1. Introduction to Network Design
Network design is
Create network structure (blue print)
Decide how to allocate resource and spend money
Two 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
11/20/2018
C. Edward Chow

2. 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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C. Edward Chow

3. Example 1 Four designs for a network design problem 11/20/2018
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4. Cheap Network (by Intrepid)
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5. Messy Network
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6. Rank Designs by Attributes
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7. 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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C. Edward Chow

8. Compare Designs
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9. 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
11/20/2018
C. Edward Chow

10. 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/day Note 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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C. Edward Chow

11. 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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C. Edward Chow

12. Public Switched Telephone Network Solution
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C. Edward Chow

13. Cost of PSTN Solution Assume 21 2/3 work days=65/3 days
Local 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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C. Edward Chow

14. 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.
11/20/2018
C. Edward Chow

15. Design Principle 2.1
Good network designs tend to have many well-utilized components.
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C. Edward Chow

16. PBX Solution $487.5/month for local calls saved
With$60*2=$120 amortized PBX cost, we actually save $367.5/month
Reliability degraded?!
Performance?
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C. Edward Chow

17. 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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18. Famous 2 camel hump Telephone Traffic Daily Pattern
Traffic measured in Erlangs.
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19. Erlang: the Traffic Measure Unit
Definition 2.1
If call arrive rate=l and departure rate=m,
Then the call intensity is E=l/m Erlangs.
In honor of Danish Telephone engineer Erlang.
Example 1. Calls arrive 2 per min., and hold for an average of 3 min, then l=2 and 1/m=3, E= l/m =6 Erlangs. Note that hold time (H)= 1/departure rate; H=1/m.
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%?
11/20/2018
C. Edward Chow

20. 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?
l=15*4 calls/8 hr = 15/2 calls/hr
H=5 min/call =1/12 hr/call
m=1/H=12 calls/hr = 0.2 calls/min
E=l/m=(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?
l=60 calls/day * 0.2 = 12 calls/hr = 0.2 calls/min
E=l/m=12/12=1 Erlang.
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C. Edward Chow

21. 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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C. Edward Chow

22. M/M/2 Queue
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23. Loss with m Lines (m servers, no queue)
A: Arrive Rate; D: Departure Rate; E=A/D
APk-1=kDPk  Pk=E/k * Pk-1
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C. Edward Chow

24. Erlang-B Function
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25. 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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C. Edward Chow

26. 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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C. Edward Chow

27. 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)= min*6*0.4*(21+2/30=1560
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C. Edward Chow

28. 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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C. Edward Chow

29. 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 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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C. Edward Chow

30. 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 busy hour traffic.
Dialup cost saving = *$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.
11/20/2018
C. Edward Chow

31. 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=
Cost saving for the 3RD leased line during off-peak hours =(0.0643)*$1560=$100.25/month.
$ $143=$243.25> $225  justified!
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C. Edward Chow

32. Final Design
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33. 2PBX’ 3 leased lines 4 PSTN lines
Cost of Final Design
2PBX’ 3 leased lines 4 PSTN lines
$ $ =$ /month saving
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C. Edward Chow

34. Homework #1
Exercises 2.1 & 2.3 For Exercise 2.1, design for handle busy hour traffic. Indicate how many lines will be needed and how many of them should be leased lines. You need to generate tables similar to Table 2.3 and 2.5 to guide your decision. Hint: You may want to use spreadsheet to calculate Tables 2.3&2.5
Exercise A: Use Erlang-B function to decide # of modems for an ISP. Assume that it has 1000 customers, each connects once for 1 hour during the day. If the blocking probability of 0.2 is acceptable, how many modems are needed in the modem pool? Note that this is 24x7 operation.
11/20/2018
C. Edward Chow