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TCOM 540

Network Optimization: Routing, Flow Management, Capacity Modeling

Dr. John G. Leigh

jleigh@mitretek.org

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Introduction• Course Objectives

– Illustrate techniques and approaches appropriate for designing different types of networks

– Illustrate ways of discriminating between good and bad network designs

– Provide basis for effective communication with users, network designers, and telecommunications vendors

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Introduction

• Text: Wide Area Network Design by Robert S. Cahn, Publ. Morgan Kaufmann, ISBN 1-55860-458-8

• Other supplementary readings

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Introduction (2)

• Approximate schedule for TCOM 540– Week 1 – Basic network design principles– Week 2 – Some theory – graphs, trees, and tours; basic

design algorithms– Week 3 – Importance of data– Week 4 – Traffic and cost generators– Week 5 – Access and backbones– Week 6 – Capacity, routing and reliability (TCOM 540

term paper due if applicable)– Week 7 – TCOM 540 final

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Introduction (3)

• Evaluation weightings– Homework 25%– Term paper/project 25%– Finals 30%– Class Participation 20%

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Network Optimization …

• Is generally not possible …– Conflicting objectives– Combinatorial explosion defeats exact solutions– Inadequate /inaccurate information– Rate of change, especially for data networks

• Usually have to settle for a “pretty good” design

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Conflicting Objectives

• Cost

• Performance

• Reliability

• Trade-offs are inevitable!

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Combinatorial Explosion

• Number of possible pairwise interconnections between n nodes is

N = 0.5*n*(n-1) = O(n2)

• Complexity of overall network design problem is O(2N)

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Inadequate/Inaccurate Information

• Traffic data can be hard to get– Traffic flows may not be measured– Carrier may not be willing to provide data (it

means work for him)

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Rate of Change

• “Best” network today may not be best tomorrow– Traffic growth and changes– Price changes– Technology changes

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Types of Networks

• Circuit-switched– Also called connection-oriented

• Connectionless– Packet, frame, or cell switched

• Dedicated– Circuits permanently established (“nailed up”)

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Circuit-Switched Networks

• Connections or circuits established for each call

• Resources are released when call is completed

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Connectionless Networks

• Packets of data are routed independently– Packet Switched, Frame Relay, Asynchronous

Transfer Mode

• However, Permanent Virtual Circuits may be set up

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Dedicated Networks

• Circuits are permanently established using dedicated resources– No call set-up time, very low latency

• User decides what/how/when to transmit - voice, data, ...

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Example of Trade-Offs

Design Cost (k$/mo)

Delay (ms)

Reliability

Cheap 131 92 0.989

Mesh 142 126 0.998

High Perf 157 42 0.995

Compromise 139 133 0.992

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Criteria Measurement - Cost

• Commitment (size and duration)

• Lease vs. buy

• Provision for expansion (flexibility)

• Choice of provider (where competition exists)

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Criteria Measurement - Delay

• Single parameter inadequate to describe a distribution

• Measurement– User may inject test packets - requires diligence– Or rely on provider’s data

• Delay may depend on traffic characteristics - e.g., time of day

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Criteria Measurement - Reliability

• Measurement of infrequent events

• May have to rely on provider to collect data– User may only notice that a circuit is down if he

tries to use it

• Single-point measurement inadequate to describe a probability distribution (e.g., lots of short outages vs. one long one)

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Circuit-Switched Two-Location Problem

• Two locations (A and B), 200km apart

• 5 employees in A, 10 in B

• Assume– Each employee calls other site 4 times x 5 mins.

per day– Each employee calls same site 10 times x 3

mins. per day

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Example Unit Costs

Item Cost

Line to PSTN $25/mo

Local Call $0.05/min

LD Call $0.40/min

PBX $1000 = $60/month

Dedicated Circuit $225/mo

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Example Total Costs

Item Cost Basis

Line Charges $375/mo 15 x $25

Local Calls $487.50/mo 150 calls x 3 mins x 21.6667 days x $0.05

Long Distance $2600/mo 60 calls x 5 mins x 21.6667 days x $0.40

Total $3462.50/mo

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Phone Utilization

Type of Call At A At B

Local, out 5 empl x 10 calls x 3 mins = 150 min

10 empl x 10 calls x 3 mins = 300 min

Local, in 5 empl x 10 calls x 3 mins = 150 min

10 empl x 10 calls x 3 mins = 300 min

Long Distance, out

5 empl x 4 calls x 5 mins = 100 min

10 empl x 4 calls x 5 mins = 200 min

Long Distance, in

200 min 100 min

Total 600 min/5 phones = 120 mins = 25%

900 min/10 phones = 90 mins = 18.75%

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Add PBXs

• Local calls cost $487.50/month

• All within same building!

• Add PBXs at $120/mo

PSTNPBX PBX5 phones...

.

.

. 10 phones

A B

5 10

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Delete Unnecessary Trunks

• Can delete 5 lines at B– Since these are now used only for long

distance, and A has only 5 phones …

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Traffic Distribution and Measurement

• Traffic peaks around 11 am and 2 pm• Assume 20% of traffic in “busy hour”• (Voice) traffic is measured in Erlangs

– Erlangs = arrival rate/departure rate

– E.g., if calls arrive at 2 per minute and hold for 3 minutes, then:

• Arrival rate = 2 per minute

• Departure rate = 0.3333 per minute

• Traffic = 2/(0.3333) = 6 Erlangs

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Traffic Parameters

• In the example, we had 300 call mins per day– So 0.2 x 300 = 60 call mins are in the busy hour– Each call is 5 mins long, so 12 calls arrive per

hour– That is 0.2 calls per minute arrival rate

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Traffic Parameters (2)

• Assume we have 5 lines – So there can be 0, 1, 2, 3, 4, or 5 calls present– Departure rate is no. of calls/call duration– That is n/5 calls per minute departure rate– Note – if a call arrives when all lines are busy it

is lost – this is called “blocking”

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Traffic Parameters (3)

• Define Pn = probability there are n calls in the system, n = 0, 1, …, 5

• P1 = P0; P2 = P1/2; P3 = P2/3; P4 = P3/4; P5 = P4/5• So Pn = P0/n!

0 1 2 3 4 5

0.2 0.2 0.2 0.2 0.2

0.2 0.4 0.6 0.8 1.0

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Sizing Long Distance Link

• Long distance link is sized so that desired blocking is not exceeded

• With 5 lines, P5 = blocking probability– P5 = 0.31%

• With 4 lines, blocking probability would be 1.54%

• Lines may be dedicated or dial up

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Traffic Carried by Lines

No. of Lines

Blocking Carried Fraction on Last Line

1 0.5 0.5 0.5

2 0.2 0.8 0.3

3 0.625 0.9375 0.1325

4 0.015 0.986 0.0475

5 0.003 0.997 0.012

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Simplifying Assumption – Traffic Profile

• Assume just two levels of traffic– 2 peak hours at 60 mins/hr– 6 other hours at 30 mins/hr

• Total dial costs – Peak: 60 x 2 x $0.40 x 21.6667 = $1040/month– Other: 30 x 6 x $0.40 x 21.6667 = $1560/month

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Designing the Long Distance Link

• First dedicated line carries 50% of peak traffic @ 0.5 x $1040 = $520 per month

• Cost of line is $225/month, net of access lines – makes sense to keep it

• Second line carries 30% @ 0.3 x $1040 = $312/month – keep this one too

• Third line carries 13.75% @ 0.1375 x $1040 = $143, etc.

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Designing the Long Distance Link (2)

Line Carried % Value

1 50 $520

2 30 $312

3 13.75 $143

4 4.75 $49

5 1.2 $12

• In order to justify lines 3 through 5, we must add the value of non-peak traffic carried

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Erlang Recursion

• Let B(E, n) = blocking when E Erlangs of traffic offered to n lines

• Then

B(E, n) = E*B(E, n-1)/(E*B(E, n-1) + n)

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• For off-peak hours B(0.5, 1) = 0.3333

• Value of off-peak traffic carried by line 1 is (1 – 0.3333)*$1560 = $1040/month

• Total value of traffic carried by line 1 is $520 (peak) + $1040 (off-peak)

Designing the Long Distance Link (3)

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Designing the Long Distance Link (4)

• B(0.5, 2) = 0.5*0.3333/(0.5*0.3333+2)

• Value of off-peak traffic carried by line 2 is (0.3333-0.0769)*$1560 = $400/month

• Total value of traffic carried by line 2 is $312 (peak) + $400 (off-peak) = $712

= 0.0769

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Designing the Long Distance Link (5)

• Similarly, value of traffic carried by line 3 is $143 (peak) + $100.25 (off-peak) = $243

• This is just $18 more than the $225 cost of the line

• Lines 4 and 5 fail to be justified

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Long Distance SummaryLine Peak

BlockingOffpeak Blocking

Peak $ Carried

Offpeak $ Carried

1 .5000 .3333 $520 $1040

2 .3000 .0769 $312 $400

3 .1325 .0127 $143 $100

4 .0475 .0016 $49 $17

5 .0120 .0002 $12 $3

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Final Design

Line Type Cost Value

1 Dedicated $225 $1560

2 Dedicated $225 $712

3 Dedicated $225 $243

4 and 5 Dial-up $81 $81

Total $756

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Final Design (2)

• Cost reduction from $3462.50 per month (slide 14) to $1126 per month

Item Cost per month

PBX $120

Dedicated lines $675

Access Lines $250

Long Distance Dial-up $81

Total $1126

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Comments on Voice Example

• This example is showing its age– Nobody pays $0.40/min for voice

• Large users may pay as little as $0.03/min

– Dedicated DS0 costs at $275/month may be high

– Access line charges at $25/month may be low

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Data

• Data is harder to classify than voice traffic– Many different types – email, file transfer, web

browsing, database access, …

• While voice is circuit switched, data is (usually) packet, cell, frame switched – Different data streams using the same circuit

contend for the same bandwidth

• Data is bursty – high peak to average ratio

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Contention

• Happens when two or more users want to transmit data over the link simultaneously

• Resolution by coordination or queueing

• Wide area networks generally rely on queueing

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Data (2)• Data network design principles are different

from voice– Voice likes highly-utilized links– Data hates highly utilized links

Voice Data

Fixed bandwidth Varying bandwidth (bursty)

Short calls (avg. 4-5 minutes) Often long calls

One call per link Often shares links

Very delay sensitive Varies

Tolerates some loss Varies

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Queuing Theory (1)

• Needed to understand/calculate link delays

• Store-and-forward

• Service time = packet size/link speed

• Delay determined by packet size distribution and packet arrival distribution

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Queuing Theory (2)

• Service time is N/S, where:– N = number of bits/packet– S = link speed in bits/sec

• Assume interarrival and packet length PDFs are of form c*exp(-c*x)

• Called an M/M/1 queue

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• Define = ratio of arrival rate () to service rate ()

• Average waiting time Tw = ( • Average service time Ts = 1/

• Average total time = Ts + Tw

= (1/

Queuing Theory (3)

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Queuing Theory (4)

• Note these are only valid when < 1– I.e., when arrival rate < service rate

• As approaches 1, delays get long– Practically, knee in curve about 70% utilization

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Cahn Data Network Example

• Three locations• Four types of traffic – internal email,

external email, WWW, database access• Multiple components/speeds• Make assumptions to build traffic model

– Traffic per employee– Each source can be modeled by the average

flow – law of large numbers

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Build Traffic Matrix

From/To A B C

A X (4/3)X (3/4)X

B (4/3)X (16/9)X X

C (3/4)X X (9/16)X

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Traffic in Tabular Form

FROM TO BANDWIDTH COMMENTA B 11070 Internal EmailEtc etc etc etc

•Additional consideration – need to add gateway(s) for external email

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Routing

• Network designer may have limited control over actual routing of traffic in the network– SNA (Systems Network Architecture)– OSPF (Open Shortest Path First)– RIP (Routing Information Protocol)

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Design Approaches for Data Example

• Use of average (busy hour) traffic rates to design network

• Aim for 50% link utilization, with few under-utilized links

• Start with a fully-connected design, use a drop algorithm

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Drop Algorithm1. Mark all links deletable2. Find most expensive deletable link

2a. Resolve ties by selecting link with lowest utilization

3. Delete link, redistribute traffic, resize links3a. If network is cheaper then

delete link, go to 23b. If network is not cheaper then

mark link undeletable, go to 2.

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Homework

• Read Chapters 1,2, and 3 of Cahn

• Recompute optimal network design, assuming voice costs $0.025/min, PBX costs same

• Write a paragraph discussing the implications of your result

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Homework (2)

• Go to http://netinfo.mitretek.org

• Open an account and use the SDP pricer

• Find the Year 5 MCIW costs of a DS0 link and access between 703-225 (Fairfax, VA) and 309-401 (Peoria, IL)– Use access and transport charges only– Ignore UNI (user-to-network interface) charges

and SICs (service initiation charges)

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Finally ...

• The administration has asked me to ask you to activate your GMU email accounts.

• They say this is IMPORTANT.