8/10/2019 A Framework Model for Packet Loss Metrics Based on Loss Runlengths
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A F r a m e w o r k M o d e l f o r P a c k e t L o s s M e t r i c s B a s e d
o n L o s s R u n l e n g t h s
H e n n i n g S a n n e c k a n d G . C a r l e
G M D F o k u s , B e r l i n / G e r m a n y
f s a n n e c k , c a r l e g @ f o k u s . g m d . d e
M M C N 2 0 0 0
J a n u a r y 2 5 , S a n J o s e , C A
8/10/2019 A Framework Model for Packet Loss Metrics Based on Loss Runlengths
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8/10/2019 A Framework Model for Packet Loss Metrics Based on Loss Runlengths
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I n t r o
M o t i v a t i o n
M u l t i m e d i a a p p l i c a t i o n s a r e t o s o m e e x t e n t l o s s t o l e r a n t
( s i g n a l r e d u n d a n c y / s i g n a l i n t e r p o l a t i o n u s i n g d e c o d e r s t a t e )
T i m e - s c a l e o v e r w h i c h l o s s i m p a c t h a s t o b e a s s e s s e d i s s t i l l \ s h o r t " h o w e v e r
L o s s r e c o v e r y m e c h a n i s m s ( F E C ) a r e a l s o s e n s i t i v e t o s h o r t - t e r m l o s s
( s h o r t t r a n s m i s s i o n g r o u p s ! s h o r t d e l a y )
N e e d a d d i t i o n a l m e t r i c s t o d e s c r i b e t h e l o s s p r o c e s s
V a r i e t y o f m o d e l s / m e t r i c s p r o p o s e d i n t h e l i t e r a t u r e
! W h i c h m e t r i c s a r e u s e f u l ?
! C a n a c o m m o n f r a m e w o r k f o r t h e m o d e l s / m e t r i c s b e i d e n t i e d ?
A F r a m e w o r k M o d e l f o r P a c k e t L o s s M e t r i c s B a s e d o n L o s s R u n l e n g t h s 2
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I n t r o
W i n d o w - B a s e d M e a n L o s s R a t e
A v e r a g i n g d o n e o v e r s l i d i n g w i n d o w o f m = 5 a n d m = 1 0 0 p a c k e t s r e s p e c t i v e l y
0 100 200 300 400 500 600 700 800 900
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
sequence number s
m e a n
l o s s r a
t e s o v e r w
i n d o w m
p100 (s)p5(s)
L o n g - t e r m m e a n l o s s r a t e ( m = 1 0 0 ) d o e s n o t r e v e a l d i e r e n c e s i n p e r c e p t i o n
A F r a m e w o r k M o d e l f o r P a c k e t L o s s M e t r i c s B a s e d o n L o s s R u n l e n g t h s 3
8/10/2019 A Framework Model for Packet Loss Metrics Based on Loss Runlengths
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I n t r o
W i n d o w - B a s e d M e a n L o s s R a t e ( c o n t d . )
w (s)m
p (s)m
m
l(s)
s
s1
s1
1
analysis window
loss indicatorfunction
mean loss rateover window
p
m
( s ) =
l ( s ) w
m
( s )
m
=
P
a
= 0
l ( ) w
m
( s )
m
s : s e q u e n c e n u m b e r , a : n u m b e r o f p a c k e t s s e n t
A F r a m e w o r k M o d e l f o r P a c k e t L o s s M e t r i c s B a s e d o n L o s s R u n l e n g t h s 4
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I n t r o
W i n d o w - B a s e d M e a n L o s s R a t e ( c o n t d . )
w (s)m
p (s)m
s
s
1
1s
l(s)
1
m
k=2
analysis window
loss indicatorfunction
mean loss rateover window
k=3
- p
m
d e p e n d e n t o n p o s i t i o n s ( o c c u r e n c e o f k l o s t p a c k e t s w i t h i n t h e w i n d o w m )
- u s e o c c u r e n c e o f k c o n s e c u t i v e l o s t p a c k e t s w i t h i n t h e w i n d o w m i n s t e a d
- ! o n l y d e p e n d e n t o n k , o c c u r e n c e o f l o s s r u n l e n g t h s ( o
k
) i s b a s e m e a s u r e
A F r a m e w o r k M o d e l f o r P a c k e t L o s s M e t r i c s B a s e d o n L o s s R u n l e n g t h s 5
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L o s s r u n l e n g t h m o d e l w i t h l i m i t e d s t a t e s p a c e
= X= 2=
20
m0
12 23p
p
p
p p(m-1)m
X=0
01p
=p00 pmmX= 1 X= m
p10
X = k : \ e x a c t l y k c o n s e c u t i v e p a c k e t s l o s t "
X k : \ a t l e a s t k c o n s e c u t i v e p a c k e t s l o s t "
X = m : \ m c o n s e c u t i v e p a c k e t s l o s t "
m ( m o d e l o r d e r ) s e t e . g . t o l o w e s t n u m b e r o f p a c k e t s f o r w h i c h a n a u d i o
\ d r o p o u t " i s p e r c e i v e d
! e s t i m a t i o n o f m o d e l p a r a m e t e r s w i t h l o s s r u n l e n g t h s k
A F r a m e w o r k M o d e l f o r P a c k e t L o s s M e t r i c s B a s e d o n L o s s R u n l e n g t h s 6
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L o s s r u n l e n g t h m o d e l
M e t r i c s ( p a c k e t e v e n t s )
b u r s t l o s s ( 0 < k < m ) p
L ; k
=
o
k
a
P ( X = k )
b u r s t l o s s ( k = m ) p
L ; m
=
1
X
n = m
( n m + 1 ) o
n
a m + 1
P ( X = m )
l o s s o v e r w i n d o w m ( s t a t e p r o b a b i l i t y )
m e a n l o s s p
L
=
1
X
k = 1
k o
k
a
E X ]
c u m u l a t i v e l o s s p
L ; c u m
( k ) =
1
X
n = k
o
k
a
P ( X k )
( 0 < k < m ) ( s t a t e p r o b a b i l i t y )
c o n d i t i o n a l l o s s p
L ; c o n d
( k ) =
p
L ; c u m
( k )
p
L ; c u m
( k 1 )
P ( X k j X k 1 )
( 1 < k < m ) ( s t a t e t r a n s i t i o n p r o b . p
( k 1 ) ( k )
)
c o n d i t i o n a l l o s s p
L ; c o n d
( m ) =
1
X
n = m
( n m ) o
n
d m
P ( X = m j X = m )
( k = m ) ( d : n u m b e r o f d r o p s ) ( s t a t e t r a n s i t i o n p r o b . p
m m
)
A F r a m e w o r k M o d e l f o r P a c k e t L o s s M e t r i c s B a s e d o n L o s s R u n l e n g t h s 7
8/10/2019 A Framework Model for Packet Loss Metrics Based on Loss Runlengths
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L o s s r u n l e n g t h m o d e l
M e t r i c s ( b u r s t l o s s e v e n t s )
Y = k : \ l e n g t h o f b u r s t l o s s i s e x a c t l y k p a c k e t s "
L o s s r u n l e n g t h m o d e l a a r r i v a l s a ! 1
b u r s t l o s s l e n g t h ( k > 0 ) g
k
=
o
k
P
1
n = 1
o
n
P ( Y = k )
m e a n b u r s t l o s s l e n g t h g =
d
P
1
k = 1
o
k
=
P
1
k = 1
k o
k
P
1
k = 1
o
k
=
1
X
k = 1
k g
k
E Y ]
A F r a m e w o r k M o d e l f o r P a c k e t L o s s M e t r i c s B a s e d o n L o s s R u n l e n g t h s 8
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L o s s r u n l e n g t h m o d e l f o r m = 1 : G i l b e r t m o d e l
X=1X=0
p
00p
01
1-P(X=1|X=1)
P(X=1|X=1)
G e o m e t r i c d i s t r i b u t i o n f o r r e s i d e n c e i n s t a t e X = 1 :
P ( Y = k ) = P ( X = 1 j X = 1 )
k 1
( 1 P ( X = 1 j X = 1 ) ) ; k > 0
A F r a m e w o r k M o d e l f o r P a c k e t L o s s M e t r i c s B a s e d o n L o s s R u n l e n g t h s 9
8/10/2019 A Framework Model for Packet Loss Metrics Based on Loss Runlengths
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A p p l i c a t i o n o f t h e m o d e l a n d i t s m e t r i c s
T r a c e a n a l y s i s ( r e a l / s i m u l a t i o n t r a c e s ) : w h a t m o d e l o r d e r i s a p p l i c a b l e f o r a
c e r t a i n a p p l i c a t i o n i n a c e r t a i n n e t w o r k e n v i r o n m e n t ?
T r a c e s y n t h e s i s : p e r f o r m a n c e a s s e s s m e n t o f h o p - b y - h o p l o s s c o n t r o l a n d e n d - t o -
e n d l o s s r e c o v e r y
\ D e r i v e d " m e t r i c s ( I E T F d r a f t - i e t f - i p p m - l o s s - p a t t e r n - 0 2 . t x t ) ,
\ c o m p o s i t e " m e t r i c s ( u s i n g b o t h l o s s a n d n o - l o s s r u n l e n g t h s ) :
n o t i c e a b l e l o s s r a t e : N L R
E x a m p l e s f o r t r a c e a n a l y s i s :
- p e r i o d i c t r a c ( v o i c e w i t h o u t s i l e n c e d e t e c t i o n )
- 1 0 0 0 0 0 5 0 0 0 0 0 p a c k e t s p e r t r a c e ( c a . 1 = 2 3 h o u r ) ; v i s u a l s t a t i o n a r i t y
c h e c k
- v a r i o u s l o n g p a t h s (
>
1 5 h o p s ) w i t h i n E u r o p e a n d E u r o p e $ U S
- e x a m p l e s s h o w p e r s i s t e n t n e t w o r k b e h a v i o u r ( o v e r s e v e r a l h o u r s o r e v e n d a y s )
A F r a m e w o r k M o d e l f o r P a c k e t L o s s M e t r i c s B a s e d o n L o s s R u n l e n g t h s 1 0
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E x a m p l e 1 : G i l b e r t m o d e l t
0 5 10 15 20 25 30 35 40 45 5010
6
105
104
103
102
101
100
b u r s t p a c k e t l o s s p r o
b a b i l i t i e s P ( . )
length of loss burst k
P(X=1|X=1) k1 (1P(X=1|X=1))P(Y=k)
P(X=1|X=1) = 0.47
P(Y=k) (Gilbert model)
P(Y=k) (measured)
length of loss burst k
1
0 50-6
10
A F r a m e w o r k M o d e l f o r P a c k e t L o s s M e t r i c s B a s e d o n L o s s R u n l e n g t h s 1 1
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E x a m p l e 1 : S t a t e P r o b a b i l i t i e s
0 5 10 15 20 25 30 35 40 45 5010
6
105
104
10 3
102
101
100
b u r s t p a c k e t l o s s p r o b a b i l i t i e s P ( . )
length of loss burst k, length of loss window m
P(X=k)P(X>=k)P(X=m)P(X=1)=0.04
P(X>=k): cumulative loss
P(X=m): loss over window m
P(X=k)
1
0
length of loss burst k, length of loss window m
50
-610
A F r a m e w o r k M o d e l f o r P a c k e t L o s s M e t r i c s B a s e d o n L o s s R u n l e n g t h s 1 2
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E x a m p l e 1 : C o n d i t i o n a l L o s s P r o b a b i l i t i e s
0 5 10 15 20 25 30 35 40 45 500.3
0.4
0.5
0.6
0.7
0.8
0.9
1
b u r s t p a c k e t l o s s p r o b a b i l i t i e s P ( . )
length of loss burst k
P(X>=k|X>=k1)
A F r a m e w o r k M o d e l f o r P a c k e t L o s s M e t r i c s B a s e d o n L o s s R u n l e n g t h s 1 3
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E x a m p l e 2 : G i l b e r t m o d e l t
0 5 10 15 20 25 30 35
10 4
103
102
101
100
b u r s t p a c k e t l o s s p r o b a b i l i t i e s P ( . )
length of loss burst k
P(X=1|X=1) k1 (1P(X=1|X=1))P(Y=k)
P(X=1|X=1) = 0.79
length of loss burst k
P(Y=k) (measured)
P(Y=k) (Gilbert model)
1
0 3510
-5
A F r a m e w o r k M o d e l f o r P a c k e t L o s s M e t r i c s B a s e d o n L o s s R u n l e n g t h s 1 4
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E x a m p l e 2 : S t a t e P r o b a b i l i t i e s
0 5 10 15 20 25 30 35
104
103
102
101
100
b u r s t p a c k e t l o s s p r o b a b i l i t i e s P ( . )
length of loss burst k, length of loss window m
P(X=k)P(X>=k)P(X=m)
P(X=1)=0.79
P(X=m)
P(X>=k)
P(X=k)
length of loss burst k, length of loss window m
0 35
1
10-5
A F r a m e w o r k M o d e l f o r P a c k e t L o s s M e t r i c s B a s e d o n L o s s R u n l e n g t h s 1 5
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E x a m p l e 3 : G i l b e r t m o d e l t
0 2 4 6 8 10 12 14 16 18 20
104
103
102
101
100
b u r s t p a c k e t l o s s p r o b a b i l i t i e s P ( . )
length of loss burst k
P(X=1|X=1) k1 (1P(X=1|X=1))P(Y=k)
P(X=k)P(X>=k)
1
2010
-50
P(X>=k)
P(X=k)
P(Y=k) (Gilbert model)
P(Y=k) (measured)
length of loss burst k
P(X=1|X=1)=0.99
A F r a m e w o r k M o d e l f o r P a c k e t L o s s M e t r i c s B a s e d o n L o s s R u n l e n g t h s 1 6
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E x a m p l e 3 : S t a t e P r o b a b i l i t i e s
80 90 100 110 120 130 140
104
103
102
101
100
b u r s t p a c k e t l o s s p r o b a b i l i t i e s P ( . )
length of loss burst k, length of loss window m
P(Y=k)P(X=k)P(X>=k)P(X=m)
length of loss burst k, length of loss window m
P(X=m)
P(Y=k)
P(X=k)
1
80 14010
-5
P(X=1)=0.49
P(X>=k)
A F r a m e w o r k M o d e l f o r P a c k e t L o s s M e t r i c s B a s e d o n L o s s R u n l e n g t h s 1 7
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C o n c l u s i o n s / F u t u r e W o r k
F r a m e w o r k m o d e l w i t h v a r i a b l e c o m p l e x i t y b a s e d o n l o s s r u n l e n g t h s
E x p r e s s i o n o f w e l l - k n o w n a n d n o v e l l o s s m o d e l s a n d m e t r i c s
U s e f u l f o r t r a c e a s s e s s m e n t a n d t r a c g e n e r a t i o n
A u t o c o r r e l a t i o n a n d c o m p o s i t e m e t r i c s ( c r o s s - c o r r e l a t i o n l o s s / n o - l o s s
r u n l e n g t h s )
P a c k e t - l e v e l m e t r i c s : o w / A D U s t r u c t u r e i s n o t t a k e n i n t o a c c o u n t ( v i d e o ) ,
h o w e v e r e s t i m a t i o n / m a p p i n g p o s s i b l e
F o r s o m e o w t y p e s ( w a v e f o r m - c o d e d a u d i o ) : p a c k e t = A D U
L i n k t o a p p l i c a t i o n - l e v e l m e t r i c s / u s e r p e r c e p t i o n n e e d e d
A F r a m e w o r k M o d e l f o r P a c k e t L o s s M e t r i c s B a s e d o n L o s s R u n l e n g t h s 1 8