TCOM 540

1
TCOM 540

• Network Optimization Routing, Flow Management,
  Capacity Modeling
• Dr. John G. Leigh
• jleigh_at_mitretek.org
• jgleigh_at_mindspring.com

2
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

3
Introduction

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

4
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

5
Introduction (3)

• Evaluation weightings
• Homework 30
• Term paper/project 30
• Finals 30
• Class Participation 10

6
Network Optimization

• Is generally not possible
• Conflicting objectives
• Combinatorial explosion defeats exact solutions
• Inadequate /inaccurate information
• Rate of change, especially for data networks
• Generally have to settle for a pretty good
  design

7
Conflicting Objectives

• Cost
• Performance
• Reliability
• Trade-offs are inevitable!

8
Combinatorial Explosion

• Number of possible pairwise interconnections
  between n nodes is
• N 0.5n(n-1) O(n2)
• Complexity of overall network design problem is
  O(2n)

9
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)

10
Rate of Change

• Best network today may not be best tomorrow
• Traffic growth and changes
• Price changes

11
Types of Networks

• Circuit-switched
• Also called connection-oriented
• Connectionless
• Packet, frame, or cell switched
• Dedicated
• Circuits permanently established (nailed up)

12
Circuit-Switched Networks

• Connections or circuits established for each call
• Resources are released when call is completed

13
Connectionless Networks

• Packets of data are routed independently
• Packet Switched, Frame Relay, Asynchronous
  Transfer Mode
• However, Permanent Virtual Circuits may be set up

14
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, ...

15
Example of Trade-Offs
16
Criteria Measurement - Cost

• Commitment (size and duration)
• Lease vs. buy
• Provision for expansion (flexibility)
• Choice of provider (where competition exists)

17
Criteria Measurement - Delay

• Single parameter inadequate to describe a
  distribution
• Measurement usually relies on injecting test
  packets - requires diligence by user
• Delay may depend on traffic characteristics -
  e.g., time of day

18
Criteria Measurement - Reliability

• Requires 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)

19
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

20
Example Unit Costs
Item Cost
Line to PSTN 25/mo
Local Call 0.05/min
LD Call 0.40/MIN
PBX 2000 120/month
Dedicated Circuit 275/mo
21
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
22
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
23
Add PBXs

• Local calls cost 487.50/month
• All within same building!
• Add PBXs at 120/mo

PSTN
PBX
PBX
5 phones
5
10
10 phones
A
B
24
Delete Unnecessary Trunks

• Can delete 5 lines at B
• Since these are now used only for long distance,
  and A has only 5 phones

25
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

26
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

27
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

28
Traffic Parameters (3)
0.2
0.2
0.2
0.2
0.2
0
1
2
3
4
5
0.2
0.6
0.8
1.0
0.4

• Define Pn probability there are n calls in the
  system, n 0, 1, , 6
• P1 P0 P2 P1/2 P3 P2/3 P4 P3/4 P5
  P4/5
• So Pn P0/n!

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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

32
Designing the Long Distance Link

• First dedicated line carries 50 of peak traffic
  _at_ 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 _at_ 0.3 x 1040
  312/month keep this one too
• Third line carries 13.75 _at_ 0.1375 x 1040
  143, etc.

33
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

34
Erlang Recursion

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

B(E, n) EB(E, n-1)/(EB(E, n-1) n)
35
Designing the Long Distance Link (3)

• 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)

36
Designing the Long Distance Link (4)

• B(0.5, 2) 0.50.3333/(0.50.33332)
• 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

38
Final Design
Line Type Cost Value
1 Dedicated 275 1560
2 Dedicated 275 712
3 Dedicated 275 243.25
4 and 5 Dial-up 184.75 84.75
Total 1009.75
39
Final Design (2)

• Cost reduction from 3462.50 per month (slide 14)
  to 1129.75 per month

Item Cost per month
PBX 120
Dedicated lines 825
Access Lines 1100
Long Distance Dial-up 84.74
Total 1129.75
40
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

41
Homework Exercise

• Go to http//www.netinfo.mitretek.org
• Open an account and use the SDP pricer
• Find the Year 3 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)

42
Homework Exercise (2)

• Recompute optimal network design, assuming voice
  costs 0.025/min, PBX costs same
• Write a paragraph discussing the implications of
  your result

43
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

44
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

45
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
46
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

47
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 cexp(-cx)
• Called an M/M/1 queue

48
Queuing Theory (3)

• Define r ratio of arrival rate (l) to service
  rate (m)
• Average waiting time Tw (r/m)/(1- r)
• Average service time Ts 1/ m
• Average total time Ts Tw
• (1/m)/(1-r)

49
Queuing Theory (4)

• Note these are only valid when r lt 1
• I.e., when arrival rate lt service rate
• As r approaches 1, delays get long
• Practically, knee in curve about 70 utilization

50
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

51
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
52
Traffic in Tabular Form

• FROM TO BANDWIDTH COMMENT
• A B 11070 Internal Email
• Etc etc etc etc
• Additional consideration
• need to add gateway(s) for external email

53
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)

54
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

55
Drop Algorithm
1. Mark all links deletable 2. Find most
expensive deletable link 2a. Resolve ties by
selecting link with lowest utilization 3.
Delete link, redistribute traffic, resize
links 3a. If network is cheaper then delete
link, go to 2 3b. If network is not cheaper
then mark link undeletable, go to 2.
56
Homework

• Read Chapters 1,2, and 3 of Cahn