TCOM 540/1 1

TCOM 540

Session 5

TCOM 540/1 2

Agenda

• Quiz

• Review Session 3 assignments

• Access and backbone design

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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

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Access and Backbone (2)

Access

Backbone

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Access and Backbone (3)

IXC1 POP

IXC2 POP

LECCentralOffice

LocalLoops

IXC1 Backbone

IXC2 BackboneAccess lines to IXCs

To otherLEC COs(often SONET ring)

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RedundancyIXC1 POP2

IXC2 POP

LECCentralOffice1

LocalLoops

IXC1 Backbone

IXC2 Backbone

Access lines to IXCs

To otherLEC COs

Your Site

LECCO2

IXC2 POP

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Local Access Costs Are Significant• Relative cost of local access has been increasing

Source: Bureau of Labor Statistics

0.020.0

40.060.0

80.0100.0

120.0140.0

160.0180.0

200.0

83 85 87 89 91 93 95 97 99

Year

Local Residential

Interstate Residential

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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

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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 (< 10% of market) – but this fraction is increasing

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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?

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Local Access Design ExampleFr. To BW

1 2 12000

1 3 11000

1 4 9000

1 5 13000

1 6 8000

1 7 6000

1 2 3 4 5 6 7

1 400 1929 1985 1328 667 2112 1629

2 400 2814 2168 2031 1526 1225

3 400 1483 2044 3243 2714

4 400 1427 2551 2024

5 400 2136 1689

6 400 1327

7 400

Traffic (symmetric)(Note: Site 1 is hub)

Costs (symmetric)

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Local Access Design Example (2)

• Use some nodes as concentrators

$1929

$1985

$1328 $667

$2112

$1629

1526

1225

1929

6671328

1985

1225 1327

1629

1328

1483

667

$9650 $8660 $7659 (OPTIMAL)

1

2

7

6

5

4

3

1

2

7

6

5

4

3

1

2

7

6

5

4

3

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Local Access Design Example (3)• If traffic grows by 50%, links (1,4) and

(1,7) must be doubled

1225 1327

3258

2656

1483

667

$10616

1

2

7

5

4

3

1327

1629

1328667

$8865 (OPTIMAL)

1

2

7

6

5

4

3

6

1929

1985

IMPROVEMENT

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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

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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)

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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

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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

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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

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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??

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Traffic Scale

• Depends on relationship of node size to smallest desired link size

– Smallest link size determined by factors such as packet size/delay

1. Traffic from access node much smaller than smallest link we wish to use

- Create access trees to group sites efficiently

- Capacitated spanning trees

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Traffic Scale (2)

2. Traffic from access node comparable to smallest link

- Low speed link to hub vs. concentrator part way to hub

- Concentrator placement problem

3. Traffic from access node significantly larger than smallest link

- Multiple lower speed links vs. single higher speed link

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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?

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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 = 0.3– Hundreds of designs tested

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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.

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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

iTj wi < W

trees l Links Cost(end1l, end2l) is a minimum

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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) = minj[Cost(Ni,Nj)] –Cost (Comp(Ni),N0)

• Computes cost of linking to neighbor vs. cost of going to center

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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)) < W– Algorithm limitation – often desirable to

increase link capacities in real life

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Esau-Williams Algorithm (3)

N4

N3

N1

N2

N0

Scanning node N3:

1. Examine costs of these links

2. Compare with cost of this link

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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)

-100-200

-700 -400

-1000

0

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Heaps (3)

-400-200

-700 -100

-1000

0-100-200

-700 -400

-1000

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

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E-W Implementation (2)

• Let’s say top of heap for a node is –1000

-100-200

-700 -400

-1000

inf

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E-W Implementation (3)

• Say this is infeasible – change value to inf

-100-200

-700 -400

inf

inf

But now this is not a heap any more - “bubble down” offending node

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E-W Implementation (4)

• Swap with best child

-100-200

inf -400

-700

inf -100inf

-200 -400

-700

inf

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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

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E-W Implementation (6)

Algorithm1. Top of global heap is node n1, which has the best tradeoff2. Go to heap of N1 and find partner n2 which appears to have best tradeoff3. Remove n2 from node heap4. Find components of n1 and n25. Tricky bit: When we start this loop, all tradeoffs are correct, but we do not update

all tradeoffs as we go along 1. Wait until an n1, n2 pair appears, then check tradeoff 2. If tradeoff is incorrect, reset and push pair back into heap

6. If tradeoff is correct, check if merge of components is feasible1. If feasible, merge

7. Update global heap with new n1 tradeoff

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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

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Esau-Williams Failure Rate

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0 20 40 60 80

No. of Sites

Fa

ilure

ra

te, %

E-W

Four sites per line

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Sharma’s Algorithm

• E-W sometimes introduces crossings– We know the design can be improved if

crossings are removed

• Sharma’s algorithm builds MSTs in “wedges” from the central node

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Sharma’s 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 setw(node) > W– Start next set with that node

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Sharma’s Algorithm (3)

• Sharma’s algorithm builds Capacitated Minimum Spanning Trees without crossings– So long as no set has more than half the pie

(i.e.,

• However, Sharma is generally inferior to E-W– Poorer creditability– Higher cost

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Multiple Link Speeds

• In real problems, almost always have a variety of link speeds to choose from– DS0 @ 64kbps– N x DS0– T1 @1.5 Mbps– T3 @ 45 Mbps– Etc.

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Multiple Link Speeds (2)

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

Root

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Predecessor Function

• A tree T rooted at node Root can be represented uniquely by a predecessor function pred:V V on the set of vertices:– pred(Root) = Root– No other node is its own predecessor– For any node N there is an n>0 such that

predn(N) = Root

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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 > 0

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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

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Multispeed CMST Definition (2)

• Then the multispeed CMST problem is to find the tree rooted at N0 with link assignments such that

ancestors(N) w(i) < WLink(N, pred(N))

And Linksc(end1L, end2L, typeL) is minimized

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MSLA Algorithm for Multispeed CMSTs

1. Assign each node n the smallest link l to connect it to root. Compute spare_capacity(n) = Wl – wn

2. 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

3. Add edges as long as tradeoffs are less than or equal to 0

TCOM 540/1 51

Session 5 Assignment

• Read Cahn, Chapter 7

• Do Exercises 5.3 and 6.1