Passive Estimation of TCP Round-Trip Times

Passive Estimation of TCP Round-Trip Times Hao Jiang

Constantinos Dovrolis

Computer and Information Sciences University of Delaware

Computer and Information Sciences University of Delaware

[email protected]

[email protected]

ABSTRACT 
   
 
 
   
!
"  
!
#$!
%&''(

  ) *+&,
-./
0&
12- 32 45768 (:9;9?97A@05BC&2
!9ED7FHG 2
GIJ K&/$L"MN& 2) &2
% ( MO PQJ2P R7S'GA&6>9?9T- J322 U!   A#EJ32VW
I /  2)2XG 2Y) 2A/ K 52 GIJ
[Z#2

\.  )
!
#"X" 
%
G%  5OG 2)
- ]
   2 J
C A^_G R_97&2
1   
 !
I&'2  ) *`Q3 
"a `bMO]
GA&JZ#
%RH97&2
Y-Q
GI&( 2JZ'2
.J_ 2JG 3
.97&
[–CRS R ˜h
%!
#rŠ &J™%
"KE
'2G%
€2- 3

2#15i ˜h/
%2!
#_  
1 :MEf&2( -AJ2)! #*QG '*') &#8A &
%
 ;R

G"1š-2-8AP
0!
E 5Š&2
0
'(d (e
.3
&/' 81&rR ›b` 22f ;X7   
! f 2)2#
.2 .# '2G%
 A^!G /
%&2
" WX‡&'hfK#
,,#
%A G%hME&+ME&/K03
) !
" 2
"WR œ “'+žŸB "¡‘%¢}i£ ¡+}B~ai¤#}B¥1|¦I|2¡I}i¥ež€¡I¥¢}B”!¦:¡+i¤¡§Ež“~’ ¨A©I} | ©k}B”!¡I¥4ªB§U©?©k¥e«ž-¬i¤¡l©7­;®¯‘ž ~2~W¡ ‘%¢}dž ~2¥i¤2¦ Kž]i¤'-ž “ /¤°¦ ~W¡I¢±[ž  ²]³ }B~²´,“'¥}B~'|¦¥A¥}B£ ¡”!¡¦¥A“' ¡I”.¡I~¢¥¦ ,i¤2¦ C³ }B~²R]›b  &2
%KM7A2XkMO
!-A KMEf& A^_G_ A G
_5ˆ µP XŠ &
%`/ 
!2C!
" 2
&2
6>9?9¶ 5h

% *€9ED7FNG 2
GI(  v3'*° f*T
-)2)`&
4G 2
G% ; “~2}d’ }B ¡ ‘%¢}dž ~ ¦ ³ · ž ±€
GA2
"&K A G%
RQ›:5E9ED7FvG 2
G% 3
%bMO

 & -!¸•N¹lM7 !G%
f*] 

]3'*¸,X‡¢R
RJX7¸‰
#$&
Y-CS#º0‚c!
 )
X;M7
!
%Y2
C&/C¸HJ,&2
‘¦ ³B³J¡Ih H¹] &
K‘¦ ³i³J¡A¡IR>sJ
%G%  9ED7F4L/Ms.h A G
EG"!3
?5i &
EG"J
IO,&
?G"J
%
X O5ˆ c&
?G"J
%
U0&
EG"J
I"R[‚U 
&/C A G
Q2#
%C2 C fM?*12G2
!3 &L"ME$ 5U9ED7F G 
%G% ;X'
%
_ME&
%.&2
E   
8! 2f >
G AO A^_GU 3  &2f
GIJ ?5‡&
UJ2P »&2
U
"  J7&7&2
8 2
?3
I( bMO

$&
OG 
%[ ,&
[G" 

?.*,3
?-*!!
% G RŠ¼hkY- !
" 2
!
#7
%GI&2JZ#
X'G"J
½>¹r¾,¨B¿$­‡À¯ªe½'¿?«!¡I¥A¢}i”!¦ ¢}dž~X 0G"3
CQ \9ED7FaL"ME85i y&
KG"J
%h.&2
CG 

R ¼h2U
G !
" 2
!
#E
GA&2ˆZ#2
XG"J
½³ž ±>¨e½2e¦ ACªd½½ « ¡I¥¢}B”!¦¢}dž ~X28 2JG 3
0C  !
,9ED7FlL"ME?5i ‰&
0G"J
%
?&
>G" 
%"X !
f*h& 
[&r A -5i
%\/k
" -‡Y
>G 2
G( 
?
) !
#X &
7Y2-Š5B 2[ 5 ME&GA&!
Uj/t2CcS'
) !
# S™
= jS2S@O GAP
%R 97&
hG !2J
I
0
-.  ) f&{2'G
E6>9?9a  
5BCn x/(bŒ xp¯5[&2
_9ED7F°G 2
GIJ X; +5i $n n/(:on p¯ 5[&
9ED7Fc3'*'
X>&
. A G
%1&/_M7

%t2 !
"WRj -. 58&
G 
%G% ?&EM7
,G"2 E!
" 2
K 6>9?9Á5i U
KG"J
%
%(  (eG"J
IUL/MEE&/U2_2 8-5i*&
,2
% UjSS#(e
%ˆ/
" 
"Z#f
!
%'"R$U  f*#XWM7
_
%5B
I,) 2 
_G 2
G% 2 5BME&2GI&aMO
&"
  !

%J
G
&.&
6>9?9{
-.
.*Q3
hM? 2)2X
%   )!
-. 5¢J
R797&28!
  &/UMO
C) 
1!&2J) &
%U2:*. G%G2AG%*&4Â
-.  *
JrR[¼h2>
%t
%!
#\ &"M`&O 3  2Ow xpà 5 &2
E   
!
" 2
!
#Š/
OMEf&zxpÄ [n/!X ME&2GI&2

%\\J)
I"X# 5 &
,6>9?9Á  
h&E|}B~#hM7 2J!
"  
ROj
"  
!
#E  

IA ‚hƒ‡8‚h6E(-j¼8[9&2
8S2s _SS
-. 9?9+&k?G 2
G% $
It2
IJ
%G
‡ /J
%X 
Š8Z#
2
%( 2)a2
%ˆ*T J 2  2)sGI& )
Rµ¼h
-.  
%GI&2JZ#
./ 
!2!]/J
 2
!
"  
!
#!
%QG 2( 2
G% rXŠME&GA&J.i¤¡!§U©?©°i¤2¦ ,i¤2¡‘ž ~~ ¡‘%¢}¢ž ~Á ¡ I|2¡IA}e¡I~‘I¡ ’ ’“A}B~#C‘ž ~~ ¡ ‘%¢}dž ~¡I¥Ae¦ Ÿ³ }B¥-¤'”.¡I~2\ž 8’ “'A}B~'0}B¢ ¥ \I¥‡¥A³ž ±>¨d¥e¦ I -ž “'~ ’ ¨d¢A} |ROS'*K 5
-.)8
% A 2 !J   1!
% = 6>9E¼,@ ]‹ „"k &"ME8&?AP'J2)! 2* 2
,6>9?9°!
05BU&2
,6>9E¼
%-J./ UM7 P'85¢ ff*MO
dR$‹fz%Š
%   U fJ Š!
"  
%( !
%'? &
,6>9?9Á J 28&U_G 
%G% G"
%t
%f(
%G
K2)CEf5B
%!
R 97&2
P'2/ME
")
Q 5UG 2
GIJ 6>9?97__
%:M7 P4J2P&  
%
%A  2JG 2
R kf-"X&2
8 ! 2#[5W
"Z#f
"1322VW
%) /?,P!

[ _&
E6>9?97O5;&2
U9ED7FG 2
G% 2[&/ ) 0&2 ) &$&/[P.‹ „ Xz/n"dR>U1
%-J./
? 5&2
E9ED7F6>9?97 $  2
%5B2[&2
_G Y) 2A ] 5EG%
.Z#
2
1. )
%( !
%'C!'22
‹fzgdX7]&
QJ2
#fYG"/ l 5UG 2)
-  22
    
$ A^!G‹ …#X[z z%dR_97&2
_2   
"+6>9?9H
-.  
%GI&2JZ#
8G" /J
,J28_&2

K
%:M7P2/'  2)  A/^!G,.  )
!
#?!'22
R 97&2
U 
%O7- G%
"! >5B J"MER7S
G% „0) J
O&
E3  G J
"85i k&2
>:M786[9?94
-. K
GA&JZ#
%XSl $S2SWRS'
G%(  !gh
 G%3
Š&
7!2J
%!
#A $ 5&2

O
GA&2JZ'2
X  
It22J 0  !
1   \
-./J +&
J-G0 G 
G% ( 2
 KGI&2
GAPRS'
G%    J2
,&
_
IYG"  22GI&2
 &$M7
.5B J"M7
s] &"ME$b*G"? GG%2A GI*
 2RS'
G%(  n1

#h6>9?9T2- 3J E5i 2fVW
%
%'8! f 
" P'X[5B#G2 J2) €&2
 J 2! 5U&
Q6[9?9•2- 32  /
IU3 & &2  U J)
K!
 G 
R 2. 
C5i#BASIC G, 46>9?TECHNIQUES 9H
-. 9° 
‹fz"odR197&
$ A G
 = &
$G  
%   '( ).‚0ƒ;U‚U6vY
A@8
$!
" $½}B:¡K¿hŸ"Ÿ% ¡I£"}d¦ ¢}dž~¨K©k}B”.¡I¥A¨ e¦ ”U| R Q
%t2 !
X?&2
 A G
4¼,S'–U(:w w x xnx„ n'z+M?QAP
 z"…  n …  gz OS9¶ an 'zŒ  „ x x'z4!&
¼h&S#A
–U
% (  fb* = ¼,S–0@7 GG%
 UP R>97&2
,G" 2
0!
?5\ ; AG
8

  
" > -
%<S#A A97!
= OS9E@IR 2.1 Á&2
QSYN-ACK MO
0

,KL"MÁ5i(SA)  1estimation 9ED7F€G" 
%E_$G" 

X&
h6[9?9

K
-.
"+5i &2
_GIP
%,
%tGI& 2)
"GIP
%  ™
= 3'*'
A@IX;+  !
_9ED7FÁL ) R197&
$5B "ME)
,) J
&2
h!
h  G) = Â 2
fA @7 5;&/E GAP
%O
J
h$&
h
%( ' 2O GAP
%"X'[M7
%JW[&2
8 GAP
%[ ™
0_  !
89ED7F]L ) R 97&2
+6[9?9{
-.
&.
 f.MEf&a&
4S2¯
%GI&2JZ#
 ) 
+J -"R,‚U 
K&U&
$ ft6>9?9v
-.
%0+&2 09?9?F 
%  J 
_Z'2f
CG 
= ME&lz
  5O
" GA&&
%I@IRC97&0M7 
It2
%G%
"rXrU&2

C ftG% 2
G% 2,
$
-A3 &
"£ ¡‘ž ~2¥%¡‘%“'¢}B£ ¡ ¥%¡d ”.¡I~2¢¥´>i¤2¡ >A¥A¬%ž “'0ž-¬E±k¤'}d‘A¤Q¦¡ +½2½C|¦‘A²¡I¢¥RO97&
UjSS   2
G" €3

-./
"l5ˆ &2
G 
%G% ; _ AG
X?G _( )_&2
0L"M, UJ/)
-h
) !
#8 ™
,MEf& 2
$5Š&
CÂ M7
%Jf( P'2/MErWjS2S J2
X  2GI&+Cz  Πx.3#*
%X‡z n „!3#*
%X ,n g Π3#*'
 = 

.‹fz  Š5i h! 
K GA&  
A@IR897&'2X&
CSSQ
-.(  
GA&2ˆZ#2
h?E 2G" 32J
05i U9ED7FL"ME?&O A -5i
%  f*. . W
) !
#X' E
) !
#OMEf&22 rjSS_ 
R E5i
%\&2
O&2

I(eM7*K& 2 & P
7\G !
%
"WX &2
73
&"' \5 K9ED7F2Ah A 2-5B
%OO) /
I
"_3#*$&
E /M`-A O ) f& ‹fzxXŠg/dR_—0J2) "MN-A "Xr&
19ED7Fv
2
%KGI
!
#U&2
G% )
- `ME2"M{ /J 3
=   @C3#* 
+jS2S5i .
"GI& 
%G

"€8
D &/! GAP'"ME
"2)
!
IMyA'R€97&
 J2
5 &2
›b2fˆ8aJ2"M = ›:°@1J!2 Jf*sl4:M7ljS2S‹fz"x/eR Št
%!
#A ;9ED7Fs
%t'
2  J"MEU&U_9ED7F`.*Q
0 J/)
%8fJ WG )
%-J ME"M°!$5i UjSSU‹ gdR\Á&
 ‰„ OXk +f57&
C

%K&,
 ) &2AX‡f0MEJ 
%bMOQjSS GAP
%E_&
0
G%

%"R?‚U 
,&/U&2

0bMO Y2-,jS2SGIP
%h/
K
#U3 GAP#(e(e3 GAP X+_322-"RO
0
%( 5i
%1&2

jSSGIP
%1C&2
QL/M,  >A¥A ½½sŸ%“'I¥¢X[   !2* >A¥AUŸ%“'A¥A¢R,a&
&2
18
D ‰5i 0&2

C:M7.GIP
%h 
%G

"  X7&

%2
I.J2G%
"
   ]
0
%5i
%  Áf&—0
J*#
"'(:U
D ,XW&2
%
1ME[3
_ f*?Ž&BDCEFH+CE!J  ‘J#$  ’ ?-?>“ABD&BEBE!J ” !CE•‡BEK–  J  &  CEKJ  B L HŒ

&2

_ GAP
%K 0&2
1L"M, !¥%¡‘ž ~’4Ÿ%“'A¥¢Rl©;¤¡!ŸA¦¥A}¢‘.}d’¡¦ }B~l½½`¡I¥¢}B”_¦ ¢}dž ~€}B¥_i¤2¦,i¤¡Q¢}B”!¡.¥d|¦‘%}B~#ŸA¡I¢±7¡¡I~si¤¡ >A¥ ¦ ~’.¥%¡ ‘ž ~ ’Ÿ%“'A¥¢¥,}B¥0 ž“/¤'³ —:¡ %“2¦ ³rež.i¤¡C‘Až~~W¡ ‘%¢}dž†~ ˜ ¥h§U©?©kR 97&KK &"ME k) 
!g(:'RQ97&
_Y-K322-7šb-C5ˆ
%K&
S'ºh‚08
D • GAP
%, &2 2ˆ+G  -$ 5?/K
" -,:M7jS2S+ GAP#(
%X‡ 97&2
h&fAQ .5B 2 & GIP
%\G 2-
7&
OY2->32-\1&2
OL"M,R\E5i
%[KÂ  
G%

%'rX#  !
E 22f 2A0 GAP
%\
E
#Š5ˆ Ã&
O
3 
%
IŠU&
[G
#\3 GAP#(d (e3GIP = 
%G C3-I@IRŠ97&2
O6>9?9]
-.
!5ˆ c&/7 
G
8
%'rX#ME&2GI&.? 3  2>&
8 !


Caller

Monitor

Callee

Caller

Monitor

SYN

Callee

SYN

CK

CK

SYN−A

SYN−A

ACK Request

ACK Reque st

Data

Data

t

1st burs

ACK

t

2nd burs

Delay

RTT m

ACK

RTT s

Data

> RTT

Data ACK

RTT s

Data

time

(a) Initial cwnd = 2

time

time

(b) Initial cwnd = 1

time

packets seen in the trace packets not seen in the trace

!ƒ"%$'&
/*-,/‰!J 2R,/CDH$ŸC84,%,?A&BDCEFIHCE!J ML

5i U3  &G 2
G%  = z zŒlz zo_!A@IR 3. 97&2
02FURTHER 
% ?
G% IMPROVEMENTS 2
% G%3
"Q&2
h3 G0J2
"1.&
0SS. 

Sµ
GA&2JZ'2
RµUv G%G2A/
€6>9?9
-./J Ã )  f&X &2"M7

I"X?

2_G%  J
%Q

%A0Â &A2
I.G" 
X8 GA&s  G% 2
G% 2;&;
%t
%
G
\  
%X 
% A !   2X ŠZ#
%
%( 2)2R,›:&h
GIJ ;XWM7
C2

%'h  !
$ 22f  \
-.  &2
2-G!G 
G%
% _
-C&1MO


 
9?9 = ™ošš @;MEJ23
?/
%
-.
rRŠ8GGA( 2).!6 kD°„w o o'XW&
,fJ ‡
I A  !   !
 2 = 6>9E¼,@  &2 2ˆ$3
7
%ŠUgh
G ?‹ „#z%dR \
K& 2) &$G
% AJC-*-
! 2
_
"Z#2
%!
#E‹zŒdR\Á&
%_ ?S`
-.
E[J/)
%[&  g.
G X;MO
12
% !
,&/,f,G
,6>9E¼N   G"Af"R[97&8!
" 27&/?&
,6>9?97?&?MO
,G" !
"  
MEf&&2
$S2v
GA&2JZ'2
,
K!f
".g_
G RO]
,
It2
%G% &O f*.05i
%M°9ED7FlG 2
G% O&"
h.6[9?9l&/7O!
& gC
G 2E'2"*W E›b#
%2
%"R

3.1.1 Losses in the SA technique

NPORQTS4SVUXWZYV[:QTSVNV\ ]V^ WZ_RNR\ `baRc4dfeKm4lXpR\Zlj:k4cRpR\TdXm4p@nRk4cXp4pXm4m4h4iPj:qXcXl:d@nRqXcV\TdXhXzs:t4uXcXr4r>jZv4u-k4O:} ]V^ WZ_RN4hw`KxycD\4\ZiweKi4r{D| s:tXuXc4r4dPkXO:} ]V^ WZ_RN4pw`Kxyc-lweG\4\‚{E| s:t4uRcV\Zg:d4dPqRj -kXO:} ]V^ WZ_RN:rf`Kxyc>dfeG\Td@{E| s:t4uRcV\Zg:d4dPqRj -kXO:} ]V^ WZ_RN4gw`KxycD\4\ZgweKlXpo{D| s:tXuXcV\Zg:dXdqRj k4O:} ]V^ WZ_RN4zw`Kxyc>dfeG\Zh{E| s:t4uRcV\Zg:d4dPqRj -kXO:} ]V^ WZ_RN4mw`Kxyc>dfeG\Zh{E| s:t4uRcV\Zg:d4dPqRj -kXO:} cX~P4a4a`y\X\ZgweKl4p@{D| NPORQTS4SVUXWZYV[:QTSVNXh ]V^ WZ_RNR\ `baRcXhweKp4iXp4h4lj:k4cRpR\TdXm4p@nRk4cXp4pXm4m4h4iPj:qXcXl:d@nRqXcV\TdXpXhs:t4uXcXr4r>jZv4u-k4O:} ]V^ WZ_RN4hw`KxycD\Zz:dfeKiXlo{D| s:tXuXc4r4dPkXO:} ]V^ WZ_RN4pw`Kxyc-pwe€dXg{E| s:t4uRcV\Zg:d4dPqRj -kXO:} ]V^ WZ_RN:rf`Kxyc>dfeG\Zh{E| s:t4uRcV\Zg:d4dPqRj -kXO:} ]V^ WZ_RN4gw`KxycD\4\ZmweKlXmo{D| s:tXuXcV\Zg:dXdqRj k4O:} ]V^ WZ_RN4zw`Kxyc>dfeG\Zp{E| s:t4uRcV\Zg:d4dPqRj -kXO:} ]V^ WZ_RN4mw`Kxyc>dfe€dXl{E| s:t4uRc-g:d4r>k4O:}  u cX~P4a4a`y\X\ZmweKl4m@{D| !ƒ"%$'&%* ,/H#FIˆŠ‰!& CV$ŸH  & J#Œ,, &BDCEFIHCE!J  ‘J#$ H  ’ ?>?-“ BD&BEBEKJ Œ !CD•ŒC J  J  &  CEKJ  B L

&
hG" 
%" 8Y2-?
"Z#
-"/A1GIP
I,‹fz/…/dR
>
&2 ) &Q&2  #GAP
%! 2 l"
_ 
U
D ¯GIP
I15B_&
QG
#"XOf1G"  G"
0 ) 2fYG"'E6>9?9`/
I
-. 
%  ?&2
,SÁ
%GI&( JZ#
R_8, 9?9•
-./
_&/_&
S2{
GA&JZ#
) 
Q  *5i  3  „ nx !!g w x !RT›: KJP
%*+&,&
%
!ˆ/)
! J C
_G"
"43
G" 2
_&
G
#K2
%ˆ*h&2
C A 2 !  J 45O&2
$Y2-K8
D _R]
12Q  &"
hC)

%Ar
%-7_
%
G%7&2?2 32
R h"MO

%"XG
I ( A .G"
[MO
UG"!J2
#f5i*CME&
%&2
%[&2
US2a
-.
E[M? )  2)_  !
0 !2J
0
%-E&?MO
K2
 G%3
K
It"R ›b  h9?9?FsG 2
G% rX&
hG" 
% = GJ
%'I@7
28  09?9?F 
"Z#
%-0Q&2
1G"J
%
= 
%
%I@h/5i
%,&2
CG% 2
G% 4,
-A 3(  &
"WRaE5i
%_&2
G
#_
G%

_&
QY-! 
 !bMO2A GIP
% 5_&2
09?9?Fy
f*#X,f<
+ Á8D
† GAP
% &

I
%"R U+ &"MEH k) 
lŒX$&
]!
]#
%  3
%:M7

4&
09?9?FT
"Z#
-C ? J ˆ%H   &C ‰!JƒBEB B  &  H$ KJƒB   CE•%& Š$ŸBDC C J ? 5-= “ 9?9Á
-.
,:/  X2 8G"3
0

J kJ) 2
Kg'R

3.2.1 The effect of the Initial Window

ŠF GIP
%K  K K GAP
%$¼h (-¼U5ˆ(b¼UA2
% = ¼,¼,¼,@82

% *&
09?9?F
Z'2
-\&/[&2
8G%J
#[
#"X 3
%5i 
,&
KG%k/A1 A 2-5B
%U-A RO›:EU
 -*1

,& &
.!
.J#
%    3
IbM7
%
&
S'º0‚h8
D ¯]&/122
8
D •0/,
" -0 
$6>9?9 = 

k) 2
Cw@IRU]
$
K&U!
#
%    $+Â  2:*GA&
%GIP W5BC 2CS2SSVQZY-UTSDQ    ^ Y ^]D^ WT_RUZYD|

j4j>cXUZYRURWTY j4j ^  V U! q  0 

] 4SX_4SVQ :S j4j [ Q 9  j4[ZcVj\0>(  d[4( g |T[_V [   [  ! q! [ P cXc j4j  *G [ >cq ![ V\ ebYV[ {VU>Nq![febYV[ {DU U  |:U |T_V[ ]  PSVQZY UTSVQ   j4j ]V^ WT_RU:YV| [   *G \ R ~4~*! h% % *G \ R ~4~*K r   4a4a c*K p    T O>c \ U  |:U 4a4a c{ ^  K h *K p  *K r  +   h T OŒr [  ] R U4N4k4O:} ^  YRU - jZvXuXk4O:}  c>q€ k4O:}f ebYV[ {DUNqK j:v4uXk4O:}f ebYV[ {DU [    Xa4a V UZY: S 4a4a   |:U U |T_V[ ]  + + !ƒ";$Ÿ& (/*P“BD&" J  J & J#$ž,,)&BDCDFIH+CD!J ML

3.3 97&2
%
$Skip 
K. cases #*9ED7F`G 2
G% 285i hME&2GI& 2U
-. 


%GI&2JZ#
,G"2 K2'G
_ ]6>9?9hR;97&

  P'G"
Š/
-
"_!9k3
,z R\a  Pr#GG>ME&2
_ 2[ ) f&c2
%5i
% . G"A_G% 2
G% rXA/&
%E&2'G2). 
-./
ME&2GI&.OP
f*_M? )2R>97&2
U  [
   2OK P'J.,G 2
G%(  4/
K
%tJ 
J&2
,Y-UG !rRE97&
,A3
1 Q) 
 &2
$ ! 2#h5O9ED7F` A/^!GK&85¢JhJ+
"GI&G 
C 0_5ˆA G%(  5‡G 2
G% 2X .?K5ˆA G% 5; A-5B
I 
"Q3#*'
[J
 GA&/A 
%"R –U25i  
f*#Xr3  &&\MO
8&"
?
%t2 !
 = 3
%:M7

 xpHKnxpH5B [G 2( 2
G% 2XU °z/n p   #n p 5i 3'*'
A@IR°›eQJ.!   A#Q 2 
!&/K| ¦‘%¢}¢‘A¦ ³B³ —4¦ ³B³[¥-²} |`‘¦ ¥%¡I¥ž"‘A‘%“'.}B~s‘¦ ³B³J¡¡%¨dež ¨b‘¦ ³i³J¡I · ž±>¥1¦ ~’½½€¡I¥¢}B”_¦ ¢}dž ~2R_97&2
1! -hG !! 
"   45BK) ( 2 )+G 

%(d (eG"J
%1L"M•K&/Cf12#
$$J2G
/ 
"-h5i 2UG 
G
$jSS GAP
%U5ˆ
%U&2
,G 2
GIJ 
-( A3 &!
#"R\97&2[O5i
!&2
?G" 
EMEf&_aa  !JG%
X#ME&  
%A2)-*-
!h&/K2,
%,&
C›b2J\aJ2"MÃ Cf
? 5;jS2SWX $ME&.2JG"/ >&/[
I 5B c

%A   .0Â M?f
\4&2
9ED7FN #GIP
%!-
" €5,+ ) 
J)
 
R\
0
h&/E

5‡&
KS2S.
GA&2ˆZ#2
U5¢JE_'2G%
!6>9?9s
-.
?5i 7
 GA&!G" 

%(d (eG"J
I?L"M,X#fOG .-J3
2
"Q) 
_9?9H- J322 rXW3
"9?9`
-.
% 
KG !/
"1&2
,!
"2J  5Š&
0
%|}B~#K!
" 2
!
%'R 97&
h2
' 272#G
22
UM? 7
%
"
"Q Q5B 82fVW
%
#E2*2 5BE
" GA&Q!
"  
!
#[A/)
%"X$G 
G%8K A W5k3  2 o x G !  ]  #,5B _S2N
-. rX\ ] 3  2$g n xG _( /  €  #C5BQSS
%-J./ ;R]97&
Q'13
IC5,S2S
-f( .
%8E ) 2YG" #f*J"MO
%"XW E  !
, 5k&2
09?9?F€ A-5i
% 2Jl!!

%_&2
Q
Z'2f
!
#150&
SS
-. ` ) ( f& = 

k) 2
_z"x @IR ›:h0!   A #82 
K&/, f&2 ) &&
Q2
' 2!
%fYG"/ s GI& 2#
%.P
&
+   
+6>9?9y
-./J °
"  
%J°#* M?*#R4S'
G rXŠ&2
Q6>9?9csG% 2
G% r 1/&1G
% Af* >G 2-A #"X'22
7,Z#
2
),
J*1 J R  \&2JŠ
"/(   rX'M7
h2
U&2
h!
"ˆ. 5‡&2
8|}B~'U!
  2
%!
#7 7C3  5BhG% !/  MEf&&2
KS2v SS.
-.
R[U2 &2
%8 ( 2  GA&€MO 2ˆ3
Q! 
,Cf
%t)!
'G
 =  2
I  a-MEfGI&2
A@IXh# '22G)GI
" 
"]šb 
Ia&
+ G) 3
%:M7

€&
 GAP
%!5,G% 2
G% rRÁŽ f 
%.€&
g/(eM7* & & P
U GAP
%X' 7J.&
EY-ObM7$ "M?(:-A/ E3-X'G"   2 ) 2YG" #$ 
!J4&
.S• SS
GA&JZ#
%X;
 
%G%( 
f*#R

4.2 ›:, A
%Indirect ;?
% Jverification
\&
\
-. Kapproach  ) &2!‡ 0&
\‚0ƒ;U‚h6

 AG
X ME&GI&1
?G J
%G%
"$5ˆ Ã
")
?2$3 GAP'3  2
OP'X MO
2
$ 
%G%h
%fYG"/J 9?9v5B1.G
% A G% 2
G% rX#M7
E
%t
G%\&>&>6>9?9lJ>G 
G%f*!
-.
rR

k) 2
z/„ &2"ME$&2
.2- 32 ] 57&2
.2fVW
%
2G
!3
%:M7

 &2
7Sl $S2S,
%-J./
k2 J2)U
%
%A  AG
\/‡5B 2\fVW
%
# P'R•q2fVW
%
2G
9?9•-(  3J '
I 5¢ G%
%( z_57&
_D?¼,SMEf& 6>9?9ÁJ
% E& +nx x!R

k) 
.zg1 &"MEE&/8&2
06>9?9°2- 32 E 5Š&2
hbMO!J2P #
% 5¢G
E
0Z'2f
U !J"XME&
!&
h2- 3J ?/
0 ( 
"`a
%!.5KG 2
G% Rc97&2JQ&2
G" 
+MEf&`&

/ GJ$P',3
G"
_&2
%*+  f*G"/  *9?9v5O!G
I ( A CG 2
G% _>#
% 5¢G
%(z X f\JŠP
f* = 3Š> fM?*Š&


G 
/@[&7MO
UME; _
-.
8&
86[9?9s 5‡&OG 2
G%  4J#
% 5B G
I(-„#R1›:9?9Ã2- f( 322 2K 5?&
CbM7J#
% 5B G
%CG"]3
! ) 2YG" #f*2fVW
%
#"R 97&2Q.
%t
G%
rX?.! -Q9ED7F•G 2
G% 2_ A -5i
%A  f*J 2
K2f
G% rR 
,  _'
-) 
".&
hG%  
J 3
%bMO

$G 2
GIJ ;  6>9?90 A 2-5B
%> ™
O8
%t2 !
>ME&
%&2
%Š &2  
% (e6>9?9G 2( 2
G% 2O
1$ A-5B
I?! 
U/AR 7
"Q !&
8!
"  
%( !
%'>&/OM7
U&"
U  f*™
". C5¢/"X7JOJ2G 2G 
8C* &U&Uh&2
KG" 
$*. fRTT  J2)_,variations  A G
U 5k22A/in different ? X
"GI&Q&"#(

2).2A + 3   š
2XMO
CG 
%t2 !2
K&2
K-A fb* 5C&2
+6[9?9¯2- 3J °Ja&2
J!
% G" 
5C
%Q 5C
G%(  R . € A *€‚hƒ‡U‚U6• A G%
X š !  f*s 3   w x
G Xk4 
" GA&4 AG
%(:Z#/ 
%,$ 3  $„ „Q
G 2R

k) 2
4z + &"ME1&
!5i 2C
 f)9?9‰- J322 2 .5i  3 &'
I 5¢ G%
0 5\&2
1S'—KDaJ2P REuh Jf*#X&2
CDO— k0/U&2
5i 8Z' 
%E/
, ! -7&
0!
X'2/'J2)C  !
U
'ˆ
G%
&k&2
[6>9?9]- J322 2Š28kGA&)
[ ) fYG" #f*K$&2
!
 G 
Š 5
2k 5
G 2‡5i k&2
[ AG
‡MO
O
%t2 !2
"rRk¼hG%( G    f*#Xr&2
%
$
$  !
K!
" 2
!
#E
%'0/
%8ME&GI& &2
?6>9?92- 32 _[Z#2
EfVW
%
#"X 322Š&2J\2  f*C& ( 
%\ME&
!&
EG 
   2), AG
%(:Z# 
I7#
O2 [J2G

% 2) &!
  2
%!
#?  #R ›:ME&'*$&
E6>9?9l2- 3J [JC&
,z  #… ‰ .…  n „  AG
O
8ˆ/)
%73'*Qz"x x(:g x x !O5i 7 3  ?nxpà 5W&
EG 2
G%(  ?&&#
  „ w 2  A G
R ›:€&2
!
 G"J
%Q5,2"*X[M7
+
J#
%
%-
"ss2fVW
%
2G
 3
IbM7
%
M7

%P22*28MO

P
2R[]
0M7
I
$2JJf*
It2
%G% ( 2)__!
"  
,/MO
%U6[9?97U2)C&2
0M7

%P
WXh$
 f 5O"M7
I0
IbM7P)
Xr&'8"M7
%KZ#2

2).2
J*RU›e 
"4 2"Xk&"M7

%"XŠ&/$&CC2 $&
!G"
X>C
" -1J &2
,J2P'E&?MO
,&"
,
%t
%!
#
"!MEf&;R k) 2
_zŒ_ &"ME &2
U6>9?9s2- 32 O5i ?3 &!J#
% 5B G
%? 5r&
8›b‚h—°P!/ 3  $&2
! !
_!
_ &2

.fVW
%
#$*KJ]S

13
I 97&
75B J"ME)$6>9?9l2- 32 >
8 2JC
%!Š 5WG 2
G%(  R %]
.
!]&
.
" 
%_&.J?&2
Q
  
"J!
%_
J [S29hX Q C&
hG%  
   22)1!
hS —hJ
%) 1MO JQ3
&

,& 2?
"/J
I"R

„ x xz R‚U 
!&/C&2
%
/
.+!   A #$ 1G 2 -
#!2f5ˆ( 5B
I
G
%,J+&
%
16>9?9H2- 3 ,3
IbM7
%
<MO

P*, M7
%
P
2R197&
1
"  4."*+3
$&/,&
_Z#2

2)
J"*, 

IA 3 GAP3  
E
IbM7P' = G2)0&2
U83

"@>/
hZ#f
"MÄG !/
"Q1&2
02 ) +2
J*R ›b4&
!!
 G" 
C 58! #&2Xk J 21]&
.6>9?9N2- f( 3 G 3
_2
$
GA&2  )*GA&)
 =
R )2RX\ 2f 4 5 
IM¶P'_ C 
%A@IX> .
!4 ) (d
%µ›b#
%2
%C
 (  ° 
 =
R )RJX0) A Jf*°"M7
%9?9‰J- 322 ]/
I1!
_& ]*#
" = jGA&„x x x82>„ x xz/@,/$9k?–CRW846>9?9Ã2- 3  !
"  
"a5B+

% *°&
%! #&;RyFŠJaS'
2
%13
% „ x x x'X‡!J)
$5ˆA G% 45[G% 2
G% 2h& J)
I06>9?97U&  x x !R8S' !
%!
,/ 2¼hG% 3
%0„ x x xX&2
%
,M?h_."š-  &f5ˆJ2)45U&2
.6[9?9‰2- 3J /M7A_ 
$&CM7
%
 3  2,„ x x!0"M7
%"R0c    3
1
%t2ˆ/J 5B h&hGA&)
7&/?C/

hJ2P_ME&Q 2(d .2
%ˆ*.5Š 3  2  x x! M?C
2J G
"]MEf&l A 2J #GP<MEf&] (d 2
I( J*+ 5?3  $„ x x !XrG" 2 )„ x x !06>9?9v
"G% 44  &
h›b-A
%(e–0S2T A/^!G R[97&
02- 32 5i z"x #z  „ x x x.   !
IME&
%
$+&2
C!J22
X2G"2)Q&h&2
K
%:M7 P."* &"
3

aÁ4 A f Á-A/
+222)&/.! #&;XO ) 3  &Q&
,/
Jf
$ Q AJ'GKP'R 5.3 ¼h
%AdEffect XWMO
1&"of
$queueing , 32
%
"delays 
% -
#f*+G%
 
"+6>9?97

2)0G
I A !J!
%>72*2Š&>M7
EG" ./  32
7KZ#2

%( )!
J*2ROU8
%tG
J 1&2
h
X&"M7

%"X k) 2
!z"o  &"ME1&2
6>9?9‰2- 32 !/.S—,DN sj*Áz/n#X?„x x x =  j *@C/z z  „#z"† s„  n  2 [S29hR>97&2
„  n  µ A G
)"
1 9?9H2- 3J 4&0, &25ˆ
"+3'* "t2./
f* z"x x !h"M7A2,J/)
%K  
%,,3 &+J#
% 5B G
%R1Ã    J32

%tJ K5i ;&;GA&)
>r&ŠÂ &
\›b#
%2
%rG $/ 2 S—,SDU23
G" !
, ) fYG"#*G 2)
-
+ &/h!)X( L /)1&2
06>9?9°5Š! -8G 2
G% 283#* 3  2,zx x !R 7
"9?9hR

6. ]
>2SUMMARY
%
#
"K K
  AND /
"K8FUTURE    
[!
"  WORK 
!
#‡!
I&'(

  ) *$&>/ 
!2;h
-.
[&
O6>9?9]5Wh9ED7F+L"Ms22 ( ),&
EG 2
G% r OJ2fˆ-A )
ROj
"  
!
#> .

%A ‚0ƒ;U‚U6] A G
Š &2"M&;&
[
-. 1 ) &2H2'G
%  6>9?9a J2
U5i hn n"(bo n p•5‡&
09ED7F€M7P'J  WX
I!7 5 3#*'
Rk›:1
%!\ 5rGG2AG%*#X MO
?5B 2C&[ 3  2Ow x pÃ5 &
  
C!
  2
%!
#h/
$MEf&z"x pyKn!XME&GI&2

%h J)
%"X? 58&
6>9?9• 
&C|}B~'.M7 2Js!
" 2
R€8J X
%t
%!
#,MEf&‚0ƒ‡8‚h6c A G
%1 &"MO
"&/$&2
S2¶ SSQ   
$6>9?9T
%-J./
U ) 
%
$MEf&ž ”1”C“~2}d‘¦ ¢}dž ~§E¡I£"}e¡I±\X g x = n @IXW¼hG%"R „ x x x'R ‹ „"$j4RU. u$R2FŠt  rRW¼h \-.) \(d( \.‚h
IbM7PFŠ/&FŠ 
% 
R›b®7 ž"‘A¡¡ ’ }B~# ¥ ž-¬U¿$%­  ½ 0­ œ +XS
"Rrzw w wR ‹ g/$j4RU. ;X2uCR2FŠ/t2  ;X .HRS'

%R>©7­;® ­>ž ~##¡I¥A¢}¢ž ~s­>ž~¢ ž ³ X U"RWz"w w wR › [9 6 kDÁ„ n oz R ‹  CR 7ˆP#J &2;Xu$R‚CRFŠ 2.3&;XSWRS'
 &;X j4RS'
!X6KR CR K™ R9ED7F O
%&"'Jh5\ O2-* ›b#
%2
%US
I
% >U f* UQ›b!2/
%!
#R#›b ®7 ž"‘A¡¡’}B~' ¥Cž-¬   
¾ œ ­ œ +X2U"Rrzw w oR ‹ n",6KR [A 2
rRW§E:¡ %“'}B¡I”!¡I~¢¥>¬ž  A~2:¡II~ ¡I  ,ž ¥¢¥  ­>ž ”C”1“'~}d‘¦ ¢}¢ž ~ ‡ ¦ —¡II¥XW¼hGI"R;zw o w'R › >9 6 ‡Dvz z"„ „'R ‹ Œ/KŽ2R DOJ
 *#XSWR2—0 2
f*#X›IR˜UA & X$RjG/˜U
) "X  j4RFk
"  ;R—h
 ) +FŠJ2G
?5B08GGA
,FŠ  J
j
" 2
!
#"R2›b®?-ž"‘I¡¡ ’ }B~# ¥U®8¦¥A¥}B£ ¡C¦ ~ ’1¿8‘%¢}B£ ¡ ¡ ¦ ¥“'¡I”!¡I~¢¥.ªi®;‚¿ Q«1±[ž  ²¥-¤2žI|X U2"R„x x x'R

‹ …"CSWR kJ"*2 _R dRF\ ! )C&
0–U
, 5 >(d ( \DO )
- ž ”h|“¢}i~'9 l6 kDÁ„w o oR ‹ „ „"$ƒ>Rƒ>RFk
%
%    URWS R—,"
R>­>ž ”U|“':¡I,¾K¡I¢±[ž  ²¥A´ ¿c+½ —¥:¡I”1¥h¿O|| ž"¦ ‘A¤'Rrj )   K25B.rX„x x xR ‹ „ g/$$Ru[
I
R
%„/
'(eJ#
%
%-E. J2)_-"R &'   /M?M?M,R Gf"R  ) /L"*2 / &2
%" u>
%
R Ui„x x'z X U2"R„x xz R ‹ „ CDURuUJJ !™"/0DUR S' 2)2R U) &Fk
% 5i .G
K9ED7F€J U‚,S'#‚ >9hR¿$%­  ­>ž”h|“':¡I.­>ž ”1”C“'~}d‘¦ ¢}dž~§E¡I£"}e¡I±\X ¼hG%"R;zw w 2R

SP'G"
S2T f:*GA&
%GIP' SS. f:*GA&
%GIP' FŠ GAP
%8ƒr    ¼,¼,¼Ã
J
% * Ur &
IUSSQ P'G"
 9‡ A ?yH Š< ‰!& (+*-,  !ˆ  H+BD&B-H

U—8uU(:w w x xo„wz S—KD[(:w o w…w o o x g [aºU(bw o w o w o „ w 9k?–U(:w w „'z"g „ o x„ p‰G 2 p•3#*'
 ‰ p G% 2 p•3#*
% ‰ p G  p•3#*'
 N p G 2 p•3#*'
 xR x x'R x 'x R g xRz x R x xR x 'x Rz x'R x gRz „xR x z R g ŒR g x R g xR … 'x R Œ n#R „ xR  x'R o x'R o „'R n z R x z/„'R „ 'x R g x'R … g…'R n „#z Rz z R … „ x'R Œ ##… R  n'R „ '… Rz g „'R g 2z R x z R w  2R z „ w'R n o'R … z"oRz  oR z g oR „  CE•%&  J#$'$'&BDˆJ    )‘$'H  CEKJ  B J#‚? 5-“  J  &  CD!J  B H  ? 5>“ B "%& CVJ ;";&";&  &‰!H;B

2000

2500