A Framework Model for Packet Loss Metrics Based on Loss Runlengths

8/10/2019 A Framework Model for Packet Loss Metrics Based on Loss Runlengths

1/19

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


2/19


3/19

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


4/19

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



5/19

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



6/19

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



7/19

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



8/19

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

)



9/19

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 ]



10/19

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



11/19

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


12/19

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)


1

0 50-6

10



13/19

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


50

-610



14/19

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



P(X>=k|X>=k1)



15/19


0 5 10 15 20 25 30 35

10 4

103

102

101

100



P(X=1|X=1) k1 (1P(X=1|X=1))P(Y=k)

P(X=1|X=1) = 0.79


P(Y=k) (measured)


1

0 3510

-5



16/19


0 5 10 15 20 25 30 35

104

103

102

101

100



P(X=k)P(X>=k)P(X=m)

P(X=1)=0.79

P(X=m)

P(X>=k)

P(X=k)


0 35

1

10-5



17/19


0 2 4 6 8 10 12 14 16 18 20

104

103

102

101

100



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) (measured)


P(X=1|X=1)=0.99



18/19


80 90 100 110 120 130 140

104

103

102

101

100



P(Y=k)P(X=k)P(X>=k)P(X=m)


P(X=m)

P(Y=k)

P(X=k)

1

80 14010

-5

P(X=1)=0.49

P(X>=k)



19/19

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 Framework Model for Packet Loss Metrics Based on Loss Runlengths

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