SLIDE 1
◗✉❡✉❡✐♥❣ ❙②st❡♠s
❙❤❛♥❦❛r ▼❛② ✼✱ ✷✵✶✺
SLIDE 2 ◗✉❡✉❡✐♥❣ ❖✈❡r✈✐❡✇
◗✉❡✉❡✐♥❣ s②st❡♠ s❡r✈❡rs ✰ ✇❛✐t✐♥❣ r♦♦♠s ❝✉st♦♠❡rs ❛rr✐✈❡✱ ✇❛✐t✱ ❣❡t s❡r✈❡❞✱ ❞❡♣❛rt ♦r ❣♦ t♦ ♥❡①t s❡r✈❡r q✉❡✉❡✐♥❣ ❞✐s❝✐♣❧✐♥❡s ♥♦♥✲♣r❡❡♠♣t✐✈❡✿ ✜❢♦✱ ♣r✐♦r✐t②✱ ✳✳✳ ♣r❡❡♠♣t✐✈❡✿ r♦✉♥❞✲r♦❜✐♥✱ ♠✉❧t✐✲❧❡✈❡❧ ❢❡❡❞❜❛❝❦✱ ✳✳✳ ❖♣❡r❛t✐♥❣ s②st❡♠s ❛r❡ ❡①❛♠♣❧❡s ♦❢ q✉❡✉❡✐♥❣ s②st❡♠s s❡r✈❡rs✿ ❤✇✴s✇ r❡s♦✉r❝❡s ✭♣r♦❝❡ss♦r✱ ❞✐s❦✱ s❝❤❡❞✉❧❡r✱ ✳✳✳✮ ❝✉st♦♠❡rs✿ P❈❇s✱ ❚❈❇s✱ ✳✳✳
- ✐✈❡♥✿ ❛rr✐✈❛❧ r❛t❡s✱ s❡r✈✐❝❡ t✐♠❡s✱ q✉❡✉❡✐♥❣ ❞✐s❝✐♣❧✐♥❡s✱ ✳✳✳
❖❜t❛✐♥✿ q✉❡✉❡ s✐③❡s✱ r❡s♣♦♥s❡ t✐♠❡s✱ ❢❛✐r♥❡ss✱ ❜♦tt❧❡♥❡❝❦s✱ ✳✳✳
SLIDE 3 ❇✉rst② ❚r❛✣❝✿ ❲❤② ◗✉❡✉❡s ❆r✐s❡
❈♦♥s✐❞❡r ❝❛rs tr❛✈❡❧✐♥❣ ♦♥ ❛ r♦❛❞ ✇✐t❤ ❛ t✉r♥ ❡❛❝❤ ❝❛r t❛❦❡s ✸ s❡❝♦♥❞s t♦ ❣♦ t❤r♦✉❣❤ t❤❡ t✉r♥ ❛t ♠♦st ♦♥❡ ❝❛r ❝❛♥ ❜❡ ✐♥ t❤❡ t✉r♥ ❛t ❛♥② t✐♠❡ N(t)✿ ★ ❝❛rs ✐♥ t❤❡ t✉r♥ ❛♥❞ ✇❛✐t✐♥❣ t♦ ❡♥t❡r t❤❡ t✉r♥
1 2 4 5 6 7 8 9 10 11 12 3 13 14 15 t 1 2 1 2 1 2 3 3 4 4 N(t) 1 2 4 5 6 7 8 9 10 11 12 3 13 14 15 t 1 2 2 1 3 4 N(t) 1 2 3 4
arrival rate 1/4 load 3/4 uniform arrival rate 1/4 load 3/4 bursty
▲♦❛❞ < ✶✿ st❛❜❧❡ ✇✐t❤ ✇❛✐ts ❞❡♣❡♥❞✐♥❣ ♦♥ ❜✉rst✐♥❡ss ▲♦❛❞ > ✶✿ ✉♥st❛❜❧❡✱ ❡✈❡r✲✐♥❝r❡❛s✐♥❣ ✇❛✐ts
SLIDE 4
■♥st❛♥t❛♥❡♦✉s ▼❡tr✐❝s
❈✉st♦♠❡r i ♠❡tr✐❝s ❛rr✐✈❛❧ t✐♠❡ Ai s❡r✈✐❝❡ t✐♠❡ Si ❞❡♣❛rt✉r❡ t✐♠❡ Di r❡s♣♦♥s❡ t✐♠❡ Ri✿ Di − Ai ✇❛✐t t✐♠❡ Wi✿ Ri − Si ◗✉❡✉❡ ♠❡tr✐❝s N(t)✿ ★ ❝✉st♦♠❡rs ✐♥ q✉❡✉❡ ✭✇❛✐t✐♥❣ ✰ s❡r✈❡❞✮ ❛t t✐♠❡ t NW (t)✿ ♥✉♠❜❡r ♦❢ ❝✉st♦♠❡rs ✐♥ ✇❛✐t✐♥❣ r♦♦♠ ❛t t✐♠❡ t Y (t)✿ ✉♥✜♥✐s❤❡❞ ✇♦r❦ ✐♥ q✉❡✉❡ ✭✇❛✐t✐♥❣ ✰ s❡r✈❡❞✮ ❛t t✐♠❡ t
SLIDE 5
❙t❡❛❞②✲st❛t❡ ▼❡tr✐❝s
❆ss✉♠❡ ✉♥❡♥❞✐♥❣ str❡❛♠ ♦❢ ❝✉st♦♠❡rs ❈✉st♦♠❡r ♠❡tr✐❝s✱ ❛ss✉♠✐♥❣ N → ∞ ❛✈❣ s❡r✈✐❝❡ t✐♠❡ S✿ (S✶ + · · · + SN)/N ❛✈❣ r❡s♣♦♥s❡ t✐♠❡ R✿ (R✶ + · · · + RN)/N ✴✴ st❛❜❧❡ ❛✈❣ ✇❛✐t t✐♠❡ R✿ (W✶ + · · · + WN)/N ✴✴ st❛❜❧❡ ◗✉❡✉❡ ♠❡tr✐❝s✱ ❛ss✉♠✐♥❣ t → ∞ ❛rr✐✈❛❧ r❛t❡ λ✿ ✭★ ❛rr✐✈❛❧s ✐♥ [✵, t]✮ ✴ t ❧♦❛❞ ρ✿ ✭t♦t❛❧ s❡r✈✐❝❡ t✐♠❡ ❛rr✐✈✐♥❣ ✐♥ [✵, t]✮ ✴ t t❤r♦✉❣❤♣✉t X✿ ✭★ ❞❡♣❛rt✉r❡s ✐♥ [✵, t]✮ ✴ t ❛✈❣ q✉❡✉❡ s✐③❡ N✿ ✭❛r❡❛ ✉♥❞❡r N(t) ♦✈❡r [✵, t]✮ ✴ t ✴✴ st❛❜❧❡ ✉t✐❧✐③❛t✐♦♥ U✿ ❢r❛❝t✐♦♥ ♦❢ [✵, t] ✐♥ ✇❤✐❝❤ s❡r✈❡r ✐s ❜✉s②
SLIDE 6
❙♦♠❡ ❙t❡❛❞②✲st❛t❡ ❘❡❧❛t✐♦♥s❤✐♣s
❋r♦♠ ❞❡✜♥✐t✐♦♥s ▲♦❛❞ ρ = λ × S ❙②st❡♠ ✐s ✉♥st❛❜❧❡ ✐❢ ρ > ✶ ❋♦r st❛❜❧❡ s②st❡♠✿ X = λ ❛♥❞ U = ρ ❋♦r ❛♥ ✉♥st❛❜❧❡ s②st❡♠✿ X = ✶/S ❛♥❞ U = ✶ ▲✐tt❧❡✬s ▲❛✇ N = R × X ❛ss✉♠✐♥❣ st❡❛❞②✲st❛t❡ ❤♦❧❞s ❢♦r ❛♥② q✉❡✉❡✐♥❣ s②st❡♠✿ ❡❣✱ ❛ ❝❧❛ss ♦❢ ❝✉st♦♠❡rs
SLIDE 7
❙t❡❛❞②✲st❛t❡✿ ◗✉❡✉❡ ❙✐③❡ ✈s ▲♦❛❞
N ✐♥❝r❡❛s❡s ✏❡①♣♦♥❡♥t✐❛❧❧②✑ ❛s ρ ✐♥❝r❡❛s❡s✱ ❜❡❝♦♠✐♥❣ ∞ ❛s ρ → ✶ N ✐♥❝r❡❛s❡s ❛s ❜✉rst✐♥❡ss ✐♥❝r❡❛s❡s N ρ 1.0 increasing burstiness
SLIDE 8 ❙t❡❛❞②✲st❛t❡✿ ❲❛✐t t✐♠❡ ✈s ❙❡r✈✐❝❡ t✐♠❡
◗✉❡✉✐♥❣ ❞✐s❝✐♣❧✐♥❡s ❝❛♥ ❞✐s❝r✐♠✐♥❛t❡ ❜❛s❡❞ ♦♥ s❡r✈✐❝❡ t✐♠❡s W (S)✿ ❛✈❣ ✇❛✐t t✐♠❡ ❢♦r ❝✉st♦♠❡rs ✇✐t❤ s❡r✈✐❝❡ t✐♠❡ S ❋❛✈♦r ❝✉st♦♠❡rs ✇✐t❤ s♠❛❧❧ S ❙❏❋✲♣r❡❡♠♣t✐✈❡ > ❙❏❋ > ❘❘ > ❋■❋❖✱ ▲■❋❖ ❘❘ ✇ q✉❛♥t✉♠ → ✵✿ ❧✐♥❡❛r ❞✐s❝r✐♠✐♥❛t✐♦♥ ✴✴ ✐❣♥♦r✐♥❣ ♦✈❡r❤❡❛❞
S FIFO RR (qs −−> 0) W(S) SJF
SLIDE 9
❘❡❧❛t✐♦♥s❤✐♣ ❜❡t✇❡❡♥ ✐❞❧❡ ❛♥❞ ❜✉s② ♣❡r✐♦❞s
❙❡r✈❡r ❝②❝❧❡s ❜❡t✇❡❡♥ ✐❞❧❡ ♣❡r✐♦❞s ❛♥❞ ❜✉s② ♣❡r✐♦❞s ❲♦r❦✲❝♦♥s❡r✈✐♥❣ ❞✐s❝✐♣❧✐♥❡✿ s❡r✈❡r ♥♦t ✐❞❧❡ ✇❤❡♥ ❝✉st♦♠❡r ♣r❡s❡♥t Pr♦♣❡rt② ❢♦r ✇♦r❦✲❝♦♥s❡r✈✐♥❣ ❞✐s❝✐♣❧✐♥❡s✿ ❚❤❡ s❡q✉❡♥❝❡ ♦❢ ✐❞❧❡ ❛♥❞ ❜✉s② ♣❡r✐♦❞s✱ ❤❡♥❝❡ ✉t✐❧✐③❛t✐♦♥✱ ✐s ✐♥❞❡♣❡♥❞❡♥t ♦❢ q✉❡✉❡✐♥❣ ❞✐s❝✐♣❧✐♥❡✳ Pr♦♦❢ ✐s ♦❜✈✐♦✉s ❜② ❧♦♦❦✐♥❣ ❛t t❤❡ ❡✈♦❧✉t✐♦♥ ♦❢ Y (t) ❛rr✐✈❛❧ ✐♥❝r❡❛s❡s Y (t) ❜② ❛rr✐✈❛❧✬s s❡r✈✐❝❡ t✐♠❡ ✇❤✐❧❡ Y (t) > ✵ ❤♦❧❞s✱ ✐t ❞❡❝r❡❛s❡s ✇✐t❤ s❧♦♣❡ −✶
SLIDE 10 ❊✈♦❧✉t✐♦♥ ♦❢ ✉♥✜♥✐s❤❡❞ ✇♦r❦ Y (t)
unfinished work
t 1 2 1 2 3 4 5 4 Y(t) 5 3 S1
