,3)8-80
• Tradeoff(2,1) is lowest butadd link(2,1) result
  a componentwith 5 nodes violate Swilt3.
• Reject(2,1) recompute Tradeoff(2,0)8-80
• Reject(1,2) similar reason. Recompute
  Tradeoff(1,0)7-70
• Pick link(1,0)
• Pick link(2,0) complete the access network.