TCOM 540

1
TCOM 540

• Session 5

2
Agenda

• Quiz
• Review Session 3 assignments
• Access and backbone design

3
Access and Backbone

• We already encountered access and backbone in the
  first session
• To over-simplify, access lines provide local
  connectivity, backbone provides long-distance
  transport
• Balance between access and backbone costs can
  vary widely

4
Access and Backbone (2)
Backbone
Access
5
Access and Backbone (3)
IXC1 Backbone
IXC1 POP
LEC Central Office
IXC2 Backbone
Access lines to IXCs
IXC2 POP
Local Loops
To other LEC COs
6
Local Access Costs Are Significant

• Relative cost of local access has been increasing

Source Bureau of Labor Statistics
7
Local Access Costs Are Significant (2)

• Situation regarding dedicated local access is
  less clear
• Accurate information regarding real prices paid
  for dedicated access circuits is not easy to find
• Probably has been some decrease, at least in
  areas where there is local access competition

8
Local Access Costs Are Significant (3)

• The Telecommunications Reform Act of 1996 was
  supposed (among other things) to foster local
  competition
• Appears to have been relatively unsuccessful
• Competitive Local Access Carriers (CLECs) have
  been decimated by collapse of high-tech stocks
• Relatively little facilities-based local
  competition (lt 5 of market)

9
Local Access Costs Are Significant (4)

• Appears that whatever competition there is for at
  least residential local access (high speed) is
  coming from satellite and cable, not CLECs
• Legislative action Tauzin-Dingell bill?

10
Local Access Design Example
Traffic (symmetric)
Costs (symmetric)
11
Local Access Design Example (2)

• Use some nodes as concentrators

6
6
6
1526
2
2
2
1225
1327
1629
1225
7
7
7
2112
1929
1929
1629
1
1
1
5
5
5
667
667
667
1328
1328
1328
4
4
4
1985
1985
1483
3
3
3
9650
8660
7659 (OPTIMAL)
12
Local Access Design Example (3)

• If traffic grows by 50, links (1,4) and (1,7)
  must be doubled

6
6
2
1327
2
1225
1327
7
1929
7
1629
IMPROVEMENT
3258
1
5
1
667
5
1328
667
2656
4
4
1985
1483
3
8865 (OPTIMAL)
3
10616
13
Frame Relay (FR)

• Frame Relay Permanent Virtual Circuits (PVCs) use
  concepts of Committed Information Rate (CIR) and
  Port Speed
• Charges for
• Access
• Port (connection to network)
• CIR of PVC does not vary with distance

14
Asynchronous Transfer Mode (ATM)

• ATM uses similar concepts to FR
• Constant Bit Rate (CBR)
• Variable Bit Rate non-real-time (VBR-nrt)
• Variable Bit Rate real-time (VBR-rt)
• Available Bit Rate (ABR)
• Unspecified Bit Rate (UBR)

15
ATM Definitions
Constant Bit Rate (CBR) - fixed bit rate in which
bits are sent in a steady stream. A CBR is useful
for applications requiring small but near
constant transmission, for example, remote-site
monitoring.
Variable Bit Rate (VBR) - while overall
transmission capacity (bits per second) is
guaranteed, the rate at any given second may not
equal the stated capacity. A VBR of 28 Kb/s, for
example, may have periods where the transmission
rate ranges from 23 to 33 Kb/s.
VBR(rt) means a variable bit rate in real time
transmission VBR(nrt) means a variable bit rate
transmission in near-real-time conditions. Both
are used in voice and videoconferencing, where a
quality channel is reserved but over which data
does not flow evenly.
Unspecified Bit Rate (UBR) - a transmission
service which does not guarantee a fixed
transmission capacity. Any application that can
tolerate delays is ideally satisfied by an UBR.
Source BCE Teleglobe
16
ATM Definitions (2)
Available Bit Rate (ABR) -The bit rate left after
the predictive and guaranteed service traffic
(CBR/VBR) is served. In essence, it is simply a
fair share of the remaining bandwidth amongst the
VPs and VCs that have asked for this service.
Source cell-relay.indiana.edu
17
Rules of Thumb

• Cannot choose between a leased line and a FR/ATM
  design until both are done and costs compared
• Availability of FR and ATM just complicates life
  
• Note that leased lines may have security
  advantages

18
Rules of Thumb (2)

• If sites vary widely in size (traffic
  originated/terminated), choose the bigger sites
  as aggregation points
• Define weight of a node as sum of all traffic
  flowing into and out of it
• Design problem then has two parts
• Access gets traffic from small sites to
  backbone
• Backbone carries traffic between backbone
  nodes
• Which comes first??

19
Traffic Scale

• Depends on relationship of node size to smallest
  desired link size
• Smallest link size determined by factors such as
  packet size/delay
• Traffic from access node much smaller than
  smallest link we wish to use
• - Create access trees to group sites efficiently
• - Capacitated spanning trees

20
Traffic Scale (2)

• Traffic from access node comparable to smallest
  link
• - Low speed link to hub vs. concentrator part
  way to hub
• - Concentrator placement problem
• Traffic from access node significantly larger
  than smallest link
• - Multiple lower speed links vs. single higher
  speed link

21
One Speed, One Center

• Example problem with 20 nodes one of which is
  the hub
• 1200 bps/node, 9600 bps links, utilization 50
• What algorithm to use?

22
One Speed, One Center (2)

• Star design costs 26,358
• Link utilization 12.5
• MST cost 18,730
• Uses multiple (up to 4) links on some legs
• Prim-Dijkstra tree cost 15,930
• Using a 0.3
• Hundreds of designs tested

23
One Speed, One Center (3)

• For n nodes, there are nn-2 different spanning
  trees
• 2018 2.621 1023
• This is a rather large number
• And partitioning does not help much
• Groups of 4 can be done in 2.546 1010 ways
• Not to mention groups of 3 etc., etc., etc.

24
Esau-Williams Algorithm

• Esau-Williams creates a Capacitated Minimum
  Spanning Tree (CMST)
• Given a central node N0 and a set of other nodes
  (N1, N2, Nn), and 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
• Si e Tj wi lt W
• Strees S l e Links Cost(end1l, end2l) is a
  minimum

25
Esau-Williams Algorithm (2)

• Central concept is tradeoff function
• Build good trees
• Each tree starts off as one node
• Component (graph theory meaning) Comp(Ni)
• Tradeoff function is Tr() where
• Tr(Ni) minjCost(Ni,Nj) Cost (Comp(Ni),N0)
• Computes cost of linking to neighbor vs. cost of
  going to center

26
Esau-Williams Algorithm (2)

• Negative value of Tr means it is preferable to
  link to neighbor tree rather than running a link
  to the center
• Must check that the design is feasible i.e.,
  does not exceed link capacity
• W(Comp(Ni)) W(Comp(Nj)) lt W
• Algorithm limitation often desirable to
  increase link capacities in real life

27
Esau-Williams Algorithm (3)
N4
N2
N3
N1
Scanning node N3 1. Examine costs of
these links 2. Compare with cost of this link
N0
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Heaps

• Code for implementing Esau-Williams in Cahn uses
  heaps (not essential, but interesting)
• A heap is a special type of binary tree
• Binary tree each node has at most 3 edges
• Parent
• Left child
• Right child

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Heaps (2)

• Heap
• Root at level 0 smallest element
• Any node has a value no larger than either of its
  children
• Heaps are not unique

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Heaps (3)
-1000
-700
-400
-100
-200
0
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Heaps (3)
-1000
-1000
-700
-100
-700
-400
-400
-200
0
-100
-200
0
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Esau-Williams Implementation

• Uses a heap for each node nHeap(i) and a global
  heap tHeap
• Heap for a node has tradeoff values with respect
  to neighbors
• Subject to feasibility

33
E-W Implementation (2)

• Lets say top of heap for a node is 1000

-1000
-700
-400
-100
-200
inf
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E-W Implementation (3)

• Say this is infeasible change value to inf

inf
But now this is not a heap any more -
bubble down offending node
-700
-400
-100
-200
inf
35
E-W Implementation (4)

• Swap with best child

-700
-700
inf
-400
-200
-400
-100
-200
inf
-100
inf
inf
36
E-W Implementation (5)

• Heaps are efficient
• Number of levels in the heap grows as the order
  of log2(n)
• Where n is total number of elements in the heap
• On average, each level is twice the size of the
  level above

37
E-W Implementation (6)

• Algorithm
• Top of global heap is node n1, which has the best
  tradeoff
• Go to heap of N1 and find partner n2 which
  appears to have best tradeoff
• Remove n2 from node heap
• Find components of n1 and n2
• Tricky bit When we start this loop, all
  tradeoffs are correct, but we do not update all
  tradeoffs as we go along
• Wait until an n1, n2 pair appears, then check
  tradeoff
• If tradeoff is incorrect, reset and push pair
  back into heap
• If tradeoff is correct, check if merge of
  components is feasible
• If feasible, merge
• Update global heap with new n1 tradeoff

38
Creditability of E-W

• E-W is heuristic
• Guarantees resulting design is feasible
• Does not guarantee that design is optimal
• Poorer performance as number of sites increases
• Works well for both homogenous and inhomogeneous
  traffic

39
Esau-Williams Failure Rate
Four sites per line
40
Sharmas Algorithm

• E-W sometimes introduces crossings
• We know the design can be improved if crossings
  are removed
• Sharmas algorithm builds MSTs in wedges from
  the central node

41
Sharmas Algorithm (2)

• Compute the angle from the central node to each
  other node
• Sort the angles
• Move clockwise from node with smallest angle
• Create sets of nodes such that adding another
  node would put Ssetw(node) gt W
• Start next set with that node

42
Sharmas Algorithm (3)

• Sharmas algorithm builds Capacitated Minimum
  Spanning Trees without crossings
• So long as no set has more than half the pie
  (i.e., q gt p)
• However, Sharma is generally inferior to E-W
• Poorer creditability
• Higher cost

43
Multiple Link Speeds

• In real problems, almost always have a variety of
  link speeds to choose from
• DS0 _at_ 64kbps
• N x DS0
• T1 _at_1.5 Mbps
• T3 _at_ 45 Mbps
• Etc.

44
Multiple Link Speeds (2)

• Intuitively, wed like the access tree to use
  higher speeds closer to the root, and lower
  speeds out towards the edges

45
Predecessor Function

• A tree T rooted at node Root can be represented
  uniquely by a predecessor function predV V on
  the set of vertices
• pred(Root) Root
• No other node is its own predecessor
• For any node N there is an ngt0 such that predn(N)
  Root

46
Ancestors

• Given a tree T and the associated predecessor
  function, the ancestors of N are all the nodes N
  where
• predn(N) N for some n gt 0

47
Multispeed CMST Definition

• Given
• A set of nodes N0, N1, , Nn
• A set of weights (w1, , wn) for each node
• A set of link types L1, L2, , Lm
• Capacities W1, W2, , Wm
• A cost matrix C(i,j,k) for the cost of link type
  Lk between Ni and Nj

48
Multispeed CMST Definition (2)

• Then the multispeed CMST problem is to find the
  tree rooted at N0 with link assignments such that
• Sancestors(N) w(i) lt WLink(N, pred(N))
• And SLinksc(end1L, end2L, typeL) is minimized

49
MSLA Algorithm for Multispeed CMSTs

• Assign each node n the smallest link l to connect
  it to root. Compute spare_capacity(n) Wl wn
• Create tradeoff heap for n (similar to E-W)
  tradeoffs represent savings by connecting site n
  to site i rather than to the root
• Tradeoffn(i) c(n,i,L) Upgrade (i, wn)
  c(n,0,L)
• The function Upgrade() computes the cost of
  adding wn units to the links that connect i and 0
  by following back the predecessors
• Add edges as long as tradeoffs are less than or
  equal to 0

50
Session 5 Assignment

• Read Cahn, Chapter 7
• Do Exercises 5.3 and 6.1