Tesis de Maestría - Colibri

PEDECIBA Informática

Instituto de Computación – Facultad de Ingeniería Universidad de la República

Montevideo, Uruguay

Tesis de Maestría en Informática

Demos connectivity model (DCM)

Martín Giachino

2013

Martín Giachino Demos connectivity model (DCM) ISSN 0797-6410

Tesis de Maestría en Informática Reporte Técnico RT 13-02 PEDECIBA Instituto de Computación – Facultad de Ingeniería Universidad de la República. Montevideo, Uruguay, 2013

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!" #$%&'&() *$+,'-

!" #$%%$&'() '* + *,--+./ $# 0!" 1"*0 2($&( -$1'%'0/ -$3"%*4 0+2'() +* ),'3" 0!" 5%+**'65+0'$(

3"*5.'1"3 '( 7"50'$( 89:989 !'* 3"5'*'$( 3$"* ($0 '-;%/ %$** $# )"(".+%'0/4 +(3 5$,%3 !+<" 1""(

5!$*"( +(/ $0!". 5%+**'65+0'$(9 =!'5! &'%% 1" ,*"3 &+* 5!$*"( 1"5+,*" '( 0!'* 5%+**'65+0'$( '* -$."

'(0,'0'<" 5+0")$.'>+0'$( $# *$-" -$3"%*9

!"!# $%&'() *%+,' )(*-.-/0 )(',.+

?$3"%* '(5%,3"3 '( 0!'* 5+0")$./ +." +%*$ 5+%%"3 +* "(0'0/@-$3"%* +(3 !+<" *0$5!+*0'5 5!+.+50".'*0'5*4

1"5+,*" 0!"/ 5!$$*" 0!" 3'."50'$( +(3 *;""3 '( + .+(3$- &+/ .")+.3%"** $# ;."<'$,* -$<"-"(0*4

*$ 0!"/ +." -"-$./%"** -$3"%*9

!"!#!# $%&'() *%+, )(-.+./0 )('1+

!'* '* 0!" *'-;%"*0 -$3"%4 &!'5! &+* 3"6("3 1/ A'(*0"'(4 +(3 '0 '* +%*$ 2($&( ,(3". 0!" (+-"

$# !"#$%&$ '"(%"$9 B00"-;0* 0$ .";."*"(0 0!" -$<"-"(0 $# -+(/ "(0'0'"* $# (+0,."4 #$. "C+-;%"

"-,%+0'() 0!" ,(;."3'50+1%" -$<"-"(0 $# ;+.0'5%"* $# ;!/*'5*9

!" .,%"* 0!+0 )$<".( 0!" -$<"-"(0 $# "+5! ($3" +." +* #$%%$&*D

A+5! ($3" 5!+()"* '0* *;""3 +(3 3'."50'$( +0 5$(*0+(0 '(0".<+%* $# 0'-" t4 $. &!"( + 6C"33'*0+(5" d !+* 1""( 0.+<"%"3 E*"" F'),." 89G $( ;+)" HI +(3 F'),." 89J $( ;+)" HH ."*;"5@0'<"%/K9

!" ("& ($3" 3'."50'$( θ(t) '* $10+'("3 .+(3$-%/ +(3 ,('#$.-%/ '( 0!" '(0".<+% (0, 2π]

B(3 0!" ("& ($3" <"%$5'0/ v(t) '* $10+'("3 .+(3$-%/ +(3 ,('#$.-%/ '( 0!" '(0".<+% [0, Vmax]

L0!".* -$3"%* 3".'<"3 #.$- )&$*"' +&,- +." ./4 0/4 1/2 +(3 */ #&,-3 +(3 )&$*"' +&45

6"%$( 7"*8,2 7&!-"9%&$ +&46"%$( 7"*8, :7+;< $. +33'0'$( $# +00.+50'$( ;$'(0* MHGN9 ?$." 3"0+'%*

5$,%3 1" #$,(3 '( =0>2 ?@AB

!"!#! $%&'() *%02(.&/ )(-.+./0 )('1+

!" )&$*"' +&46"%$( 7"*8, :)+;< M88N -$3"% '* $(" $# 0!" -$*0 *'-;%" +(3 &'3"%/ ,*"3 #$.

-$1'%" +3@!$5 *'-,%+0'$(*9 O0 3"*5.'1"* -$<"-"(0 ;+00".(* $# '(3'<'3,+% ($3"* &'0!$,0 +(/ ."@

*0.'50'$(* +1$,0 0!"'. 3"*0'(+0'$(4 3'."50'$( +(3 <"%$5'0/9 ?$<"-"(0* $# ($3"* +." )$<".("3 1/ 0!'*

*"0 $# .,%"*D

O('0'+%%/4 ($3"* +." *;."+3 $( 0!" *'-,%+0'$( +."+ ,('#$.-%/9

P$3"* +." '( 0&$ ;$**'1%" *0+0"*4 ;+,*"3 +(3 -$<'()9

O( ;+,*"3 *0+0"4 ($3" ."-+'(* '( 0!" *+-" %$5+0'$( #$. + 5".0+'( 0'-" Tpause9 P$0" 0!+0 &!"(

Tpause = 0 '0 5$.."*;$(3* 0$ 0!" )&$*"' +&,- 7"*8, E*"" 89G9H9HK9

=!"( Tpause '* 6('*!"34 ($3" .+(3$-%/ *"%"50 + %$5+0'$( +* '0* ("& 3"*0'(+0'$(4 +(3 <"%$5'0/

'* *"%"50"3 '( 0!" *+-" &+/ #.$- [0, Vmax] '(0".<+%9 B#0". 0!+04 ($3" 1")'(* 0$ -$<" 0$ 0!"("& 3"*0'(+0'$( &'0! 0!" *"%"50"3 <"%$5'0/9

L(5" 0!" ($3" ."+5!"3 0!" 3"*'."3 %$5+0'$(4 0!" ;.$5"** 1")'(* +)+'(9

Q

vmin = 0

[0, 2π]

[vmin, vmax]

[0, π]

!"#$%& '( )$"$% *+ $!% "&$

!"#$% &'() *+%$,"% -%!"./0$ 1%$2%-3,"% +4 3!5% 63,7%- 8$05 !"#9'

!"!#!" $%&'() *(+',+-(.&/ )(0.1./2 )(',1

:$0104%; !- <=>?@ !3 !4 , 50;!A2,3!0- 08 $%& ,-;@ ,3 3.% 4,5% 3!5%@ !3 .,4 4!5!B,$!3!%4 C!3. $'('

D.% ;!E%$%-2% 08 3.!4 50;%B C!3. $%41%23 30 $%& !4 3.,3 3.% 104!3!0- !4 2.04%- 8$05 3.% /0$;%$

,$%, !-43%,; 08 8$05 3.% C.0B% ,$%,@ ,-; !34 5,!- 0/F%23!+% !4 30 43#;G -0;% 104!3!0- ;!43$!/#3!0-

/%3C%%- 3.%5 6!- 4H#,$% ,-; 2!$2#B,$ ,$%,49'

*4 , $%4#B3 08 3.,3 C0$7@ ,#3.0$4 20-2B#;% 3.,3 -0;% ;!43$!/#3!0- 08 3.!4 -%C 50;%B !- 2!$2#B,$

,$%,4@ -03 !- 4H#,$% ,$%,4@ 1$%4%-34 , "00; #-!80$5 -0;% ;!43$!/#3!0-@ ,4 !3 20#B; /% 4%%- !- !"#$%

&'== 0- 1,"% =( ,-; !"#$% &'=I 0- 1,"% =J'

!"!#!3 4156/,+,' )(0.1./2 )(',1

K,4%; 0- 3.% 8,23 3.,3 5,-G 402!,B@ -,3#$,B@ ,-; /!0B0"!2,B -%3C0$74 ,$% 2.,$,23%$!L%; /G )*+,-./0--

123-0.,+3 *244-*567658 96)506:;5624 ,-; , 8%C ;%-4%BG 101#B,3%; -0;%4 7-0C- ,4 <;:) <M@ =&J?@

,#3.0$4 !- <NM? 1$0104%; 3.% =,;)5-0-9 (2:6,658 (29-, >=((?' D.% 5,!- "0,B4 08 3.!4 50;%B !4

30 ,+0!; 3%510$,B ,-; 41,3!,B 1$0/B%54 1$%4%-3 !- 03.%$ $,-;05 50;%B4@ B!7% 3.% -0-O#-!80$5

;!43$!/#3!0- 1.%-05%-0-@ C.!2. 5,7%4 -0;%4 50+% 2B04%$ 30 .!".BG 20--%23%; -0;%4@ 40 2B#43%$%;

-0;%4 ,$0#-; .#/4 ,$% %P.!/!3%;' Q- 3.!4 C,G@ =(( !4 ;%4!"-%; 30 1044%44 20-4!43%-3 43%,;GO43,3%

50/!B!3G 1,$,5%3%$4'

=(( 20-4!434 08 3C0 1.,4%4@ @0235< ,-; 0-36064@ 6/,4%; 0- 3.% 1$!-2!1B% 08 1$%8%$%-3!,B ,3O

3,2.5%-39' Q- 3.% "$0C3. 1.,4%@ 3.% 2051B%3% 4!5#B,3!0- ,$%, !4 B0"!2,BBG ;!+!;%; !- 4#/,$%,4'

*83%$ 3.,3@ -0;%4 ,$% B02,3%; !-!3!,BBG /,4%; 0- , 1$0/,/!B!3G +,B#%@ 30 5,7% -0;% 50+%4 30 2.004%

C!3. "$%,3%$ 1$0/,/!B!3G@ , 4#/ ,$%, .!".BG 101#B,3%; 3.,- , 41,$4% 0-%@ ,-; 0-2% !3 .,4 , 4#/ ,$%,@

$,-;05BG 4%B%234 , 104!3!0- 0- !3 64%% RH#,3!0- &'=9'

=&

!"#$%& '( )$"$% *+ $!% "&$

!"#$% &'() *!+, -$%.,."% /0' 01%%2 /0' 1.#0% 3!4% 53.,%+ 6$74 !"#8'

!"#$% &'9) :%+0!3; 67$ 3<% $.+274=>.;17!+3 472%? 53.,%+ 6$74 @ABC8

ϕi =(ki + 1)α

∑

j(kj + 1)α5&'D8

where :

ϕi is the probability that a node selects subarea si as destination

α is the clustering exponent

ki is then umber of nodes in subarea si

si is a subarea with 0 3< 1<.0% !0 F+!0<%2G ϕi !0 H.?H#?.3%2 .+2 !3 >!?? +73 -% H<.+"%2 .+;47$% !+ 3<%

$%&'$'() 1<.0% #1 37 3<% 0!4#?.3!7+ <.0 F+!0<%2' I%$% !0 3!4% 37 "!/% 47-!?!3; 37 +72%0G 0%?%H3!+" .

0#- .$%. -.0%2 7+ ϕi .+2 . 170!3!7+ !+0!2% .0 !30 +%J3 2%03!+.3!7+' K72% 0%?%H30 . 01%%2 #+!67$4?;

2!03$!-#3%2 !+ [vmin, vmax] 5>!3< vmin > 0 !+ 7$2%$ 37 4!3!".3% *+%%, ,%-./ @A(C8 .+2 03.$30 37 47/%

DL

!"#$%& '( )$"$% *+ $!% "&$

!"#$% &'() *+, -./%-%01 2311%$0 4.$ .0% 0.5%

1.63$57 !1'

89!7 -.5%: 3::.67 1. ;.01$.: 19% 0.0<#0!4.$- 29%0.-%0.0 =0.1 :!>% !0 !"?@ AB 19% #7% .4

;:#71%$ 6!19 2$.A3A!:!1B 4#0;1!.0 ϕi 305 1. 1#0% !1 AB 19% ;:#71%$!0" %C2.0%01 =α?' D!- %1 3: 3:7.

;.0;:#5% 1931 !1 $%3;9%7 19% 71%35B<7131% !0 :%77 1!-% 1930 .19%$ $305.- -.5%:7'

!"! #$%&'()* +$&$,+$,-.$/

E.6 !7 1!-% 1. 5%7;$!A% 19% -.5%:7 69%$% 3 0.5% -./%-%01 5%2%057 .0 19% 2371 -./%-%017 .4

19% 0.5%'

!"! !# $ %&'()(*+*,-*. /0&,*'1 '2 3)14'5 6)+7

F9!30" 2$.2.7%5 3 -.5!G%5 /%$7!.0 .4 !# HIJK 1. 2$./!5% 3 -.$% 713A:% =305 7-..19? 0.5%

-./%-%01 = !"#$% &'JI .0 23"% JL?@ ;.01$.::!0" -./%-%017 AB 3 19$%%<7131% ,3$>./ ;93!0 37

79.60 !0 !"#$% &'J& .0 23"% JM@ !0 69!;9 3 7131%<1$307!1!.0 -%307 ;930"%7 !0 N<5!$%;1!.0 305

O<5!$%;1!.0 =A.19 !0 7131% =P? !0!1!3::B?' 89!7 -.5%: !7 !-2:%-%01%5 37 3 2$.A3A!:!1B -31$!C)

P =

P (0, 0) P (0, 1) P (0, 2)P (1, 0) P (1, 1) P (1, 2)P (2, 0) P (2, 1) P (2, 2)

69%$% P (i, j) 5%0.1%7 19% 2$.A3A!:!1B 1931 3 0.5% 6!:: ". 4$.- 7131% ! 1. 7131% Q' RB 1#0!0"

19% 2$.A3A!:!1B /3:#%7 .0 19!7 ,3$>./ ;93!0@ 5!S%$%01 2311%$07 -3B A% -.5%:%5@ 305 1%-2.$3:

5%2%05%0;B ;.#:5 A% 9305:%5@ "!/!0" -.$% .$ :%77 2$.A3A!:!1B 1. 1$307!1!.07'

!"! ! 8'914+0,, :*59+)-*'1 $&0) 5'(*+*-; 5'40+

89!7 -.5%: !01$.5#;%7 3 0./%: 322$.3;9 3A.#1 19% 7!-#:31!.0 3$%3@ !0 69!;9 .0;% 3 0.5% $%3;9%7 3

A.#053$B@ !1 6$327 3$.#05 1. 19% .19%$ 7!5% .4 19% 3$%3 H&T@ UPK@ -322!0" 3 $%;130"#:3$ 7!-#:31!.0

3$%3 !0 3 1.$#7 = !"#$% &'JV .0 23"% JL?'

JV

!"#$%& '( )$"$% *+ $!% "&$

!"#$% &'()* +,-% -!./$!0#/!,1 !1 2!$2#34$ 4$%4 5/46%1 7$,8 9(:;<'

=>!. 8,-!?24/!,1 /$!%. /, $%8,@% />% ! "# $%!&' !() ($*+&$,#+$! A>%1,8%1,1B A$%.%1/ !1 />%

$41-,8 8,-%3. 5.%% !"#$% &'(C ,1 A4"% (D<' E!/> />!. 8,-%3B 8,@%8%1/. ,7 1,-%. >4@% /%8A,$43

-%A%1-%12!%.B 846!1" A$%.%1/ ($&)-+$! ,7 /$4@%3 41- *.))( -%A%1-%1/ ,7 />% A$%@!,#. ,1%. 9DF;'

G,@%8%1/. ,7 4 1,-% 4$% "#!-%- 0H 4 @%3,2!/H @%2/,$ ~v = (v, θ) I>!2> -%.2$!0%. 1,-% @%3,2!/Hv 41- !/. -!$%2/!,1 θB 41- />% 1,-% A,.!/!,1 (x, y) !. #A-4/%- %@%$H ∆t /!8% ./%A.B 4. 7,33,I*

v(t+∆t) = min[max(v(t) + ∆v, 0), vmax];

θ(t+∆t) = θ(t) + ∆θ;

x(t+∆t) = x(t) + v(t) ∗ cosθ(t);

y(t+∆t) = y(t) + v(t) ∗ sinθ(t);

vmax !. />% 84J!8#8 @%3,2!/H -%?1%-B 41- v !. />% 2>41"% !1 @%3,2!/H #1!7,$83H -!./$!0#/%-0%/I%%1 [−Amax ∗∆t, Amax ∗∆t]' Amax !. />% 84J!8#8 422%3%$4/!,1K-%2%3%$4/!,1 7,$ 4 1,-%B ∆θ!. />% 2>41"% !1 -!$%2/!,1 #1!7,$83H -!./$!0#/%- 0%/I%%1 [−α ∗∆t, α ∗∆t]B 41- α !. />% 84J!8#8

41"#34$ 2>41"% !1 />% -!$%2/!,1 7,$ 4 1,-%'

L@%1 I>%1 />!. /HA% ,7 8,-%3. .%%8. /, ?/ I%33 7,$ 2%$/4!1 .2%14$!,. 5%'"' $4!3I4H A$,03%8

I>%$% /$4!1. $#1 ,1 $4!3. I!/>,#/ 2,33!.!,1.B 2,$$%34/!,1 ,7 8,@%8%1/ /, /%2>1!243 4.A%2/. 9();%!$ %M%2/.B !/ >4. !/. ,I1 -!.4-@41/4"%.'

N#/>,$. !1 9&F; 1,/% />4/ /# ()*$&)( *$() )0)-+* +12+ 3!#4( !--#& %&!' 244!3$ 5 +1) 67* +! '!8)

2&!# ( 2 +!&#*9 :!& );2'.4)< ! ) *+2+$- 67 2 ( ! ) 67 +12+ -! +$ #)* +! '!8) $ +1) *2')

($&)-+$! ,)-!') )$51,!&* 252$ 2 ( 252$ 9 = 2(($+$! < 2 *$'#42+$! 2&)2 3$+1!#+ )(5)* 3!#4(

%!&-) '!($>-2+$! !% +1) &2($! .&!.252+$! '!()4 +! 3&2. +&2 *'$**$! * %&!' ! ) )(5) !% +1) 2&)2

+! +1) !+1)&? '

(C

!"#$%& '( )$"$% *+ $!% "&$

!"#$% &'(() *+,% ,!-.$!/#.!+0 !0 1 -2#1$% 1$%1 3.14%0 5$+6 7(89:'

!"! !# $%&''()%*+,- .,/01023 .,451

;<+-% .+ .=% !"#$% &!'($)"* 6+,%< !- .=% +!,--./!01$2 %$#34 7>>9? @=!A= !0A<#,%- -+6% %0B

=10A%6%0.- .+ .=% $%-#<.!0" C1.= .+ 1,1C. ,!D%$%0. <%E%<- +5 $10,+60%-- E!1 +0% .#0!0" C1$16%.%$'

F=!- 6+,%< 1,,- 1 4!0, +5 6%6+$G .+ %1A= 6+/!<% 0+,%? -+ ,%A!-!+0- 1. .=% @1GC+!0. 1$% 61,%

.14!0" !0.+ A+0-!,%$1.!+0 C1-. E%<+A!.!%- 10, ,!$%A.!+0 E1<#%- 3!0 HI%, !0.%$E1<- +5 .!6%

: !0 .=%

5+<<+@!0" @1G)

sn = αsn−1 + (1− α)~s+√

(1− α2)sxn−13&'&:

dn = αdn−1 + (1− α)~d+√

(1− α2)dxn−13&'J:

@=%$% sn 10, dn 1$% .=% 0%@ -C%%, 10, ,!$%A.!+0 +5 0+,% 1. .!6% !0.%$E1< n? α ∈ [0, 1] !- .=%

$10,+60%-- C1$16%.%$? ~s 10, ~d 1$% .=% -C%%, 10, ,!$%A.!+0 6%10 E1<#%- 1- n → ∞ 10, sxn−110,

dxn−11$% $10,+6 E1$!1/<%- 5$+6 1 K1#--!10 ,!-.$!/#.!+0'

L%$!E%, 5$+6 C$%E!+#- %2#1.!+0-? .=% A1<A#<1.!+0 +5 0%I. 0+,% C+-!.!+0 !- 1- 5+<<+@)

xn = xn−1 + sn−1cosdn−1 3&'8:

yn = yn−1 + sn−1sindn−1 3&'M:

@=%$% (xn, yn) 10, (xn−1, yn−1) 1$% .=% 0+,% C+-!.!+0 1. .!6% !0.%$E1< n 10, n − 1 $%-C%A.!E%<G?

!"#"$%& '()*+ ,%*- *-!".%("/$ 0/! 1/$("$)/)'2(",-3 4)( #".-$ '/,- 5!%1("1%& &","(%("/$'3 1%!' )'- *"'1!-(- (",-

"$(-!.%&'6

(N

!"#$%& '( )$"$% *+ $!% "&$

!"#$% &'(&) *+$,-. /0+!1 2-$ 3-/+4!-1 4$+15!4!-15 64+,%1 2$-7 89(:;'

+1< 5=%%< sn−1 +1< <!$%/4!-1 dn−1+$% 40% /-$$%5=-1<%14 5=%%< +1< <!$%/4!-1 +4 4!7% !14%$.+3 n−1'

>1% 7-<!?/+4!-1 !14$-<#/%< !1 8(&@: 2-$ 40% !"##$%!&'() 7-<%3 <%?1% + 7%/0+1!57 4- +.-!<

40+4 + 1-<% $%7+!15 2-$ 3-1" 4!7% 1%+$ 40% %<"%A 40+4 /-15!545 !1 /0+1"!1" 7%+1 <!$%/4!-1

~d' B1%C+7=3% -2 40!5 7%/0+1!57 !5 <%=!/4%< !1 8&D:A 40+4 !5 -13E +==3!%< F0%1 + 1-<% !5 F!40!1 5-7%

<!54+1/% -2 40% %<"% +5 !45 50-F1 !1 !"#$% &'(D -1 =+"% &G'

H-$$%3+4!-15 I%4F%%1 =+54 +1< =$%5%14 5=%%< +1< <!$%/4!-1 %3!7!1+4% 40% 5#<<%1 54-= +1< 50+$=

4#$15 %1/-#14%$%< !1 $+1<-7 7-I!3!4E 7-<%35 65%% !"#$% &'(J -1 =+"% &(;'

B5 /-15%K#%1/% -2 40% $+1<-71%55 4#1!1" =+$+7%4%$ αA 40%5% 7-<%35 I%0+.% !1 <!L%$%14 F+E5A<%=%1<!1" -1 40% .+3#% -2 !4 +//-$<!1" F!40 6&'9; +1< 6&'&;)

M2 α = 0A 40% !"##$%!&'() 7-<%3 !5 + 7%7-$E3%55 7-<%3 5!7!3+$ 4- 40% *!+,(- .!/' 7-<%3A+1< %K#+4!-15 $%7+!15 +5 sn = ~s+ sxn−1

+1< dn = ~d+ dxn−1

M2 α = 1A !"##$%!&'() 7-<%3 !5 4-4+33E <%=%1<%14 -1 3+54 =+54 .+3#%5 -2 5=%%< +1< <!$%/4!-16+$% 40% 5+7%;A +1< %K#+4!-15 $%7+!15 +5 sn = sn−1 +1< dn = dn−1' N0!5 7-<%3 !5 /+33%< +5

O#!< O-F 7-<%3A !1 40% 1-7%1/3+4#$% -2 .%0!/#3+$ 4$+P/ 40%-$E'

Q+$E!1" α I%4F%%1 (0, 1) !4 !5 =-55!I3% 4- "%4 <!L%$%14 3%.%35 -2 $+1<-71%55A 7+,!1" 40+4 1%C4=-5!4!-15 7-$% <%=%1<%14 -1 40% 3+545 5=%%< +1< <!$%/4!-1A -$ 7-$% $+1<-73E /0-5%1 2$-7

sxn−1+1< dxn−1

'

!"! !" #$%%&' ()*+%$ $%,-.-&/ $%+0.

N0!5 7-I!3!4E 7-<%3 <%?1%< !1 8((: /-15!<%$ + 4%7=-$+3 <%=%1<%1/E -2 .%3-/!4E -.%$ .+$!-#5 4!7%

53-45A +1< !5 I+5%< -1 6-$ !5 +1 %10+1/%7%14 -2; *!+,(- 01&2341(+ -(,2/' *!+,(- .!56(1+4 -(,2/

=$%5%145 5#<<%1 54-=5A +//%3%$+4!-1R<%/%3%$+4!-1A +1< 50+$= 4#$15A /0+$+/4%$!54!/5 40+4 7-((48

(J

!"#$%& '( )$"$% *+ $!% "&$

!"#$% &'()* +,-%.%/0 1200%$/ 3,$ 1$,424!5!60!7 89+ :02;%/ 3$,. <&=>?'

!"#$% &'(@* +211!/" ,3 6!.#520!,/ 2$%2 :02;%/ 3$,. <&=>?'

!"#$% %$#&' 0$!%6 0, 7,/-%$0 !/ 2 .,$% $%25!60!7 .2//%$A !'%' .2;!/" 7B2/"%6 !/ 61%%C 2/C

C!$%70!,/ !/7$%.%/0255D 2/C 6.,,0B5D :6%% 2/ %E2.15% !/ !"#$% &'(F ,/ 12"% &&?'

GB!6 .,C%5 #6%6 0H, 60,7B260!7 1$,7%66%6* ,/% 0, C%0%$.!/% HB%/ 2 /,C% 7B2/"%6 !06 61%%CA 2/C

0B% 6%7,/C 20 HB20 0!.% 0B% C!$%70!,/ H!55 4% 7B2/"%C' GB%6% 7B2/"%6 2$% 2#0,7,$$%520%CA 61%%C

7B2/"%6 !/7$%.%/0255D 4D 0B% /,C% 277%5%$20!,/A 2/C C!$%70!,/ 7B2/"% !6 6.,,0BA 4%72#6% ,/7% 2

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{V 1pref , V

2pref , . . . , V

npref} H!0B .2J,$ 1$,424!5!0D 2$% #6%C :2/C #/!3,$.5D C!60$!4#0%C 3,$ 0B% $%60?A

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{

0, 3Vmax

5 , Vmax

}

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p(v) =

p(v = 0)δ(v) v = 0

p(v = 3Vmax

5 )δ(v − 3Vmax

5 ) v = 3Vmax

5

p(v = Vmax)δ(v − Vmax) v = Vmax1−p(vpref )

Vmax0 < v < Vmax

0 else

6&':<

=!1> p(vpref ) = p(v = 0) + p(v = 3Vmax

5 ) + p(v = Vmax) < 1'

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b(t+ 1) = b(t)e−1

τ + (σ

√

1− (e−1

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~M = (xv, yv)

~B = (bxv, byv)

~V = (vxv, vyv) ~B

~M = (xv, yv) = ~B + ~V = (bxv + vxv, byv + vyv)

{

|Vmember(t)| = |Vleader(t)|+ random() ∗ SDR ∗maxspeed

|θmember(t)| = |θleader(t)|+ random() ∗ADR ∗maxangle

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newposition = oldposition+ acceleration(targetoldposition) + randomvector

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1 ∗ (#newAPs+#missingAPs) when

(PrevAPs ∩ PresentAPs) = ∅ ∧ PresentAPs 6= ∅ (1.3)

0.1 when PrevAPs = ∅ ∨ PresentAPs = ∅ (1.4)

−0.1 ∗ (#recurrentAPs) when Is = ∅ ∧ APi ⊂ APs (1.5)

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Tesis de Maestría - Colibri

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