CS622 Page 1

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

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.

3
Example 1

• Four designs for a network design problem

4
Cheap Network (by Intrepid)
5
Messy Network
6
Rank Designs by Attributes
7
Justify the Designs

• There can be factors that decides the final
  choiceWhether 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.

8
Compare Designs
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

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.4515300 min/day
• call others in the same office 10 times/day about
  joint work, each last avg. 3 min. 10315450
  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

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

12
Public Switched Telephone NetworkSolution
13
Cost of PSTN Solution
Assume 21 2/3 work days65/3 days Local call
450min/day0.05/min65/3day487.5 Long distance
call 300min/day0.4/min65/3day2600
14
Utilization Analysis

• 5 employees at Anagon place 45min5100 min
  calls/day to Bregen
• 10 employee at Bregen place 45min10200 min
  calls/day to Anagon
• 300 min long distance calls are shared among 5
  employee at Anagon.
• That is 300min/51 hour/employee/day on long
  distance.
• For 8 hour day, each phone at Anagon is busy
  252/8? of the time. While phone at Bregen is
  busy 18.751.5/8?? Low Utilization
• Resaon Each employee at Anagon makes
  103min/day30min local call, but it will tie up
  other employees line. Assume no conference
  call. Therefore each line is 30min21hour/day is
  busy on local call.

15
Design Principle 2.1

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

16
PBX Solution
487.5/month for local calls saved With602120
amortized PBX cost, we actually save 367.5/month
Reliability degraded?! Performance?
17
Reducing Trunks at Bregen

• There can be 5 intersite simultaneous calls.
• Reduce 10 outgoing trunks at Bregen to 5.
• 25/month5125/month access fee saving.
• How can we reduce the cost further?
• Clue? Study the usage pattern

18
Famous 2 camel hump Telephone Traffic Daily
Pattern

• Traffic measured in Erlangs.

19
Erlang the Traffic Measure Unit

• Definition 2.1
• If call arrive ratel and departure ratem,
• Then the call intensity is El/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 l2 and 1/m3, E l/m
  6 Erlangs.Note that hold time (H) 1/departure
  rate H1/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?

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?
• l154 calls/8 hr 15/2 calls/hr
• H5 min/call 1/12 hr/call
• m1/H12 calls/hr 0.2 calls/min
• El/m(15/2)/1215/245/8 Erlangs.
• Assume 20 of the traffic in the busy hour. What
  is the call intensity in the busy hour?
• l60 calls/day 0.2 12 calls/hr 0.2
  calls/min
• m1/H12 calls/hr 0.2 calls/min
• El/m12/121 Erlang.

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 systems performance, specifically the
  blocking probability.

22
M/M/2 Queue
23
Loss with m Lines (m servers, no queue)
A Arrive Rate D Departure Rate
EA/D APk-1kDPk ? PkE/k Pk-1
24
Erlang-B Function
25
Calculating the Blocking

• In 2-location case, with busy hour, A0.2
  calls/min, D0.2calls/min.
• When 1 call in progress, departure rate is 0.2
  calls/min
• When 2 calls in progress, departure rate is 0.4.

26
Design Intersite Link

• Given we can tolerate x blocking, how many lines
  we actually need?
• Here E1 (busy hour). Carried loadE(1-B(E,m)).
  qifraction of load on link i.

27
Simplified Traffic Profile

• Instead of 2 camel hump traffic pattern, simplify
  it to two levels peak and off-peak.
• 60min20.4(212/3)104030min60.4(212/30156
  0

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

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 E60/601
  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 0.51040520/month
• The net equipment cost of leased line275-50
  (replaced two PSTN lines) 225/month.
• The net cost saving 520-225295/month
• It is justifiable.

30
2nd Leased Line Saving

• For busy hours, the 2nd leased line will carry
  0.3 traffic.
• Dialup cost saving 0.31040312/month.
• 312 gt 225 ? still justified.
• The third leased line only carries 0.1325 busy
  hour traffic.
• Dialup cost saving 0.13251040143/month.
• We need to see if the cost saving of off-peak
  hour usage of the 3rd leased line adds adds up to
  225.

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
  lineB(0.5,0)-B(0.5,1)1-(0.5B(0.5,0))/(0.5B(0.
  5,0)1)2/3.
• Cost saving for the 1st leased line(2/3)15601
  040/month.
• The fraction of calls carried by the 3rd leased
  lineB(0.5,2)-B(0.5,3)(1/13)-(0.5B(0.5,2))/(0.5
  B(0.5,2)1)1/13-1/790.0643.
• Cost saving for the 3RD leased line during
  off-peak hours (0.0643)1560100.25/month.
• 100.25143243.25gt 225 ? justified!

32
Final Design
33
Cost of Final Design
2PBX3 leased lines4 PSTN lines
3462.5-1129.752332.75/month saving
34
Homework 1

• Exercises 2.1 2.3For 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 2.32.5
• 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.