Gerenciamento autônomo de capacidade para centro de dados da internet.

!

" !

!# ! !

!

!

! + ,

./

! 2

7 % ! 2

! , # 8 +

37 2 !

7 9

% :;<℄

/ % !

>+,3 ? !

! ,# 2

3 2 #

' 8 @ !@3

9 29 3 #

3 3 !

A 3 !,

3 3 2 ! ? #

/ # , :B;℄ $

3 7 + 3

9

2 7 3

!

! :;<℄ C3 !

2 ,3

!2 3 3

3 ' 3 2 ! !

3 , A

$ 3

# ! ! ?

32 ! !

$ + 3

$ 37

% ?

2 D 2 7 2 +2

# 3 + A 3

7 3! 9

' 8

3 ! 9 7 3

8 9

> ? #

' 3 7 + 3

, , + #

$ 2 #

3A

8 2 :5E3 ;53<<℄

C3 ! !

! '

3

7

3 7 7 :5;℄ )!

32! 9

7 +

A 3 F

7

# , 3 !

9

:B;℄ ' 3 + 3

% >

:56℄3

3 ?2

9 )3

! 3 2 9 #9

F 3 A ?

! 3 ? , +

2 3 !2 A

# H

$ + 3 9

# 3 , 7

8

/ ! >

% D 2 # 3

9 3 9

? , 9 ,

$ H 3 2 8

2 3 7 F , #

% ,3

# - /

, !2

3 7 , 3

, 37 +

9

/ ,! ?

3

3 3 ,

+ , )

2 7 7 ! #

+ 3 73 3 7

2 I+- 3 3 J

$ ,37

3 3

A # % 7 ! - J

+

#3

! J

, !2 2 !, I #J

C3 +9

! , 3

9 +- 3 I J

IJ

& ? , #

3 ! 2 ,

9

#9 ! ! +2

3

A 8 3

2 7 #

3 7 A +3 #A

? # , #

!

$ , 53 3

%3 7 ' ! 7

2 3 7

3

9 7 2 :BE℄

/ 2

9 )3 7 !, 3

9 3 3?!

!, 3

+ ! >+,

$ 3 % 3 2

9 93 #

Infra-estrutura Física

Máquinas

Virtuais

Camada de Virtualização

Classe 1

...

Classe 2

Classe N

Interface para a Internet

NSLA

SSLA

Modo de Operação

Pico

Modo de Operação

Normal

0

X

X

tps

B- J ! % J'+

A

! 3?! 3 !

+ !@

'

! 3

9

) ! 7 # BIJ $

3 93 7 2 ! ,

3 AI&J3 9

+ 3A 3

3 ! 3 , & ?

3 7 3 !9 !, ,

2 & 7 F 3 2

3 # 7 #

!9 &

!,

F 3 93

F 9 8

A 3!2 # A

9 & 9?A3

& :;B℄3 7

/

, ; ) 3

+ 3 +

9

$ , <3

% 7 / , -

, 3

3 2 3 3

3 2

7

! "!

) ! ,

/ ,

3 23 7 8 + 3 ?

9 '

7 + 7

α

9 A+

R

SLA

3 ?3

P

(

R > R

SLA

₎

_≤

_α

3

R

7 F

9 !2

# F ,3

, 3 #

/ ! , 3

+ , A

X

N SLA

3

!2 93

7

X

SSLA

I

X

SSLA

_≥

_X

N SLA

J

3 7 +

3 # 3

A

8 + 7 # BIJ

/ ! ?

F 3# ?

+2 +

9

# $

/ 7 #

, 3 , 9

' &3 #

! 3 9

32 + )7 3

7 ,

!C - 3

I J IJ

)2 +

# , $ 3+ +

9 3

, 9 3 7

3 +9 #

+9 9-

K :5L℄3 " :5L℄ 3 !

#MMB3 ! :5B℄ '

+9 3 !

3 # +

%&

/ 2

> +2 ?

)#5IJ 2 3

, ),93 H ,

+ N

H

&3 +2 ? 3 2 ,

Modelo de Negócios

Modelo de Otimizacao

Carga

Prevista

Decisao de

Alocacao de

Capacidade

Parametros do

Controle de

Admissao

Parametros

do Modelo

Modelo de Desempenho

Gerenciador

de Capacidade

Monitoração

de carga

Nova

configuração

(...)

Parâmetros SLA e

de sistema

Infra-Estrutura Física

Máquinas

Virtuais

Camada de

Virtualização

Classe 1

Classe N

Previsor

de Carga

...

Previsão

de carga

(2)

(3)

(4)

(1)

...

5- J 2 J *

3

' ( ) *

)

% # 5IJ /

2 7

3 9

+2 ? 3 3 ,

9 + '

H , 9

IBJ ,

3 2 ,

! I5J O

7 3 9 3 ! +

3 3

I;J

) # 3

! 3

! !, 2 2 H

)7 93 #A

2 +9

/ + + &3 ? 7

! )

3 9 &

, + 3 3 ! 3 ,

#

) 9

7 7 # 3

9

$ A 7 3 7 2

A? # 7 2

2 3 7 I

J + ) 7

+9 ,

3 ,

/ 7 3

A3 3 +

9 3 #

' + K

+ 3 ! 3 9

C3 + 2 ! 8

2 +9 "!

# MMB ' F 2

/ 3 7 #

3 # ! )3 73

7 7 3 3

8 A3 !2 3

# 3

# &

3

+ 7 ,

)3 , P ! 9

Q@ K ! "

?! % "

% 3@@ "

) 3@ J *)

# @! @ !

3 J "M@

) " 3 +

! ! ! @ R

3 " # # S ?

! +2 T 3@ 2

" 3 @

"!@ K3 !

"3 3@ R !

@ ! "! ! !

3 S Q2) 3

38"3 3 3

3 3 2

) 3 3 ! &, )3 3

3 +3 ! !

7 ! D ! U )3

2 9 F 93 ! ) )! * 3

A ?

) 1@K * ) 3 )+ V3

*3 " !3 K 0"

+ 3

) )

1@K 0 (W 3 3 ( 3 XA K K3 A

U U 2

) 3 ? F

9 '3 ! S U3 ! U 7

$ ', 3 , 3 / K

0 2 ) 3 ! !3

' )&U3 ( (

7 3 3

# A

3 ! , #

)' I(/544;J1@K0(W I) 544<M5446J

) ! &, ) 8 1@K 0 (W

A 1* ) 337 2 3

BB 5

B5 ( <

B; /2 6

5B &2 E

<B *) 0 B6

<BB " (@ ) BE

<5 ) @ K BL

<; " 5B

<;B ) 5B

<;5 /2 5;

<< ' ! 5P

<6 " 5E

!

6B '+ ;4

65 $( ;5

" #

PB S K <4

$ %&' (&) * *

B J! % J '+

A

5 J 2 J*

5B % Y

55 % ! E

5; ) 2 L

<B '+ ! " @ !

BY

<5 54

<; " 3 5;

<< /2 5<

6B " K J

BJ 5 ;B

65 )" R! + ! "

@L4Z #3"

K + 3 @ J!

MMB J! MMB I J ;;

6; ! !J&BJ&5! MMB

;<

6< ! !J&BJ&5! MMB

I J ;<

66 ! ! J & B J& 5 ! MMB ;6

6P ! ! J& B J&5! MMB I J ;6

6Y ! ! @ " J&B

J& 53 ! MMB ;P

6E ! ! @ " J&B

<B 0 " BE

<5 & ! " @ BL

<; 55

6B *) " # + ;5

)B %" ! <5

S+ @ " !@"3%3

K3 3 3 3

! R

" ! +"

! 3 " "

" :;<℄ #"

% 3 *) I * )J :B;℄ @

" ! %

I% J

% 2 3 !

2!@ ! 3K

@ @ K ! % 3

" >+" " " #

3" 3 R

3 2

% @ " 3 @ "

#+ @@ !@3 R 3

+ 3 % #!

" ! " ! % 3

3 @ ! R3 %

K ! +3@ @ "

>+" )3

" R #"

% *) 3 3

+ ! ! I3 J

>" ! *) 3 " ! !

" " ! :;<℄

%"3@@ K " +2

" " @

3 ! " ! " Q

! !

3 @ "

3 " + " ! K" 3 3

" 1 @3 R ! "

" R " "3 "

?+ ! ! )

3 " @ ! >

- ? @ "

% + 3 @ ! +

+ ,"% %

S@ !I! "J @ !#

! % ["% "@"

? % " "3 @

@ " %

S ! +2 T @ *)

3 " " #! !

S @ K "T " > ! " R

! T # ?3 ! " !

S " ! ? ! %Q :B4℄

! I J" :5<3 <B℄ +" +

3 ! K @3 @ @

" @ K ) "3 @ ! "

@ :B43 B;℄3 @ K @ %

3@ ! @

3 +

Q I3 3 3

"3 J I3 3

" K K ! 3 !

@ K 3 " ! R

3 3 "3 T # ? $

"3 +" ! K ) ! !

+"3 !+ "3" !3

3 3 33 "3 @

" K @

0 ! K

Q !@

3 " 3 !

!" 3 R

! ! 3

" ! ! +

3 ! ! !

" ! +3

! +3 !

K"3 3 3 "

% 3

3 ! !

* 3 !

@ " "! :5E3 ;53<<℄3 !

" #+ ) 3 ! @

*) >+

" ! + +" %

" @ K " > 3@

" " ) 3

+ 3

" Q K

3@ K +" :56℄3

" + ! " #

! " *3 @ "

! ! # " " !

"3 @ ! "3 " "

K

Q ! " ! %

% + 3 @ @

+ - $,$

S@ ! "%

"

) 3 @ *) # @ @

" "! S @

@ # @ R 3 " Q

3 " ! + " I " J " @

3 %Q I3 3 3

J + 2 3

" " !

" S 3 "

! 3 @3 "

@ + 3 + 3 ?

3+ *3 @# T ?

+2 ! ! @ +

!

) " 3@ !

! ! % 3 " 3

! 3 @ K !

Q !

@ " "+ "

! 3 @ ! K

! 2 ! 3 @

@ !

BB3! !

% + 3 !

" ! 3 ! "

3 @ @ Q J +

! " ! " ! 3 ! @

" ! 3 J !

K 2 )

3 + ! Q3 @ R

+ + 3

!"! ! + ! ! 3

@ R @ % "

1 ? %Q 2

3 @3 +2 % T ?3

" @ K 3

3 " @" "

3 ! % K" 3

"3 " 3 @

!@ K

"3 "3 @ R !

3 @ " "

3 " T *)

@ !

+! .$/$

Q ! 2 ! @ 5 @ !

; @ K % "

+ <

" 3

3 !@ K3 2 3!

Q R ! 63 @

"2 !% @

# R ! "3 P

% ! 2 @

! >+ %@ +

2@ !@ 2 @ #! !

I3 "@ !%

J % " ! !@

" R !@ + " 5B

! % @ I J !

@ @ K Q !

>+" % I 5BJ @ %

+

" % 3 " "3 K @

:BP℄3 @ "@@ K

! 1 @3 2 3

" ! ! 3 @

R !

0! ! % 3 # " Q

@ K ? % 2 @

[ @ K @ K 0 @ K ""

" # @ " " /

3 @ K !

@ K %@ K " I"J

! @ " @ " I3 K J

@ @ K ! # ! %

K ! "

)@ K " ! :BP℄3 @ K

Processing Elements

Storage Elements

...

...

Switched

Network

Fabric

Physical Infra-Structure

Flexible Infra-Structure Provisioning

Internet

5B- %

" % %

) " " @ + " "

% " % ) + ! 3

@ 3 " 3 3 %M/3 @ K @3

@ @

Q"% " ! R "3

? R@ K 3@R + "

!@ S

3 " "2

% + 3 2 3 3 @ R % !

Physical infra-structure

Virtual

Machines

Virtualization Layer

Class 1

...

Class 2

Class N

Internet Interface

55- % !

+ $"$/$

)K" ! ! % " ! "

! @ R ) "3 2

:L3BE℄I ! "J " !

&2 ! 3 @ !

"I J @ "

\"] :BE3 <;℄ Q 2 R

R 3 !

! ! " 3 " @ ! :<;℄ I3

"3 3 J % @ K3@

! 2 + @

% % 3 2 ! " I3

3 J 3

! ! " " 13

! " "3 %

! ! 3"

/!3" !3

"3 %M/3 @ K3

Q % ! % 3 @ K3

55 Q 2 " $

I&J I K @ :L3 <5℄J

..

.

Resource

Class 1

Class 2

Class N

Utilization guaranteed

for each queue in the resource

20%

12%

2%

5;- ) 2

! % T "

Q ! 3

! @ 3 @ K ! ! I"J"

% ! 3 ! "" "T

! I3 J !

3 % " 2 @ "

3 "

3 ! " Q "

% Q

" ! @

! ! +3 !

1

54Z "

2

E4Z !

I3 J3 54Z ! 2

1

3 E4Z

2

) 3 % >+"

+

R 5; " @

N

R

3R3 2

&2 "

@3 " R)% I) %!J

@ # +

13 @ # " ! !

!"&

i

I

i

= 1

, .., N

J ! " ) "3 " "

:<Y℄3 # " :;6℄ :;<℄

? ! +3 & "

" " !

% R ! 3

! ! 3 !

% ;3@ K " ! %

3 +" ! ! 3

@ @ K 3 K !

" Q3 ! # %

!

"

%3 @ @ K @

@ K ! @ S "

! " % 3 @

! ! @

! " 3 @

3"3 2

Q +" ! "3@ @" K

@ !3 !

% @ K3 @ K ! !3 !

S ! !

3 @ 2 @ 3 "3

! "3 2

! !" ! ! %

3 @ @ @ K

Q "

! %Q " Q +2

2 "

3( S :;<℄" ! " !

! % :B;℄3 0

3 @ ! 3

@ K3 # K @

! @ ! "! @

( :;5℄ !

! I3 "3 3J3 @

" " ! @ ! ! !

Q ! @ K " 3 @

! #

" !

% 3 !

3 ! % !

3 SK3 3 :<<℄

" ! 3

@ :BE℄

! 2 ! )"

:P℄ ! !

@ ) 53

!3"2 3 @ # 3 @

" " " ! !

S " ! @ 3

" ! )

# K3 @"

Q @ K 2 3 " @ K

" 3 3 ! 3 ! " 2 /

+ !@ K 2 2 @!

@ " ) V :<℄ Q O :;Y℄3 @

! ! @"

@ K !"> "3K @

+ ) ! " )2?K3 ) (

:6℄ @ ! R @ K

"

1 @3 K 3 " "

! @ K ! "

( 2

! + R Q " R

+3 V :<Y℄ 2

2 @ K ^ 2 V :<P℄

! ! %

@" # K3 "

( :<4℄ + " K ! " ! "

R ! )

2 ! " 3 !

- ? "

Q ! "

" ! " " 2 !

"3 " " ! 3

+" ! 3 ! % !

!3 I !J !

" +" ! " ) "

! " 13 :54℄ % @ K3

@+ 3 "

+" " % 3 @ K

R! ! Q

! 1T K:BY℄!

! % " @ " K"

3 @ "

!@ K

Q ! " ! " @

- !

@ K @ ! !

1 @3 " " " ! 3 "

" " ^ ) + ! !

" # ! @

! " 7 0 :5Y℄

#3 !

3 !

! 3 ! !

Q

! 3 3 ! !

! ! ! Q" ! 3

3 3

3 !3 @ + 3 @

^ 2 Q 3 S :<5℄

" ) +2 ! " ! 3 " "

! ! ! "

7 0 :B5℄ ! !@ K3

@

" ) ! 3

@ ! 0"@ K " *)

0 @ 3

:B<3 5;℄ Q "

@ ! 3 @ @ !

3 3 3 + 3

" @ + !

% @ "

! @ K :53 ;℄ S @ K # !

? :B4℄ ! %Q 3 ! !

:5<3 <B℄3 @ @ " 0

7:B4℄3 @0 :B;℄3 @!!@ K! +

%Q K Q 3

!" R ?3 ! R I 3 3

3 J3 %Q @ !

? Q 3 !

R ! 1 @3 K !

3 " "3 "

3 " ! ?

"3 *3 3 S ! :5<℄ @ &3 3 (

:<B℄ @ ! !

Q

" 2 @ !

" 1 @3 " ! @

? ) 3 " @ K 3 @

! " 3 @ K @

% + 3@ " @

! " "

Q "

% " # *)

@ !

@ <B %3 !@ K "

@ " ! <5

Q <;B3

2 ! <;5 "3 <<

! +

'+ 0$1 $ "

Q *)

@ ! "M@

Q " ! +

@ *) Q @ K !

! %

*) 3

! 3

@ @ "

M @ ! @

@

Q% R" !+ ! @" @

+ @ @+ !

3 @ 3 !

3 " " :E℄ "

" ! % @ K 3 @ @ !

S @ @ @ !

# @ R 3 "

% 3 @ #

! ? " ! @ 3

3 @

+ " @ K K

Q @ ! @ @

@ K K "! !"

K ! 3 "

!" " " 2 ! Q! 3

! 3 @ *)

@ " ! + " "@ 3 @

R " @ >+"

Q @" ! %

! " 2 !

I3 J3 @ K@

- ! " Q3 *)

! !" &T " 3

" ! # )

"3 3@

! !

i

+

R

SLA

i

!

α

i

×

100%

! 3 "3

P

(

R

i

> R

SLA

i

)

≤

α

i

3

@

R

i

! !

i

Q ! " !

Q 3 " 3 ! " ? %

3 ! "

@" I! *) J

"3@ ! @ !

@ %

3 @

λ

i

3

X

i

3

µ

i

!

i

NSLA

SSLA

Surge Operation Mode

Normal Operation Mode

0

X

X

tps

<B- '+ ! " @ !

@ @

R

SLA

i

3 !

Q3 ! 3

Q

i

<

(1

−

α

i

)

3

µ

i

< X

i

3 " @

@-

µ

i

=

Q

i

X

i

+

α

i

(

Q

i

X

i

) = (1 +

α

i

)(

Q

i

X

i

)

/@3 @

Q

i

≥

(1

−

α

i

)

3 !

3 3

3

µ

i

=

X

i

<B"+ !" @ !

% ! 3 *)

! ! 3 $ *)

3 ! 3 *) Q $ *)

!

i

X

N SLA

i

3@

$ 3 !$ *)" 3@

! ! 3 @

R@$ *)

3 R " " "3

*) "

! @ K K Q3 3

X

SSLA

i

I

X

SSLA

i

≥

X

i

N SLA

J3 @ 3

@ @ !

i

" @ @ +

X

N SLA

i

) "3@

Q <B- 0 "

%"

R

i

I J !

!

i

R

SLA

i

I J !

i

α

i

" !

R

SLA

i

!

i

λ

i

I J !

i

X

i

!

i

IJ

µ

i

!

i

IJ

X

N SLA

i

I J !

i

X

SSLA

i

IJ !

i

Q

i

(!" ! @

@

R

SLA

i

Q ! ! !

I <5J ! @

Q3 !@ K3@# T

? ! " & +2 !

@

% 2 "@ *)

Q3 " # @ !" ! 3 @

R 3 ! R

"3Q <B2" "

!

' , - *

Q @@ @ " R

! + ! !

# O 3

$ *) &T "

X

N SLA

Q <5- & ! " @

" &

"

Y

i

µ

i

< X

N SLA

i

min

{

X

i

N SLA

, λ

i

} −

µ

i

(@

Z

i

µ

i

≥

X

N SLA

i

min

{

X

i

SSLA

, µ

i

} −

X

i

N SLA

! !

i

) <B3 ! R@

$ *) 1 @3

" "

X

N SLA

i

2 " !

! 3 " @

µ

i

< X

N SLA

i

µ

i

< λ

i

% 3

"

Y

i

=

λ

i

−

µ

i

1 @3 $ *)

X

N SLA

i

3 !

µ

i

< X

N SLA

i

λ

i

≥

X

i

N SLA

3 "

Y

i

=

X

N SLA

i

−

µ

i

Q3 "

? +

Y

i

=

min

{

X

N SLA

i

, λ

i

} −

µ

i

"3! ! +

$ *)3

µ

i

≥

X

N SLA

i

3 2@

" ! R@ +

$ *) 1 @3 ! @ +

X

SSLA

i

*

Z

i

! @ "

i

@ + @

Z

i

=

min

{

X

SSLA

i

, µ

i

} −

X

i

N SLA

Q ! *) @

! Q " @ ! "

0

)" @ 2Q<5 *3

@@ @

c

i

3@" ! ! $ *) 3

π

i

3 @ @ ! ! +

X

N SLA

i

!

i

'+ %$ %23

% "@" ! 3

@ <5 Q !

@3 +@ K !&3

*) 3 " ! 3 # %

Capacity

Manager

Workload

Monitoring

New IDC

Configuration

(...)

SLA and System

Parameters

Physical infra-structure

Virtual

Machines

Virtualization Layer

Class 1

Class N

Workload

Forecaster

...

Workload

Forecast

(2)

(3)

(4)

(1)

...

<5-

2 I <;5J@

" ! Q! 3 "

# @ *) " !

I <B 2 Q <; ! <;BJ IBJ Q

@ I3 @

! 3 J

Q ! "

" ! @ K ! I5J % !"

I3 J ! @ K

! " ) "3 ! + @ K

! :B℄ 3 3 @ K

K" ! "3 !

" " I;J

)! " 3 "

@ % # " I<J3 ?

2 " @ "!

! &

S! @

Q !" ! ! "

#+ ! " 3

3@ @ K ! "

2 @ # K" %

3 " !

/ 3 + " 3 @"

I3 K ! @ K J Q3

+3 @ @ K

@ K + @

+ 3 K !

" !# !

"3@ ! @! +

! ! 3 !

'+! &$4 .% "

Q " ! %3

I <;BJ3 2 I <;5J

' *

Q 3 @ "

3 Q <; ! + "

! *) @ " "

@ K !

Q *) !

<B Q " !- BJ

N

! & " 2 "3 " ! "

3 5J + 2

υ

i

@ &

i

3 ;J ! !

i

"I@ + @ "J

υ

i

!

@ @ 2 B44Z Q3

! " &3 !

υ

i

I

0

≤

υ

i

<

1

J #3 @ 2 ! &

i

S ! "

3 "

Q! 3

E

[

S

i

]

!

i

3@ + " ! !

S

i

3 + ! "

Q <;-

*)

%"

X

N SLA

i

IJ !

i

X

SSLA

i

IJ !

i

R

SLA

i

I J !

i

α

i

" !

R

SLA

i

!

i

c

i

" ! ! $ *)

!

i

π

i

@ ! ! +

X

N SLA

i

!

i

"

N

! 3 ! &

υ

i

+ 2 ! &

i

E

[

S

i

]

I J !

i

"

S K T

λ

∗

i

I J !

i

! +

P

{

Z

i

}

" ! 2 @ !

i

+

& ! ! ! " 3

K

f

i

! ! &

i

3@ + &

E

[

S

i

]

/f

i

) "3 " ! " ! I3

f

i

, i

= 1

..N

J &

i

Q! 3

f

i

!

Q @ @ !Q <; ! @ K !

) <53 " !

@ K !

λ

∗

i

! !

Business Model

Performance Model

Optimization Model

Predicted

Workload

Capacity Allocation

Decision

Admission Control

Configuration

Model

Parameters

<;- " 3

S #+ 3 #"

+3 ! @

" 2 " "

$ *) + "

# "3 @

@ @ @ 2 " ! ! Q3

2 R3 @ K ! "

" ! ! 3 3

X

N SLA

i

3 + Q3

P

{

Z

i

}

" @ 2 ! &

i

%!

" @ @ K 3 " "

1

' %& $

% 3 @ 2 @

@ ! I <<J 3 !

3 *) # @ K !

3 " +2

T ? Q ! "

3 @ 3 3

<; Q ! !@ K I

<5J

Q ? ! + !

+ " R ! + !

N

i

=1

N

i

=1

−

c

i

Y

i

+

π

i

Z

i

P

{

Z

i

}

Y

i

≥

min

(

X

i

N SLA

, λ

∗

i

)

−

X

i

(

a

)

Y

i

≥

0

(

b

)

Z

i

=

δ

i

(

min

(

X

i

SSLA

, X

i

)

−

X

i

N SLA

) (

c

)

Z

i

≥

0

,

δ

i

∈ {

0

,

1

}

(

d

)

λ

∗

i

=

λ

acc

i

+

λ

rej

i

(

e

)

X

i

=

λ

acc

i

(

f

)

P

(

R

i

≥

R

SLA

i

)

≤

α

i

(

g

)

ρ

i

=

λ

acc

i

/λ

sat

i

≤

υ

i

(

h

)

N

i

f

i

≤

1

(

i

)

0

≤

f

i

≤

1

,

ρ

i

≥

0

(

j

)

X

i

, λ

acc

i

, λ

rej

i

, λ

sat

i

≥

0

(

k

)

<<- /2

Q@ 2 << !

3 " + @ IJ IKJ

IJ IJ + @ Q <53

λ

i

µ

i

! "

λ

∗

i

X

i

I @ K

µ

i

=

X

i

J " $ 3

Y

i

≥

0

IJ3

Y

i

0

!@I3@

X

i

> X

i

N SLA

J % 3 IJ IJ3#"

δ

i

! + !

Z

i

Q3

δ

i

!

0

@

X

i

< X

N SLA

i

3

K

Z

i

= 0

! /@3

δ

i

1

" 3& !

1 @3 +

@ ! Q! 3

@ & " ! + :;B℄

@ &

λ

i

=

λ

acc

i

+

λ

rej

i

3@

λ

acc

i

@ &

i

3

λ

rej

i

@ &

i

?

Q + 2 " IJ3

λ

∗

i

+

" " &3"

%! @ 3 ! & ?

! Q! 3 + IJ

+ ! ! & !

! " 3

R

i

=

f

(

λ

acc

i

, f

i

)

3 IJ ! & "

@ !" ! "

!

f

i

3 @ ? ! K

µ

i

=

X

i

! $

α

i

+ R @ " !

%3

α

i

@ ! @ 3

@

α

i

! + !

Q 2

ρ

i

! &

i

# " IJ !

λ

acc

i

λ

sat

i

@ &

i

I <<J %

2 3 " + 3

ρ

i

! ! ! ! ! " & 3

ρ

i

=

g

(

λ

acc

i

, f

i

)

3 IJ " "

ρ

i

υ

i

×

100%

) !

λ

acc

i

"

IJ3 IJ IJ3 " + 3 ! 3

+ @ 2 "

Q " + IJ Q "

&

100%

*3 I?J IKJ !

% 2 @ "

3 " + ) "3 IJ

IJ @ IJ IJ

"

Q! 3 ! !

!

λ

sat

i

P

(

R

i

≥

R

SLA

i

)

3 " IJ

IJ "R + 3 @R

! " S ?3@ +

Q + 2 3

IJ + @@ ! !

+ I <<J3 ^" " !

@"

'+' $%$. - 5% $

Q " !

! 2 <;5 )

3 ! 3

*) 3 @ K 3 ! %

# ! ! # *)

Q ! ! !

! " ! Q

+ " ! " ! "

! :5B℄ @ " ! 3

! + + 3 ! 3 2

:<B℄ +3 + ! !

! @

! @+ " 3@

! @ K @ :<6℄ Q3 @

R + !

@@ ! 3 ""

" ! ^ 1 @3 ! K ! "3 @ K

! @ !" ½

! #

! R ! @

K-•

"

! @ :5<3 <B3 ;4℄3 @ S

! + "

•

S @ " ! ! 3

" MMB MMB @ I J Q ! @ K

3 @ " ! 3 !

+3 @ @ 3 @

! @ " 3 @ "

! ! ! "

½

:;P℄ 0 !"

! :<B3 5P℄

*"# !&

i

)"2 *@ :5P℄ ! @ + ! 2 -

ρ

i

=

E

[

S

i

]

f

i

×

X

i

Q3

-X

i

=

ρ

i

f

i

E

[

S

i

]

≤

f

i

E

[

S

i

]

=

λ

sat

_i

.

I<5J

$ "

λ

sat

i

' <5 IJ ! <<3

! @ ! ! -

λ

acc

i

≤

υ

i

f

i

/E

[

S

i

]

* @ +

" ! S K T %" :5L℄ #

+ 3 " + ! 3 @

+ ! MMB MMB I J

:5B℄-E

[

R

i

] =

E

[

S

i

]

/f

i

1

−

ρ

i

.

I<;J

Q3 " I

IJ ! <<J3 +

K T %"

-P

(

R

i

≥

R

SLA

i

)

≤

E

[

R

i

]

R

SLA

i

=

1

R

SLA

i

E

[

S

i

]

f

i

−

λ

acc

i

E

[

S

i

]

≤

α

i

I<<J

Q ! K T %" "

MMB MMB I J "

$3 ' << ! 3 ! 3

" !

/!3 K T"

""T%":5L℄ 1 @3

! Q 3 !

MMB3 "

:5B℄-V ar

[

R

i

] =

(

E

[

S

i

]

/f

i

)

2

(1

−

ρ

i

)

2

I<6J

MMB I J 3 !

@ ! ! :<6℄3 " !

?

"-V ar

[

R

i

]

≤

ρ

i

(

E

[

S

i

2

]

/f

i

2

)

(1

−

ρ

i

)

3

I<PJ

$ ' <P ! 3

@ @ " + !

"

! ! 3"T

" " ! T

*)

-P

(

R

i

≥

R

SLA

i

)

≤

V ar

[

R

i

]

(

R

SLA

i

−

E

[

R

i

])

2

≤

α

i

I<YJ

) ' <Y ! ' <<3

! 3 " !

Q + + !

! ! MMB :5B℄

+

-P

(

R

i

≥

R

SLA

i

) =

e

−

R

SLA

i

(

f

i

/E

[

S

i

])(1

−

ρ

i

)

≤

α

i

I<EJ

$ ' <E "+@ ? ! Q3

@ "3 +

+ Q! MMBI J :<6℄

% 63@ ! " " ! +

3 K 3 " 3

'+6 %%4

Q "

- " 3 !@ K3

2 3 3 #"3 ! % + 3 @

% !

% 3 @ " @

+ ! ! /

? R ! "

T "

" @ K 1 @3 !

+2 ! T ? @ + !

" ! 3 " ! % @

" 2 +3 @ @

Q3 @

! " " @ " "

! - J ! 3 J

! 3 J "

/ ! ! R +

" ) "3

& ! % " Q "

" ! &3 3

f

i

λ

acc

i

3

S

! 3 3 3

3 2 ! &

+ <<3 2

I ! J Q3 @

+ /$*5:;E℄ '+@

64 )

6+ )&$%" &

% + 3

! ! 3@ ! @

& ! "! ) ^

3 @ + " ! &

643

% K @ R R R

! ! " :;B℄ "

R ! "" 3! K !"3

! @ ! +3 "

K " Q " ! K

3 @ " Q

# I""J &3 !

λ

acc

i

!

2

% + 3 ! @ K

! ! ! % !3

!+! :B3BB3BL℄ "@

R ! " %3 @ ! 3

! K @ S

! "

@ ! ! + MMB

3 @ " @ @ +

" @

E

[

S

i

] = 10

−

3

3

MMB I J 3 +

@3 @

*3 @ " ! !

"3 2 " @ ""

" !

Q ! + @ " " @ K S K

! @ K

:5L℄ @ 6B Q #

! @

!

0

1000

3 " !

1000

3 !

100

$ @ !

!

500

6BIJ @

1000

750

500

250

0

1500

1250

1000

750

500

250

0

Arrivals

Time (sec)

1000

750

500

250

0

1500

1250

1000

750

500

250

0

Arrivals

Time (sec)

6B- " K J

BJ 5

K! " ! " ! " " "3

" " ! & + @ @ K "

) " " #! 3

"":56℄" !

@ " @ " ! +

Q _ 2 ! !

" :<℄ )

"3 "3 K @ + :;;3 <4℄3

3 K3 ! @ K ! R

3! 3@ " @ K

! "3 @ !

R 3 @ @ K !

@3 3 ! 3 "3 K !

@ " @ K 3 @ 1 @

3 @"

@ + ! @ K

" ) "3 + !

" "

1000

I " ' <5J3

! " !

0

1000

! @ K 3 " #

! @ K 3

100

3 3

Q 6B- *) " # +

υ

i

α

i

X

i

N SLA

X

i

SSLA

R

SLA

i

c

i

π

i

4L6 4B 644 B444 4B B4 46

" ! "

! @ K 3 ! 3 @

2Q6B $ @ ! !" Q

@ " 2 2 !

33 @ 2 "! $ *)

) !3 @ @ " 3

! % 3 " @

# ! ! 2 3

! @ K 3 !

"3 2 " @ K @

" @

"3 @ " ) @ @

! 3 @ K ^ " R #"

) 3 R ! @ "

! @ K 3 @ K ! 3

3 + ! @ @ +

6+ %$" "

% 3 R ! + ! ! MMB

MMB I J 3 + 3 "3 K 3

" 3 "2

S " R I3 ! @J

B4 ! + ! ! 3

! 3 @

90%

# !

65

Q 65 @! MMB3

3 " R ! + +"!

−

400

−

200

@

−400

−300

−200

−100

0

100

200

300

400

0

2

4

6

8

10

12

14

16

18

Average Payoff

Controler Interval

Percentile

Chebyshev

Markov

Static

!"!"

−400

−300

−200

−100

0

100

200

300

400

0

2

4

6

8

10 12 14 16 18

Average Payoff

Controller Interval

Chebyshev

Markov

Static

!"#" $%

65- ) " R ! + ! "

@L4Z #3"

K + 3 @ J! MMB

J! MMB I J

! " + "" R

" @ !

Q @ + +" !

0

200

% MMB I J 3 " R "

+"!

−

310

−

130

3@K +

!

−

125

100

3 " !

−

90

240

$ ! "

! @ K & % 3 K ! " R

! !@ @ @ K

) "3 @

" R3 " "

! & %3 @ K ! @ K

& " ! @

" R

S @ "2 " ! ! 3

" "2 3 ! 3

6; 6< @ ! &3

Q @ # @ 3 ! MMB 3 @

" " ! + 3 "

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0

10

20

30

40

50

P(QL <= x)

Queue Lenght

Percentile

Chebyshev

Markov

Static

&!

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0

10

20

30

40

50

P(QL <= x)

Queue Lenght

Percentile

Chebyshev

Markov

Static

&!

6;- ! ! J & B J & 5 !

MMB

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0

10

20

30

40

50

P(QL <= x)

Queue Lenght

Chebyshev

Markov

Static

&!

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0

10

20

30

40

50

P(QL <= x)

Queue Lenght

Chebyshev

Markov

Static

&!

6<- ! !J&BJ&5! MMB

I J

30

48

+"

75%

! MMB I J 3

" + 3 "

10

! N

K + 3

15

N @ K3

@

30

48

+"

75%

!

$ 3 @ 3 " @

! ! ! MMBMMB I J

:5B℄3 "

φ

i

=

ρ

2

i

1

−

ρ

i

(

ρ

i

" + 2

υ

i

= 0

.

95

3 @@ &T 3

φ

i

= 18

.

05

% "2 ! ! *)

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0

0.05 0.1 0.15 0.2 0.25 0.3 0.35

P(R

1

<= x)

R

₁

(sec)

Percentile

Chebyshev

Markov

Static

&!

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4

P(R

2

<= x)

R

₁

(sec)

Percentile

Chebyshev

Markov

Static

&!

66- ! ! J & B J& 5 ! MMB

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0

0.05 0.1 0.15 0.2 0.25 0.3 0.35

P(R

1

<= x)

R

₁

(sec)

Chebyshev

Markov

Static

&!

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0

0.05 0.1 0.15 0.2 0.25 0.3 0.35

P(R

2

<= x)

R

₂

(sec)

Chebyshev

Markov

Static

&!

6P- ! ! J & B J &5 ! MMB I J

& 66 6P! $

! &3@ 3@

@" + ) "3 !

@

0

.

1

90%

! 0" 3 +"

55%

60%

!

! & B 5 " MMB3 +"

57%

!

& MMB I J

3@ @ !

" " ! + ! @ 3

! 3" "R! !

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

−400−300−200−100 0 100 200 300 400 500

P(Magnitude <= x)

Magnitude

Static

Markov

Chebyshev

Percentile

&!

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

−400−300−200−100 0 100 200 300 400 500

P(Magnitude <= x)

Magnitude

Static

Markov

Chebyshev

Percentile

&!

6Y- ! !@ "J&B

J & 53! MMB

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

−400 −300 −200 −100

0

100 200 300

P(Magnitude <= x)

Magnitude

Static

Markov

Chebyshev

&!

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

−400 −300 −200 −100 0

100 200 300 400

P(Magnitude <= x)

Magnitude

Static

Markov

Chebyshev

&!

6E- ! !@ "J&B

J & 53! MMB I J

" R % R3"2

! @ " " !

S ! ! @

! &3 ! MMB 6Y !

MMB I J 6E

"3 3 #"

@ @"

% 3 ! K +

@ " Q @ +

@ ! 6YIJ 6YIJ3

! 6YIJ " Q 3

+3 33 3 ! &

1

3 "

" " @ MMB I J 3 R

3 " @ Q ! 65IJ

@ " R R " K " +

@" "

Q 3 @ !

" 3

" #" ! @

S K +

3 "

/ 3 " +

" R " ! MMB

3 " MMB I J 3

@ K + )

! K @ ! " !

I "J3 ! "! ! "

+ ! MMB3 @ " !

+ ! ! # 3 @ ? "

R ! ! " ! 3 MMB3 ! @

! I + + J

" ! ! R ! 3

@ 3 @ 3

! "

Q @ !

% P @ R !

Q ! "

? Q K 3

? R

@ " ! Q K 3 @

" ! %

@! R S ! +

% T *) 3

"

% 3 % @ "

! 3 @ > ! "

! @ K 3 @ *) # ! R

S @ @ #

@ R 3 " 3 @

!" 3 3 @

3 @ @ " ! + "

! @ @ K K

% 3 *) @ K @

3 " @ + 3

@3 " ! + " I

! J % ! *) 3 @

# ? +2 ! !

@

% " 3 @ ! %

! 3 " " 3 @ *)

! 3 ?

" "3 @ + 3

"K 3"3! ! !

@ R"? 3#

# I J I J

Q " @ 2

3 @ " + ! *)

@ " % "

@" T ? +2

Q " ! ! %

3 @ @ R ! /

@ 3 @ @

" 3 @ "

@ K K 3 3

K # # ! %

Q @ " ! ! +

' 3 R ! " !

+ + !

) "3 @ ! 3

K + ! @@

! 3 3 " "

@ + 33 3

" % 3" +

! " !

! !

% 3 + @ "

@ ! 3"

) "3 2 @

3 " " @ "

@ "

*3 @" " Q "

K " ! @ " +2

? %3 @ @"

3 @ "

" % 3 @ 3 " "2

! ! 3

3 " ! 3

Q 3 !

% ! @ 3 @ !

@ K

7+ 83

Q ! # ! K ! !

"3 @ " %

! 3 @ ! ! @ K "

!

Q # K " "

+ R ^ 3 + ! %

3 "3 @ ! ! 3

" & 1 @3 ! ! "

" " " K 1 @3

! @ &T" " ! 3 @

T " % 3 @ 3 ! @

T "3 @ !

" " K "? @ ^ ) 3

@ + @ 2 !

) " !

! I3 + J :;L℄3

+" + @ I @

@ KJ Q " K !

" ! ! I3 J

" ! R^ *

+ ! @ K:55℄ 1 @3+

" @ ! " ! +"

% ! 3 @ @ K + !

@ ! " !& "I3 3

K J % 3 @ ! ! @ K " !

%3

*3 @ + > ! "R@ K

% @ K @ @ R ! @ K

" ! @ 1 @3 @ K3 @ #

! Q # @ K 3@

@ K Q ) "3 +

! @ K " +3! "

K 3

" @ @K *3

" Q @ + !

^ ""3 " ^?

Q! + "3 +3

" ! @ 2 Q3 @

! > @

" ! !

" S " @ @

' ()

*)+ , ,

%+3 @ @ K

@ 6B

) :5L℄@

3 + ! " Q3 @ !

@ " @ 3 " !

λ

(

t

)

I

t >

0

J % @ K 3@

" ! @ Q)B Q#

3

λ

M AX

3 + N

s

! ! "N " "

c

N 3

o

R ! 3 @# @

Q )B- %" !

%"

λ

M AX

+

s

! "

c

"

o

R

* ! " )B @

# @ Q )5

3 ! +

" ! ! "3

λ

M AX

λ

M AX

_s

_c

_o

B444 B4 B444 4

1000

750

500

250

0

1500

1250

1000

750

500

250

0

Arrivals

Time (sec)

)B- K

" " " ! 3

c

s

Q3

+ ! " !

-λ

(

t

) =

λ

M AX

s/

2

(

t

+

o

)

s

c

(

mod

(

s/

2))

I)BJ

1 @3 ' )B ! ! @

" % 3

! ! "3 " !

λ

(

t

)

@

(

t

+

o

)

mod c <

c

:B℄ 0 ) U* ! U S"

3 BLE;

:5℄ 0 ) 3 & )3 U ) ) !

! %! " #

$ % $ &$ %$'()*3 5446

:;℄ 0 ) 3 & )3U )3)+V3 K0"3

" ! ! " ! %

% "%%%+"!", - &,- *3

) 544P

:<℄ 0 ) )+ V 2 @ K

2 ! " Q ( 1*544<B6Y3 1@

K *3 544<

:6℄ ) )2?K3 )3 U"( 0

! " Q ( 1*5445;;L3 1@K

*3 5445

:P℄ X )"3 K 3 * 3 23 X /

*) ! " % "!"+"%%% "'

" , 3 " 544B

:Y℄ X )"3 0 3 U ( 3 XS * "

". / 3 BI<;J-B54.B;63544<

:E℄ ) Q U S K 2 ! BLLE @ @

Q ( 1*BLLL;6(B3 1@K *3 BLLL

:L℄ 03 3 U ( - ) @ !" !

" %0 1 %,"2

% 4) "!"+"%%% " # 35 6

- 7 3 -3 544<

:BB℄ ` 0"K 3 ' R3 (3 0 `@ Q^

% Q 3 "3 $@ ` K3 5445

:B5℄ 0 7 ( !

" ! % "%%% "' $

35446

:B;℄ U 0 3 ( $ 3 * V *3 S3 U * S !3 `

" *) ? ".

/ 3 BI<;J-B6L.BYE3544<

:B<℄ ` 3$3 U*13 K3 Q" %/

!K ! ! @

@ % "%%%+"!" , - 3

5445

:B6℄ Q '3 X )"3 U 03 03 1 3 ) K 3 1

13 Q *3 3*0 3U)31 S

" !@ K "" ". / 3

BI<;J-LY.B543 544<

:BP℄ % X 8 9 X!3 5

3 544<

:BY℄ K Q 1 5 "

3 BLLY

:BE℄ 3 (! Xa3 &?" ?3 U "3 )K 3

) & % ! 2 " Q

( 1*544;B563 1@K3 544;

:BL℄ U13V3 )

, 3U" 5444

:54℄ X 13 3 X !- Q

+" ? b "%%% 35 3PIBJ3 5446

! %Q"@ " %"!"#<0 "

7 7

% & $*3 5446

:5;℄ c *3 c " V3 3 ) )

! % = "!"+"%%% "'

" , 35446

:5<℄ V *3 K 3 U * S ! / +2

# % $ % 3/ 544B

:56℄ 7 & ) #5 6

135444

:5P℄ 73 & )3*@ @" 5 3

13544;

:5Y℄ ) 7 $0 / !!

! " "%%% 35 3PIBJ35446

:5E℄ ) K- ) " ! "

". / 3 BI<;J-54.;B3 544<

:5L℄ ) 557 > ;57

@13< 35445

:;4℄ & + " S ^- Q ! !

"%%%+$ 8 , 3;I;J-55P.5<<3 BLL6

:;B℄ 1 X1'" - )@ "%%%

3;<IBBJ-E5.LB3BLLP

:;5℄ ) ( Q " ! !

". / 3 BI<;J-;5.<B3544<

:;;℄ U ( 3 c V3 )3 ) )2?K !

" Q 3 1@K *

3 ) 3 )3 )3 5445 1*5445B66

:;<℄ U S ( S ! " - Q !

%Q ". / 3 BI<;J-6.BL3

" "

Q ( 1*544<B<53 1@K *3 544<

:;P℄ ) 23 0 3 -

7 % U S"W 3 544<

:;Y℄ 3 3 )K 3 &?" ?3 c " V

U "3 U" ( 3 )3 O

" " Q ( 1*544<B653 1@K *3

544<

:;E℄ ) O ! " "

3;IE5J-<B;.<<E3BLLE

:;L℄ 0 K3 #3 "3K 23)

Q@ )" !

% $ "%8>" 3 5446

:<4℄ 0 K3 "3 Q " ( ( K

# ! %

1 %,"2 - 3 " 3 5445

:<B℄ &3 3 (

! " % "%%% "' # :

3 U 544<

:<5℄ S ' S3 Q 3 U/ X3 ( " !

% "%%% " $

&"$'(?*3544<

:<;℄ )@ SK3 ( +3 @3

@ @ % !

, 3 " &, 3" '(?*3 544<

:<<℄ U SK3 UR" 3 U # Q 3

1@K * 3 ) 3 )3 )3 544< 1*544<B5<

:<6℄ `K - " :

@ K ! Q

( 1*5445;4B3 1@K *3 5445

:<Y℄ c "V3 3 US3 K 0"3 (

!