st t rt - - PowerPoint PPT Presentation
st t rt tr sst rs sr Prt
❈■❋❆❙■❙ ✲ ❈❖◆■❈❊❚ ✲❯♥✐✈❡rs✐❞❛❞ ◆❛❝✐♦♥❛❧ ❞❡ ❘r♦s❛r✐♦ ✲ ❆r❣❡♥t✐♥❛✱ ♣❛r❡♥t❡❅❝✐❢❛s✐s✲❝♦♥✐❝❡t✳❣♦✈✳❛r
■♥tr♦❞✉❝t✐♦♥ ❉✉❛❧ ❛♣♣r♦❛❝❤
✶
✷
■♥tr♦❞✉❝t✐♦♥ ❉✉❛❧ ❛♣♣r♦❛❝❤
■♥tr♦❞✉❝t✐♦♥ ❉✉❛❧ ❛♣♣r♦❛❝❤
■♥tr♦❞✉❝t✐♦♥ ❉✉❛❧ ❛♣♣r♦❛❝❤
■♥tr♦❞✉❝t✐♦♥ ❉✉❛❧ ❛♣♣r♦❛❝❤
i ≥ ✵ ❞❡♠❛♥❞ ❢r♦♠ i ∈ N t♦ d ∈ D
i s❡t ♦❢ r♦✉t❡s ✭s✐♠♣❧❡ ♣❛t❤s✮ ❢r♦♠
i=d Rd i
i = r∈Rd
i xr.
r∋a xr✳
■♥tr♦❞✉❝t✐♦♥ ❉✉❛❧ ❛♣♣r♦❛❝❤
i ❤❛✈❡ t❤❡ s❛♠❡ tr❛✈❡❧ t✐♠❡ ❛♥❞
i ,
i ,
i = ♠✐♥ r∈Rd
i
2t0
f free-flow queuing jamming
■♥tr♦❞✉❝t✐♦♥ ❉✉❛❧ ❛♣♣r♦❛❝❤
✵
i =
i
■♥tr♦❞✉❝t✐♦♥ ❉✉❛❧ ❛♣♣r♦❛❝❤
a ≥ ✵ ✢♦✇ ♦♥ ❛r❝ a ✇✐t❤ ❞❡st✐♥❛t✐♦♥ d
✵
i +
i
a =
i
a ,
a ,
a ≥ ✵.
i
i ✐s t❤❡ s❡t ♦❢ ❛r❝s ✇✐t❤
■♥tr♦❞✉❝t✐♦♥ ❉✉❛❧ ❛♣♣r♦❛❝❤
d14 d24 1 2 3 4 5 6 7 8 9
■♥tr♦❞✉❝t✐♦♥ ❉✉❛❧ ❛♣♣r♦❛❝❤
■♥tr♦❞✉❝t✐♦♥ ❉✉❛❧ ❛♣♣r♦❛❝❤
✶
✷
■♥tr♦❞✉❝t✐♦♥ ❉✉❛❧ ❛♣♣r♦❛❝❤
i t✐♠❡ t♦ ❞❡st✐♥❛t✐♦♥ ✈❛r✐❛❜❧❡s ❢♦r d ∈ D ❛♥❞ i = d✳
t✵
a
a
i τ id
a := sa(✵),
■♥tr♦❞✉❝t✐♦♥ ❉✉❛❧ ❛♣♣r♦❛❝❤
t≥✵
t✵
a
a
i τ id(t)
i {ta + τ jad(t)} ✳
a = sa(f ∗ a ) ≥ t✵ a ✳ ✭❋✉❦✉s❤✐♠❛ ❵✽✻✮✳
■♥tr♦❞✉❝t✐♦♥ ❉✉❛❧ ❛♣♣r♦❛❝❤
i ∂τ id(t)
i (t)✳
■♥tr♦❞✉❝t✐♦♥ ❉✉❛❧ ❛♣♣r♦❛❝❤
i , v ≥ ✵}
i ∈ R|N| ❤❛✈❡ ❝♦♠♣♦♥❡♥ts ✲✶
i (t) = conv{δp : p s❤♦rt❡st ♣❛t❤ ❢r♦♠ i t♦ d, ❢♦r ♣❛tt❡r♥ t✐♠❡ t},
■♥tr♦❞✉❝t✐♦♥ ❉✉❛❧ ❛♣♣r♦❛❝❤
■♥tr♦❞✉❝t✐♦♥ ❉✉❛❧ ❛♣♣r♦❛❝❤
i ∂τ id(t).
■♥tr♦❞✉❝t✐♦♥ ❉✉❛❧ ❛♣♣r♦❛❝❤
k=✶ ∈ ℓ✷ − ℓ✶.
a )a∈A. ❙❡t z✵ = ✵, λ✵ = ✵
i ∈ ∂τ d i (tk−✶) ❛♥❞ s❡t
i ξd i .
t≥✵
t✵
a
a
■♥tr♦❞✉❝t✐♦♥ ❉✉❛❧ ❛♣♣r♦❛❝❤
t≥✵
t✵
a
a
i τ id α (t)
α (t) ✐s ❣✐✈❡♥ ❜② t❤❡ r❡❣✉❧❛r✐③❡❞ ♣r♦❜❧❡♠
α (t) = ♠✐♥{tv + α
i , v ≥ ✵}.
α ❛r❡ ❞✐✛❡r❡♥t✐❛❜❧❡ ❛♥❞ s❛t✐s❢②
α (t) = θid α(t) := ❛r❣♠✐♥{tv + α
i , v ≥ ✵}.
■♥tr♦❞✉❝t✐♦♥ ❉✉❛❧ ❛♣♣r♦❛❝❤
α(t) = PΩd
i (−t/α),
i := {Mv = γd i , v ≥ ✵}✱ s♦ θid α ✐s ▲✐♣s❝❤✐t③ ❝♦♥t✐♥✉♦✉s ✇✐t❤ ▲✐♣s❝❤✐t③
α→✵ τ id α (t) = τ id(t).
α(t) ∈ ∂τ id(t + αθid α(t))✳
α→✵ θid α(t) ∈ ∂τ id(t).
■♥tr♦❞✉❝t✐♦♥ ❉✉❛❧ ❛♣♣r♦❛❝❤
i θid α(t)
i θid α(t).
d
i /α✮✱ s♦ ✐t ✐s ♣♦ss✐❜❧❡ t♦ ❛♣♣❧② ❜❡tt❡r ❋✲❇ s♣❧✐tt✐♥❣
■♥tr♦❞✉❝t✐♦♥ ❉✉❛❧ ❛♣♣r♦❛❝❤
k(ckwk✷ + ˆ
■♥tr♦❞✉❝t✐♦♥ ❉✉❛❧ ❛♣♣r♦❛❝❤
■♥tr♦❞✉❝t✐♦♥ ❉✉❛❧ ❛♣♣r♦❛❝❤
t′≥✵
a
t✵
a
a
i τ id(t′)
α ✳
■♥tr♦❞✉❝t✐♦♥ ❉✉❛❧ ❛♣♣r♦❛❝❤
t′
a
t✵
a
a
i τ id α (t′)
i θid α(t)
■♥tr♦❞✉❝t✐♦♥ ❉✉❛❧ ❛♣♣r♦❛❝❤