Part 6. Confidence Interval Min Chen School of Computer Science and - - PowerPoint PPT Presentation
Introduction to NS-2 Part 6. Confidence Interval Min Chen School of Computer Science and Engineering Seoul National University 1 Outline Definitions Normal Distribution Confidence Interval Central Limit Theorem Error-Bar
Min Chen School of Computer Science and Engineering Seoul National University
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Definitions Normal Distribution Confidence Interval Central Limit Theorem Error-Bar An Example
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Population
The set of elements we are inteseted in
Sample
A subset of the Population
Population Mean μ
Always stands for the everage value
Sample Mean X
The Mean for the Sample subset
=∑ Xi N
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Variance Sample Variance Standard Deviation : Sample Standard Deviation :
2=∑ Xi− 2
N S
2=∑ Xi−X 2
N
S=S
2
=
2
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A continuous probability distribution that often
For
Probability Density Function(PDF) Cumulative Distribution Function(CDF)
2 e −x−
2
2
2
X~N ,
2
−t
2
2 dt
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Confidence Interval (CI) is a particular kind of
If Probability{c1<=µ<=c2} = 1-α Then we call (c1,c2) Confidence Interval 1-α is the Confidence Coefficient
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Central Limit Theorem (CLT) states conditions
This distribution is
X~N ,
M
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According to CLT, we can calculate the
Define Z value: Frequently used Z:
Z(90%) = 1.645 Z(95%) = 1.96 Z(99%) = 2.33
Z= X−
n
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With the value of Z, the confidence interval can
X−Z× S
M ,
XZ× S
M
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Error Bar is used on graphs to indicate the
In simulation result figures, error bar represents
The error bar in the figure are the variance of
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n1 n2 n3 n6 n7 n8 n4 n5
Random: [3,4] s
0.0 s 0.0 s
1Mb 10ms 1Mb 10ms 10Mb 1ms 10Mb 1ms UDP: Controlable Data Rate 100 ~ 500 UDP: Controlable Data Rate 100 ~ 500 13 TCP: TCP: UDP: Controlable Data Rate 100 ~ 500 step 100 UDP: Controlable Data Rate 100 ~ 500 step 100 Throughput in 5s ~ 10s Throughput in 5s ~ 10s Each simulation will be repeated for 30 times with different seeds
if {$argc != 2} { puts "Usage: ns errorbar.tcl rate_ no_" exit } #=================================== # Simulation parameters setup #=================================== set par1 [lindex $argv 0] ;# date rate for the interference flow set par2 [lindex $argv 1] ;# the number of the experiments set val(stop) 12.0 ;# time of simulation end #=================================== # Initialization #=================================== #Create a ns simulator set ns [new Simulator] #Open the NS trace file set tracefile [open out$par1-$par2.tr w] $ns trace-all $tracefile #Open the NAM trace file set namfile [open out.nam w] $ns namtrace-all $namfile 14
#=================================== # Nodes Definition #=================================== #Create 8 nodes set n0 [$ns node] set n1 [$ns node] ... set n7 [$ns node] #=================================== # Links Definition #=================================== #Createlinks between nodes $ns duplex-link $n0 $n3 10.0Mb 1ms DropTail $ns queue-limit $n0 $n3 50 ... $ns duplex-link $n3 $n4 1.0Mb 10ms DropTail $ns queue-limit $n3 $n4 50 #Give node position (for NAM) $ns duplex-link-op $n0 $n3 orient right-down ... $ns duplex-link-op $n4 $n7 orient right-down $ns duplex-link-op $n3 $n4 orient right 15
#=================================== # Agents Definition #=================================== #Setup a TCP connection set tcp0 [new Agent/TCP] $ns attach-agent $n0 $tcp0 set sink3 [new Agent/TCPSink] $ns attach-agent $n5 $sink3 $ns connect $tcp0 $sink3 #Setup a TCP connection set tcp1 [new Agent/TCP] $ns attach-agent $n1 $tcp1 set sink4 [new Agent/TCPSink] $ns attach-agent $n6 $sink4 $ns connect $tcp1 $sink4 #Setup a UDP connection set udp [new Agent/UDP] $ns attach-agent $n2 $udp set null [new Agent/Null] $ns attach-agent $n7 $null $ns connect $udp $null 16
#=================================== # Applications Definition #=================================== #Setup a FTP Application over TCP connection set ftp0 [new Application/FTP] $ftp0 attach-agent $tcp0 $ftp0 set type_ FTP set ftp1 [new Application/FTP] $ftp1 attach-agent $tcp1 $ftp1 set type_ FTP set traffic [new Application/Traffic/Exponential] $traffic set packetSize_ 1000 $traffic set burst_time_ 0.5 $traffic set idle_time_ 0 $traffic set rate_ [expr $par1*1000] $traffic attach-agent $udp 17
#=================================== # Traffic Running Time #=================================== set rng [new RNG] $rng seed 0 set RVstart [new RandomVariable/Uniform] $RVstart set min_ 3 $RVstart set max_ 4 $RVstart use-rng $rng set startT [expr [$RVstart value]] puts "startT $startT sec" $ns at 0.0 "$ftp1 start" $ns at 0.0 "$traffic start" $ns at $startT "$ftp0 start" $ns at 11.0 "$ftp0 stop" $ns at 11.5 "$ftp1 stop" $ns at 11.5 "$traffic stop" 18
#=================================== # Termination #=================================== #Define a 'finish' procedure proc finish {} { global ns tracefile namfile $ns flush-trace close $tracefile close $namfile # exec nam out.nam & exit 0 } $ns at $val(stop) "$ns nam-end-wireless $val(stop)" $ns at $val(stop) "finish" $ns at $val(stop) "puts \"done\" ; $ns halt" $ns run 19
BEGIN { Init = 0; startT = 0; endT = 0; } { Action = $1; time= $2; From = $3; to = $4; Type = $5; pktsize = $6; flow_id = $8; src = $9; dst = $10; seq_no = $11; packet_id = $12; if ( action == "r" && type == "tcp" && time>=5.0 $$ time <=10.0 && from == 4 && to == 5 ) { if(init == 0) { start_time = time; Init =1; } pkt_byte_sum += pktsize; endT = time; } } END{ time=endT-startT; throughput=pkt_byte_sum*8/time/1000; printf("%f\n",throughput); } 20
BEGIN { FS="\t"; } { ln++; throughput[ln]=$1; sum=sum+throughput[ln]; } END{ average=sum/ln; for(i=1;i<=ln;i++) { gap=throughput[ln]-average; sum2=sum2+gap*gap; } variance=sqrt(sum2/(ln-1)); confidence_interval=1.96*variance/sqrt(ln); printf("%f %f %f\n",t,average,confidence_interval); } 21
The use of parameters
awk -v t=100 -f errorbar.awk result100 >> errorbar.txt
Three columns
1 : the data rate 2 : the mean throughput 3 : the confidence interval variance
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set title "Impact of Data Rate on the Throughput" set xlabel "On-Off Flow Rate Setting (kbps)" set ylabel "Flow Throughput (kbps)" set xrange [0:600] set terminal png set output "throughput.png" plot "errorbar.txt" using 1:2:3 with errorbars 1, "errorbar.txt" with lines 1
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for($i=100; $i<=500; $i=$i+100) { for($j=1; $j<=30; $j++) { system("ns errorbar.tcl $i $j"); $f1="out$i-$j.tr"; $f2="result$i"; system("awk -f throughput.awk $f1 >> $f2"); print "\n"; } print "\n"; } for($i=100; $i<=500; $i=$i+100) { $f1="result$i"; $f2="errorbar.txt"; system("awk -v t=$i -f errorbar.awk $f1 >> $f2"); print "\n"; } system("gnuplot errorbar.gpl"); 24
Grant the privilege to the script file
Run the script
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