Introduction to Network Design

e 2 Acknowledgement Edward Chow Robert Cahn

e 3 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

e 4 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.

e 5 Example 1 Four designs for a network design problem

e 6 Cheap Network (by Intrepid)

e 7 Messy Network

e 8 Rank Designs by Attributes

e 9 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.

e 10 Compare Designs

e 11 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

e 12 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

e 13 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

e 14 Public Switched Telephone Network Solution

e 15 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$/min*65/3day=2600$

e 16 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.

e 17 Design Principle 2.1 Good network designs tend to have many well- utilized components.

e 18 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?

e 19 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

e 20 Famous 2 camel hump Telephone Traffic Daily Pattern Traffic measured in Erlangs.

e 21 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%?

e 22 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/hr H=5 min/call =1/12 hr/call  =1/H=12 calls/hr = 0.2 calls/min E=  =(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/min E=  =12/12=1 Erlang.

e 23 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.

e 24 M/M/2 Queue

e 25 Loss with m Lines (m servers, no queue) A: Arrive Rate; D: Departure Rate; E=A/D AP k-1 =kDP k  P k =E/k * P k-1

e 26 Erlang-B Function

e 27 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.

e 28 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.

e 29 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

e 30 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

e 31 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.

e 32 2 nd Leased Line Saving For busy hours, the 2 nd 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 3 rd leased line adds adds up to $225.

e 33 Off-Peak Analysis of 3 rd 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 1 st 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 3 RD leased line during off-peak hours =(0.0643)*$1560=$100.25/month. $ $143=$243.25> $225  justified!

e 34 Final Design

e 35 Cost of Final Design 2PBX’ 3 leased lines 4 PSTN lines $ $ =$ /month saving