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### TCOM 540

Network Optimization: Routing, Flow Management, Capacity Modeling

Dr. John G. Leigh

TCOM 540/1

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

TCOM 540/1

Introduction

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

TCOM 540/1

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

TCOM 540/1

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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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

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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

TCOM 540/1

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

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Example Total Costs

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Phone Utilization

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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

TCOM 540/1

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

TCOM 540/1

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”

TCOM 540/1

Traffic Parameters (3)

0.2

0.2

0.2

0.2

0.2

- 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

0.6

0.8

1.0

0.4

TCOM 540/1

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

TCOM 540/1

Traffic Carried by Lines

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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

TCOM 540/1

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.

TCOM 540/1

Designing the Long Distance Link (2)

- 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)

TCOM 540/1

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)

TCOM 540/1

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

TCOM 540/1

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

TCOM 540/1

Long Distance Summary

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Final Design

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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

TCOM 540/1

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

TCOM 540/1

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

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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

TCOM 540/1

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)

TCOM 540/1

Queuing Theory (4)

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

TCOM 540/1

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

TCOM 540/1

Build Traffic Matrix

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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

TCOM 540/1

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)

TCOM 540/1

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

TCOM 540/1

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.

TCOM 540/1

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

TCOM 540/1

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)

TCOM 540/1

Finally ...

- The administration has asked me to ask you to activate your GMU email accounts.
- They say this is IMPORTANT.

TCOM 540/1

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