title: Defining metrics for multicore throughput on multiprogrammed workloads. [Research Report] RR-8401, INRIA. 2013. &#x27E8;hal-00908864&#x27E9;
text: Defining metrics for multicore throughput on
  multiprogrammed workloads
  Stijn Eyerman, Pierre Michaud
  
  To cite this version:
  Stijn Eyerman, Pierre Michaud. Defining metrics for multicore throughput on multiprogrammed
  workloads. [Research Report] RR-8401, INRIA. 2013. �hal-00908864�
  
  HAL Id: hal-00908864
  https://inria.hal.science/hal-00908864
  Submitted on 25 Nov 2013
  
  HAL is a multi-disciplinary open access
  archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from
  teaching and research institutions in France or
  abroad, or from public or private research centers.
  L’archive ouverte pluridisciplinaire HAL, est
  destinée au dépôt et à la diffusion de documents
  scientifiques de niveau recherche, publiés ou non,
  émanant des établissements d’enseignement et de
  recherche français ou étrangers, des laboratoires
  publics ou privés.
   c=1
  
  ✸✳✸
  
  ■♥st❛♥t❛♥❡♦✉s ❥♦❜ t❤r♦✉❣❤♣✉t ✭■❏❚✮
  
  ■♥st❛♥t❛♥❡♦✉s ❥♦❜ t❤r♦✉❣❤♣✉t ✭■❏❚✮ ✐s t❤❡ ♥✉♠❜❡r ♦❢ ❥♦❜s ❡①❡❝✉t❡❞ ❜② t❤❡ ♠✉❧t✐❝♦r❡ ♣❡r s❡❝♦♥❞✱
  t❤❡ ❥♦❜ s✐③❡ ❜❡✐♥❣ ♣r♦♣♦rt✐♦♥❛❧ t♦ IP SbR ✳ ❚❤❡ r✉♥ t✐♠❡ ♦❢ ❥♦❜ b = s[c] r✉♥♥✐♥❣ ♦♥ ❝♦r❡ c ✇❤✐❧❡
  I
  T
  MC
  ❡①❡❝✉t✐♥❣ ❝♦s❝❤❡❞✉❧❡ s ✐s Tc,s
  = IP Ss[c]
  M C ✳ ❖✈❡r ❛ t✐♠❡ T ✱ ❥♦❜ s[c] ❤❛s ❡①❡❝✉t❡❞ T M C t✐♠❡s✱
  c,s
  c,s
  ❧❡❛❞✐♥❣ t♦ ❛♥ ■❏❚ ♦❢
  IJT (s) =
  
  PK
  
  T
  MC
  c=1 Tc,s
  
  T
  
  =
  
  Ib ✐s ♣r♦♣♦rt✐♦♥❛❧ t♦ IP SbR ✱ s♦
  IJT (s) =
  
  K
  X
  c=1
  
  =
  MC
  
  Tc,s
  
  K
  MC
  X
  IP Sc,s
  c=1
  
  ❘❘ ♥➦ ✽✹✵✶
  
  1
  
  R
  IP Ss[c]
  
  K
  MC
  X
  IP Sc,s
  c=1.
  Is[c].
   ASIE = K
  N s=1 c=1
  
  ✭✸✮
  
  ❋✐❣✉r❡ ✸ s❤♦✇s t❤❡ ❡①❛♠♣❧❡ ❚P❊❳✳
  ❆❧t❡r♥❛t✐✈❡❧②✱ ✐t ♠✐❣❤t ❜❡ ♠♦r❡ r❡❛❧✐st✐❝ t♦ ❛ss✉♠❡ t❤❛t ❡✈❡r② ❥♦❜ t②♣❡ ❤❛s ❛ ❞✐✛❡r❡♥t r✉♥
  t✐♠❡✱ ❜✉t t❤❡ r✉♥ t✐♠❡ ♦❢ ❛ s♣❡❝✐✜❝ ❥♦❜ t②♣❡ ✐s st✐❧❧ ✜①❡❞✳ ❋♦r ❡①❛♠♣❧❡✱ t❤❡ r✉♥ t✐♠❡ ♦❢ ❛ ❥♦❜
  t②♣❡ ❡q✉❛❧s ✐ts r✉♥ t✐♠❡ ♦♥ ❛ r❡❢❡r❡♥❝❡ ❝♦r❡✱ ❛ss✉♠✐♥❣ ❡q✉❛❧ ✐♥str✉❝t✐♦♥ ❝♦✉♥ts ❢♦r ❛❧❧ ❥♦❜ t②♣❡s
  ♦♥ t❤❡ r❡❢❡r❡♥❝❡ ❝♦r❡✳ ❏♦❜s t❤❛t r✉♥ ❧♦♥❣❡r ♦♥ t❤❡ r❡❢❡r❡♥❝❡ ❝♦r❡ ✭❥♦❜s ✇✐t❤ ❛ ❧♦✇ ■P❙✮ ❛❧s♦ t❛❦❡
  ❛ ♣r♦♣♦rt✐♦♥❛t❡❧② ❧♦♥❣❡r t✐♠❡ ♦♥ t❤❡ ♠✉❧t✐❝♦r❡✳ ❚❤❡ ♣r♦❜❛❜✐❧✐t② ❢♦r ❝♦s❝❤❡❞✉❧❡ s t♦ ♦❝❝✉r ❛t ❛
  r❛♥❞♦♠ t✐♠❡ ✐s t❤❡ ♣r♦❞✉❝t ♦❢ t❤❡ ♣r♦❜❛❜✐❧✐t✐❡s ♦❢ ❛❧❧ t❤❡ ❥♦❜s ✐♥ t❤❡ ❝♦s❝❤❡❞✉❧❡✿
  P r(s) =
  
  K
  R
  Ts[c]
  1 Y ❍✲♠❡❛♥(IP SbR )
  Pn
  =
  ,
  R
  R
  N K c=1
  IP Ss[c]
  b=1 Tb
  c=1
  K
  Y
  
  ✭✹✮
  
  ✇✐t❤ ❍✲♠❡❛♥ t❤❡ ❤❛r♠♦♥✐❝ ♠❡❛♥ ♦✈❡r t❤❡ N ❥♦❜ t②♣❡s✳ ❚❤❡ r❡s✉❧t✐♥❣ ✐♥str✉❝t✐♦♥ t❤r♦✉❣❤♣✉t ✐s
  ❞❡♥♦t❡❞ ❆❙■❈ ✭✇❤❡r❡ ❵❈✬ st❛♥❞s ❢♦r ❈❛❧✐❜r❛t❡❞ r✉♥ t✐♠❡s✮✿
  K
  
  ASIC =
  
  N
  X
  
  P r(s)
  
  K
  X
  
  MC
  IP Sc,s.
  ✭✺✮
  
  c=1
  
  s=1
  
  ❋✐❣✉r❡ ✹ s❤♦✇s t❤❡ ❡①❛♠♣❧❡ ❚P❊❳ ❢♦r ❆❙■❈✳
  ❏♦❜ t❤r♦✉❣❤♣✉t✳ ❋♦r ❥♦❜ t❤r♦✉❣❤♣✉t✱ ✇❡ ❛❧s♦ ✐♥✐t✐❛❧❧② ❛ss✉♠❡ t❤❛t ❛❧❧ ❥♦❜ t②♣❡s ❤❛✈❡ ❛♥
  ❡q✉❛❧ t♦t❛❧ r✉♥ t✐♠❡ ♦♥ ❡❛❝❤ ❝♦r❡✳ ❇❡❝❛✉s❡ t❤❡ ❥♦❜ s✐③❡ ✐s ✜①❡❞ ❢♦r ❛ ❣✐✈❡♥ ❥♦❜ t②♣❡ ❜② ❛ss✉♠✐♥❣
  ❡q✉❛❧ r✉♥ t✐♠❡s ♦♥ t❤❡ r❡❢❡r❡♥❝❡ ❝♦r❡✱ ❛ ✜①❡❞ r✉♥ t✐♠❡ ♦♥ t❤❡ ♠✉❧t✐❝♦r❡ ✐s ❡♥❢♦r❝❡❞ ❜② r❡♣❡❛t✐♥❣
  ❡❛❝❤ ❥♦❜ t②♣❡ ❛ ❞✐✛❡r❡♥t ♥✉♠❜❡r ♦❢ t✐♠❡s✳ ❚❤✐s ❛❣❛✐♥ r❡s✉❧ts ✐♥ ❛♥ ❡q✉❛❧ ♣r♦❜❛❜✐❧✐t② ❢♦r ❡❛❝❤
  ❝♦s❝❤❡❞✉❧❡ t♦ ♦❝❝✉r✳ ❚❤❡ ❆✈❡r❛❣❡ t❤r♦✉❣❤♣✉t ❢♦r ❛ ❙❝❛❧❡❞ ✇♦r❦❧♦❛❞ ✉s✐♥❣ ❏♦❜ ❛s t❤❡ ❯♦❲
  ❛ss✉♠✐♥❣ ❊q✉❛❧ r✉♥ t✐♠❡s ♦♥ ❡❛❝❤ ❝♦r❡ ✭❆❙❏❊✮ ✐s✿
  K
  
  K
  N
  MC
  1 X X IP Sc,s
  ASJE = K.
   MC
  ❍✲♠❡❛♥(IP Sb,c )
  
  ✭✼✮
  
  c=1
  
  ✭✇❤❡r❡ t❤❡ ❵✐✬ ❛❢t❡r ❆❋❊❊ ✐s ❛ r❡♠✐♥❞❡r t❤❛t t❤✐s ❢♦r♠✉❧❛ ♦♥❧② ❤♦❧❞s ❢♦r ✐♥s❡♥s✐t✐✈❡ ❥♦❜s✮✳
  
  ■♥
  
  ❝❛s❡ ♦❢ ❛ ❤♦♠♦❣❡♥❡♦✉s ♠✉❧t✐❝♦r❡✱ t❤✐s ✐s ❡q✉✐✈❛❧❡♥t t♦ ❝♦♠♣✉t✐♥❣ t❤❡ ❤❛r♠♦♥✐❝ ♠❡❛♥ ♦❢ ❛❧❧ ■P❙
  ✈❛❧✉❡s ✭❍■P❙✮✱ ❛s ♣r♦♣♦s❡❞ ❜② ▼✐❝❤❛✉❞ ❬✶✶❪✳ ❍❡r❡ ✇❡ ❤❛✈❡ ❣❡♥❡r❛❧✐③❡❞ t❤❡ ❍■P❙ ❢♦r ❛s②♠♠❡tr✐❝
  ♠✉❧t✐❝♦r❡s✱ s❤♦✇✐♥❣ t❤❛t ✐t ❝♦rr❡s♣♦♥❞s t♦ t❤❡ ❆❋❊❊ ❛ss✉♠♣t✐♦♥s ✐♥ t❤❡ ❝❛s❡ ♦❢ ✐♥s❡♥s✐t✐✈❡ ❥♦❜s✳
  ■♥ ❝❛s❡ ♦❢ ❝❛❧✐❜r❛t❡❞ ❥♦❜ s✐③❡s ✭❆❋❊❈✮✱ t❤❡ ❡①❡❝✉t✐♦♥ r❛t❡ ✐♥ ❥♦❜s ♣❡r s❡❝♦♥❞ ❢♦r ❛ ❥♦❜ ♦❢ t②♣❡
  IP S M C
  b ♦♥ ❝♦r❡ c ✐s IP Sb,cR ✱ ❤❡♥❝❡ t❤❡ ❛✈❡r❛❣❡ ❥♦❜ t❤r♦✉❣❤♣✉t ♦❢ ❝♦r❡ c ✐s
  b
  
  N
  IP SbR
  MC
  b=1 IP Sb,c
  
  PN
  
  = ❍✲♠❡❛♥
  
  MC
  IP Sb,c
  
  IP SbR
  
  !.
  ❚❤❡ t♦t❛❧ ❥♦❜ t❤r♦✉❣❤♣✉t ✐s t❤❡♥ t❤❡ s✉♠ ♦❢ t❤❡ ❍✲♠❡❛♥ ♦❢ s♣❡❡❞✉♣s ♦❢ ❡❛❝❤ ❝♦r❡✿
  
  ❆❋❊❈✐ = ❍❙❯ =
  
  K
  X
  c=1
  
  ❍✲♠❡❛♥
  
  MC
  IP Sb,c
  
  IP SbR
  
  !.
  