Introduction to Network Design

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Acknowledgement

• Edward Chow• Robert Cahn

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Introduction to Network Design

Network design is • Create network structure (blue print)• Decide how to allocate resource and spend moneyTwo basic questions:• How much it cost to build a usable network?• How much improvement does $x buy?Answer:• Depend on network services and components

available• We will concentrate the techniques and algorithms

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Network Evaluation

• Every network has three characteristics:– Cost– Performance– Reliability

• First we need to find agree-upon quantitative numbers.

• Based on the quantitative numbers of these characteristics, we can evaluate different design alternative by ordering them and ruling out losers.

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Example 1

• Four designs for a network design problem

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Cheap Network (by Intrepid)

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Messy Network

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Rank Designs by Attributes

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Justify the Designs

• There can be factors that decides the final choice:Whether the company is expanding

• Maybe the proposed designs are not as expected.• In outsourcing situation, you may ask for redesign• You may not have to serve as designer but as an

evaluator.

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Compare Designs

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What is more important, Performance or Cost?

•150 cashiers $13,725/month

•CEO $152,500/month

•One user my justify the building a high performance network

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Two-Location Problem

• It is called “Hello World” of Network Design.• It is undaunting yet interersting problem!• Design a network connecting two locations, 200km apart.• Anagon city with 5 employees, Bregen with 10.• Each employee

– call other site 4 times/day, avg. 5 min. each.4*5*15=300 min/day

– call others in the same office 10 times/day about joint work, each last avg. 3 min. 10*3*15=450 min/dayNote here we are not using C(10,2)+C(5,2) for the # of calls

• How can we best provide the communications between the two cities

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Cost of Network Services and Components

• Network equipment purchase is typically amortized at 3% per month.

• The PBX Private Branch Exchange would cost $60/month

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Public Switched Telephone NetworkSolution

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Cost of PSTN Solution

Assume 21 2/3 work days=65/3 daysLocal call: 450min/day*0.05$/min*65/3day=487.5$

Long distance call; 300min/day*0.4$/min*65/3day=2600$

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Utilization Analysis

• 5 employees at Anagon place 4*5min*5=100 min calls/day to Bregen

• 10 employee at Bregen place 4*5min*10=200 min calls/day to Anagon

• 300 min long distance calls are shared among 5 employee at Anagon.

• That is 300min/5=1 hour/employee/day on long distance.• For 8 hour day, each phone at Anagon is busy 25%=2/8? of the

time. While phone at Bregen is busy 18.75%=1.5/8? Low Utilization

• Resaon: Each employee at Anagon makes 10*3min/day=30min local call, but it will tie up other employee’s line. Assume no conference call. Therefore each line is 30min*2=1hour/day is busy on local call.

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Design Principle 2.1

• Good network designs tend to have many well-utilized components.

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PBX Solution

$487.5/month for local calls savedWith$60*2=$120 amortized PBX cost,

we actually save $367.5/month

Reliability degraded?!Performance?

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Reducing Trunks at Bregen

• There can be 5 intersite simultaneous calls.• Reduce 10 outgoing trunks at Bregen to 5.• $25/month*5=$125/month access fee saving.• How can we reduce the cost further?• Clue Study the usage pattern

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Famous 2 camel hump Telephone Traffic Daily Pattern

• Traffic measured in Erlangs.

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Erlang: the Traffic Measure Unit

Definition 2.1

If call arrive rate=and departure rate=,

Then the call intensity is E= Erlangs.

In honor of Danish Telephone engineer Erlang.

Example 1. Calls arrive 2 per min., and hold for an average of 3 min, then=2 and =3, E= =6 Erlangs.Note that hold time (H)= 1/departure rate; H=1/.

Apparently one line cannot handle this amount of traffic.

When a call comes and all lines are busy, the call is blocked.

How many lines can reduce the blocking probability to x%?

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Erlang Calculation

• In our 2-location case, 15 places 4 long distance calls/day, each call last avg. 5min. Assume 8 hr day

• What is the call (traffic) intensity for the day?=15*4 calls/8 hr = 15/2 calls/hrH=5 min/call =1/12 hr/call=1/H=12 calls/hr = 0.2 calls/minE==(15/2)/12=15/24=5/8 Erlangs.

• Assume 20% of the traffic in the busy hour. What is the call intensity in the busy hour?=60 calls/day * 0.2 = 12 calls/hr = 0.2 calls/min=1/H=12 calls/hr = 0.2 calls/minE==12/12=1 Erlang.

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Queueing Theory for System with Loss

• Assume a telephone system with multiple lines.– When a call comes and all lines are busy, the call

is blocked. Unlike data network, calls are not buffered or queued if lines are not available.

– Or, you can consider it is a finite queue, i.e., after queue full (line busy), further call are blocked.

How many lines can reduce the blocking probability to x% for a given traffic density?

• Queueing theory can be used analyzed the telephone system’s performance, specifically the blocking probability.

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M/M/2 Queue

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Loss with m Lines (m servers, no queue)

A: Arrive Rate; D: Departure Rate; E=A/DAPk-1=kDPk Pk=E/k * Pk-1

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Erlang-B Function

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Calculating the Blocking• In 2-location case, with busy hour, A=0.2 calls/min,

D=0.2calls/min.• When 1 call in progress, departure rate is 0.2

calls/min• When 2 calls in progress, departure rate is 0.4.

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Design Intersite Link

• Given we can tolerate x% blocking, how many lines we actually need?

• Here E=1 (busy hour). Carried load=E(1-B(E,m)). qi=fraction of load on link i.

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Simplified Traffic Profile

• Instead of 2 camel hump traffic pattern, simplify it to two levels: peak and off-peak.

• 60min*2*0.4*(21+2/3)=104030min*6*0.4*(21+2/30=1560

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Reduce Cost by Using Leased Lines

• Instead of charged by # of calls, pay monthly cost.• The leased line costs $275/month replacing two

PSTN lines, one on each end, for a total of $50.• The calls placed on the leased line save $0.4/min.• Strategy: Place calls on leased lines first.• Question: How many released lines should we use?• Let us figure out the cost saving of each leased line.• First focus on busy-hour analsys

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Busy Hours Analysis for Leased Line Saving

• What is the value of busy-hours traffic carried by a single leased line?

• With 60min/hour usage, traffic is E=60/60=1 Erlang.• From table 2.3, the fraction of calls on a single leased

line is 0.5. The other half got blocked.• Saving on dialup cost: 0.5*$1040=$520/month• The net equipment cost of leased line=$275-$50

(replaced two PSTN lines)= $225/month.• The net cost saving = $520-$225=$295/month• It is justifiable.

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2nd Leased Line Saving

• For busy hours, the 2nd leased line will carry 0.3 traffic.

• Dialup cost saving = 0.3*$1040=$312/month.• $312 > $225 still justified.• The third leased line only carries 0.1325 busy hour

traffic. • Dialup cost saving = 0.1325*$1040=$143/month.• We need to see if the cost saving of off-peak hour

usage of the 3rd leased line adds adds up to $225.

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Off-Peak Analysis of 3rd Leased Line

• Off-Peak hours traffic = 30/60= 0.5 Erlang.• The fraction of calls carried by the first leased line

=B(0.5,0)-B(0.5,1)=1-(0.5*B(0.5,0))/(0.5*B(0.5,0)+1)=2/3.• Cost saving for the 1st leased

line=(2/3)*$1560=$1040/month.• The fraction of calls carried by the 3rd leased line

=B(0.5,2)-B(0.5,3)=(1/13)-(0.5*B(0.5,2))/(0.5*B(0.5,2)+1)=1/13-1/79=0.0643.

• Cost saving for the 3RD leased line during off-peak hours =(0.0643)*$1560=$100.25/month.

• $100.25+$143=$243.25> $225 justified!

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Final Design

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Cost of Final Design

2PBX’3 leased lines4 PSTN lines

$3462.5-$1129.75=$2332.75/month saving