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Patriksson,!M.!:!The&Traﬃc&Assignment&Problem&:&Models&and&Methods,!1994!
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䛆3䛇 ฼⏝⪅ᆒ⾮㓄ศ
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Yes

•

Bar-Gera, H. (2002). Origin-based algorithm forthe traffic assignment problem. Transportation
Science, Vol. 36, pp. 398–417.
!
Dial, R. B. (2006). A Path-based user-equilibrium
traffic assignment algorithm that obviates pathstorage and enumeration. Transportation
Research Part B, Vol. 40, Issue 10, pp. 917–936.

         
/.,01
-2

Bar-Gera, H. (2010). Traffic assignment bypaired alternative segments. Transportation
Research Part B, Vol. 44, Issues 8–9, pp. 1022–
1046.
Inoue, S. and Maruyama. T. (2012)
Computational experience on advanced
algorithms for user equilibrium traffic assignment
problem and its convergence error, Procedia 43
pp. 445–456.

•

•

•

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•
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n = n+118!

äƜȅǁĮƮ<ȅǌơȚɊȥɉȪɃȅƸƣÕĠƠuŮƮ<ȚɊȥɉȪɃȅĬ

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Z6ĮȃFrank.Wolfećȁ
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Copyright!(c)!Inoue,!IBS!!

ǑǙ•Bar-Gera, H. (2010). Traffic Assignment by Paired Alternative Segments.
Transportation Research Part B, Vol. 44, Issues 8–9, pp. 1022–1046.
Boyce, D., Ralevic-Dekic, B. & Bar-Gera, H. (2004). Convergence of Traffic
Assignments: How much is enough? Journal of Transportation Engineering,
ASCE, Vol. 130, Issue 1, pp. 49–55. ǚDial, R. B. (2006). A Path-based User-equilibrium Traffic Assignment Algorithm
That Obviates Path Storage and Enumeration. Transportation Research Part B, Vol.
40, Issue 10, pp. 917–936. ǚFlorian, M., Constantin, I. & Florian, D. (2009). A New Look at Projected Gradient
Method for Equilibrium Assignment. Transportation Research Record, Vol. 2090,
pp. 10–16.
Nie, Y., (2010). A class of bush-based algorithms for the traffic assignment
problem. Transportation Research B 44, 73-89.
Nie, Y. (2012). A Note on Bar-Gera’s Algorithm for the Origin-Based Traffic
Assignment Problem. Transportation Science, Vol. 46, pp. 27–38.
Bar-Gera, H., Boyce, D. & Nie, Y. (2012). User-equilibrium Route Flows and theCondition of Proportionality. Transportation Research Part B, Vol. 46, Issue 3, pp.
440–462. ǚ
G. Gentile (2012) Local User Cost Equilibrium: a bush-based algorithm for traffic
assignment, Transportmetrica, DOI:10.1080/18128602.2012.691911ǒǐä×ȅȚɊȥɉȪɃȄǽǨǿɒɖɓä×ȅȚɊȥɉȪɃȄǽǨǿɒɗɓ• 1950¡ȄĬůǲȕǹɅȴɊ!(Wardrop!
1952,!Beckman!et!al.!1956)ȅǌơŹŌćȅ
ƊÕǭĬůǲȕŚǰǿǨȔɑ!
• Frank.Wolfe!ćȆZ6Į!

• ĻĮBĦŢuŮƮ<ȀŗƕƠƱǠɉɎȣƠƱȅOD7ŽȘɒäĮȄɓ¸ȄȍȔØćȎÎòǲȕǿǨȔ!.!Bar-Gera (2010),
Bar-Gera et al. (2012)!

– ŶúȸȲȵɍɐȣ~ȀȆǠUȃuŮŸȘĂ
ȍȔȄȆŹŌßƷȘŴǵȔ!
– Q<ȃWìȀȆ§ȃÐŋ¹£ǭ¬ȒȕȃǨ!
– Ðŋȅ(İɒŉǠȚȝȵȾȲȵɓǭ ǳȃǨ!

• OBA,!TAPASȎǳǯȆɁɊȱȤȚCPUȅ >Ź
Ō(OpenMPŉ)ǭçȋȕȔ!
• Č~ȅƠǀŴĔɅȴɊȅȭȽȵȝȞȚɏȿɎȰɐȅƶĬŇ!

– ŧȄȆǠŗƕƠƱȃȂ¸ȄĂŸȀǮȃǨ
ȎȅȀǧǼǹ!

• ĦĮȃɁɊȱɏȣɈȩɅȴɊȅƶĬȄȎǽ
ȃǭȔǬȎ!
– ÑĿâĮȄȆǠSUEȘBĦǵȕȇŨǨȁǨǩƅÜ
ǺǼǹǭǠĦĮȃɒ ®ǳǿBĦȀǮȔɓ!SUE!Ȇ
ȃǨǟlogit.SUE!Ȁθ→∞!
ǒǑConvergence!ȅƯŴ³• ȧȷɉȡƷȅÿƙɔȑȓȎWìƄǭǮǯȃȔȁ§ȃÐŋ¹£ǭ;ȃǨ!
• ɅȴɊȆÀƀĢȘÅƎNǳǹǣȝȭǤȃȅ
ǺǬȒɔɅȴɊ7ƫȀȆƐǳǹǣȝȭǤȘǽ
ǯǱȁǭæĦȁȃȔz_ȎǨ!
• WìǳȃǨȁɔŹŌǳǿǨǿĀÈǻµǨ!
• Bar.Gera!(2002,2010),!Dial!(2006)!ȃȂȅǌơ
ȚɊȥɉȪɃ,! >ŹŌȅôź!
      
   
        Wìí: ɉɎȣƠƱäƄġε=0.005
ǒǓ

ǒǒ

BĦŢuŮƮ<ȅĜ­
• 4IíȘ`ȁǵȕȇɔƆǭŬǼǿȎ`ǴŊǪǭ¬ȒȕȔ• <GlÓȏ<Gÿġŉȅ´¸ĮȃȺɈɄɐȯǭȃǨ• ƨ=ȃɉɎȣȺȽȠɐɁɎȩƸÓȅżȄȑȓɔƠƱȁÚŬßƷȅØȘŏ£ǌǯÍŹǵȔǱȁǭ[ť– <GƮ<ćȆȄƠƱȅ9Ģ³ȄĶ• <GƮ<ȅ;Iȁ`Ǵ^łȚȝȵȾȲȵǆĲȘŌ;[ť• §ȃÐŋ¹£ǭ¬ȒȕȔ– ƦƕÔ2ȅ©ǄȄǧȋȓƸ)ȃǨdƚƦƕȅƠƱǭ|LǵȔĢƎǭĥǴȄǯǨ• ɅȴɊȅÇ¥³ǭǌǨ
24!

BĦŢuŮƮ<ȅƹĩǽȅ<ǉƘ• ƎßƷ7(ÛǧȔǨȆÓßƷ)ȄǫǰȔǀŴ
ȅßƷ|LȘÂǪȃǨ• LĮȃĢƎȀǧȔĒĖȘƨ=ȄÂǪȃǨ• ĒĖĢƎǭsǵȔz_ȅɉɎȣȺȽȠɐɁɎ
ȩƸÓȅ_ģĮȃżǭnƾ• LĮȧɂɆɋɐȧɇɎȁȅ$Ǩ<ǰ/ÌŚǭ¯ŴǂďƽvĻĮ All or Nothing BĦŢuŮƮ<
Ʈ<
(UE)
ŗƕƩÄ
ĻġĮ
ŗƕƩÄ

– $Ǩ<ǰȅƘ:!ƴè/Ĺèɔ¢w/ğw,¿ĪŹĨ/ƁŔŹĨɔƎÐŋ(×ŶɉɎȣ/ÖƲ|N,etc)!

ďƽvĻġĮƮ<

ĻġĮBĦŢu
ŮƮ<(SUE)25!

Ƈǈ:!äƨNiǈȘŸǨǿȌȔĻġĮƮ<

x1 + x2 = q• BĦŢȆäĹŗƕ~ȎƩÄǵȔ• ŗƕƑĦȅƂĸƄȘĞņȀ`ȃȢɎȿɊ<ȘǵȔȁɌȨȲȵvŗƕƩÄɅȴɊǭǬȕȔODɀȚrsƷȅkīĲȅ
ŗƕƠƱ

exp(−θ ckrs )rs
f k = qrs
∑ exp(−θ ckrs )ǟȁǵȔȁǮɔüȅƸÓZ(x1,x2)ȘäȁǵȔ
x1,x2ȅŖȘĂȍȃǲǨɕǹǺǳɔc1,c2, q ȆÓȁǵȔɕÓȆŦęÓȀǵɕǛ"űȅǧȔȆɔǸȅȁǮȅä0ZȎĂȍȃǲǨɕ

ODɀȚrsƷȅkīĲ
ȅŗƕƑĦ

1
Z ( x1 , x2 ) = x1 c1 + x2 c2 + ( x1 log x1 + x2 log x2 )k∈K rs

ODɀȚrsƷȅODƠ
Ʊ

26!

θ

ODɀȚrsƷȅŗƕƩÄ
ţƼ_

27!

28!

ǵǱǳŧNǵȔȁK

min . Z (x) = ∑ xk ck +k =1

Lagrangeȅ

1 K&#
L(x, λ ) = Z (x) + λ $ q − ∑ xk !
k
%
"
1
&
#
L(x, λ ) = ∑ xk ck + ∑ xk log xk + λ $ q − ∑ xk !
θ k
k
k
%
"

∑ x log xθkÓćȘ$ǩȁ

k

k =1

K

s.t. ∑ xk = q, xk ≥ 0
k =1∂ L(x, λ )= 0, ∀k∂ xk(ȟɎȵɌȼɐɏȤȩȵƈfɅȴɊ)ƇǈȆK=2ȅȁǮȄĴ§

ǭäƨ³ȅí(Ĉ:UȄȆǂƏíȘÂǩ¯Ŵǭǧ
Ȕ)
30!

29!

ŧȸȲȵɍɐȣȄǫǰȔǛ
ɌȨȲȵvĻġĮƮ<ȁǛŉ'ȃäƨNiǈŹŌȅǽǾǮ∂ L(x, λ )1= ck + (log xk + 1) − λ = 0, ∀k∂ xk
θ∴ xk = exp(−θ ck ) exp(θλ − 1)Cőímin. Z (x) = ∑ xata +∑ xk = qȄ4ǳǿÔģǵȔȁakexp(−θ ck )xk = q∑ exp(−θ ck )ŗƕȤȩȵǭ 1kKȀǪȒȕȔKêȅŗƕǭǧȔz_ȅɌȨȲȵvĻġƮ<c ,c ,,c

s.t.

∑f

rs
k

1

rs
k

∑ f log fθrs
kr , s ,k= qrs , ∀rskxa = ∑∑ δ ars,k f krs , ∀akǭ¬ȒȕȔ

rskf krs ≥ 0, xa ≥ 0( KêȺɈɋɊȸȲȵɍɐȣȅz_:ɉɎȣƠƱȁŗƕƠƱǭ`)
31!

32!

Ó¤Ȁȅĳ¹ĮȃƅÜBĦŢuŮö±ȅÇ¥

min. Z (x) = ∑ xata +• WardropuŮ(BĦŢuŮ)!

a– ȂȅBĦŢȎŗƕȘ|áǵȔǱȁȀŦ<ȅÚŬßƷȘĹŞǵȔǱȁȆȀǮȃǨɉɎȣȤȩȵǆǭŃ<
vȄ

1

rs
k

∑ f log fθrs
kr , s ,kɌȨȲȵvĻġƮ<ɅȴɊ• ĻġĮBĦŢuŮ– ȂȅBĦŢȎŗƕȘ|áǵȔǱȁȀŦ<ȅÚŬßƷȘĹŞǵȔǱȁȆȀǮȃǨȁ+ǴǿǨȔĝº!
• BĦŢǭȂȅȑǩȄǣ+ǴǿǨȔǤȁšǪȔǬǛ
(BĦŢȅƂĸ÷Ƣ)ȄȑǼǿøǢȃɅȴɊNǭ[ť• ǝƂĸƄȅĻġ<ȘȂȅȑǩȄÂǩǬȀ|N• ǹǺǳɔĢȅȸȲȵɍɐȣȀŹŌ[ťȃɅȴɊȆƹȒȕȔ
(ǜɌȨȲȵvĻġuŮ)!

!

xa

min .Z (x) = ∑ ∫ ta (ω )dω +afkɌȨȲȵvĻġƮ<ɅȴɊ

f

rs
k

rs
k

r , s ,k33!

34!

ĻġĮBĦŢuŮɅȴɊ• ďƽȎšǪǹuŮȤȩȵȀɌȨȲȵvȅŗ
ƕƩÄǭ½ņǳǿǨȔexp(−θ ckrs )= qrs∑ exp(−θ ckrs )rsk∑ f log fθɌȨȲȵvĻġuŮƮ<ɅȴɊĻġuŮĝºȀȆ

rs
k

0

1

ǀŴȦȜȶǛ
BĦŢŬL

exp(−θ ckrs (f ))= qrs∑ exp(−θ ckrs (f ))kƦƕȸȲȵɍɐȣǛ
ȄǫǰȔǛ
ďƽĢƎ

xa = ∑∑∑ f kr sδ ar,skrskɉɎȣƠƱɉɎȣȤȩȵƸÓɌȨȲȵvĻġuŮǛ
Ʈ<ɅȴɊ

f kr sEǅȅäƨNiǈȅKuhn-TuckeríȑȓŻuŮí¤ǭǰȔ:ɅȴɊȁȅŉ'³ǭÓĮȄžÜȀǮȔf krs = qrs

35!

ŗƕƠƱ

exp(−θ ckrs ) ɌȨȲȵvŗƕƩ
Ä∑ exp(−θ ckrs )kta ( xa )ŗƕȤȩȵ

ckr s = ∑ taδ ar,sk
a

36!

ȋȁȍ

ĻĮ
ŗƕƩÄ

ǂďƽv

ďƽv

All or NothingƮ<BĦŢuŮƮ<min.∑ ∫ ta ( x)dx

ĻġĮƮ<

ĻġĮBĦŢ
uŮƮ<

rs
k

∑ x t ( x ) + ∑ f log f
a a

a

a

• çȋǳǨƠǀŴĔÁć!
1) ƠǀŴȅǣǬȒȉǤȅĔ!
2) ǀŴ|LvȀ5ãȘǳȃǨŗƕƩÄ!
3) ɂȣɌŗĐģƊȁȅÔ_!

xamin.∑ xata ( xa )aĻġĮŗƕƩÄmin.

(ɌȨȲȵv)ƦƕÃƒȅ(İſ'Ǐ!
(ót/ƲêǏŝūǏ2008)

a

rs
k

r , s ,k0xa

min .∑ ∫ ta (ω ) dω + ∑ f krs log f krs
a0ǱȕȒȅŴƉȄ°[ťȃBĦŢuŮ
ȅĬɅȴɊȆxêĮȄƶĬĐȌr , s ,kSUEǺȁŗƕȽɌɐŸȎh

Ǔǘ

37!

ǀŴ|LvBĦŢuŮɅȴɊøǢȃȹɉȟɐȧɇɎ• ÐŋȄȑǼǿODǀŴǭ|NǵȔ!

• ODǀŴɏƮ<ř_Ǐ(Beckmann!ɅȴɊ)!
• <ÆɏƮ<ř_!

– ƠȅUEȆɔODǀŴo!

• ÐŋȄȑȔƃĬƠɔƗÏƠȃȂȘÔ_ĮȄůĢ[ť!
• ŗĐģƊȁȎÔ_Įȃ(İſ'ǭ[ť!
• ƠǀŴĔÁćȁǳǿȅkþƻÍćȅiǈėȅƫȘŸă[ť!

– ǌơƗÏġ7ĥvȎǸȅł!

• <ɏƮ<ř_!
• <ɏ<ÆɏƮ<ř_• Ĭĥɏ<ɏ<ÆɏƮ<ř_!
• ȵɉȲȾɏȱȞȜɎƩÄř_v!
• ĊLƩÄǏetc!ȁȅř_vǟɒƲóȒɓ!
ǓǙ

ǔǐ

BeckmannvǀŴ|Lv!
ɍɐȶɌȲȾuŮȅ¤N
$!cij = λi if fij > 0#!
"cij ≥ λi if fij = 0$!cij = λi if fij > 0#!
"cij ≥ λi if fij = 0∀i ∈ I , ∀j ∈ J i∑ f ij = qi , f ij ≥ 0∀i ∈ Iqi = Di (λi )∀i ∈ Ij∈J iuŮȅĴŲ³í∑ f ij = qi , f ij ≥ 0

j∈J i∑ f ij = qi , f ij ≥ 0

j∈J i

qi (ci − Di−1 (qi )λi ) = 0

Ÿȅ³ƓɏŹŌć• ƠȅUEȅɉɎȣȤȩȵƸÓȀɔǀŴƸÓD(.)ǭēƸÓȀǧȕȇɔĲĮƸÓȆğŠ:ƸÓȁȃȓɔŸǏ(x,q)Ȇh!
• ǀŴƸÓȅżć!

−1imin. Z = ∑ ∫ ta ( w)dw
 − ∑ ∫ D (ω )dω0a∈ A

s.t. qi = ∑ ∑ f iji

0∀i ∈ I– ÁþƩÄɅȴɊȃȂȘƨĦ!
– ȟɎȵɌȼɐv<ɅȴɊŉȘƨĦ!
– Pivot!PointvɅȴɊȘBĦ!

i∈I j∈J i

xa = ∑ ∑ δ a ,ij f ij ∀a ∈ Ai∈I j∈J i

f ij ≥ 0ci − Di−1 (qi ) ≥ 0ǔǒŉ'äƨNiǈqi

qi = Di (λi )f ij (cij − λi ) = 0 Ǭǽ cij − λi ≥ 0, f ij ≥ 0

cij : OD i ȅɉɎȣǏj ȅÚŬßƷǏI : ODɀȚȅƼ_Ji : OD i ƷȅŗƕƼ_
λi : OD i ȅäÚŬßƷqi : OD i ƷȅƠǀŴ
fij : OD i ȅŗƕǏj ȅƠƱ
Di(.): ODǀŴƸÓǏ
ǔǑǟǟǟǟ(Ğņv)

xa∀i ∈ I , ∀j ∈ J i∀i ∈ I , ∀j ∈ J i• ƫ<Ŝ¨NćȃȂǭBĦ[ťǏ(ré,!
1998)!
ǔǓǔǔ

(ǀŴov)ĻġĮBĦŢuŮɅȴɊǏ(Logit!SUE)

Pivot!PointvɅȴɊ• ĹèȅōĪvĔȄæĦ!
" $

c %#

ƦƕȸȲȵɍɐȣǛ
ȄǫǰȔǛ
ďƽĢƎ

ǀŴȦȜȶǛ
BĦŢŬL

ÐŋȧȷɉȡßȅODƑĦÐŋȧȷɉȡ
Di (ci ) = Di0 exp ' ρ )1.0 − 0i * (ci , .
ßȅODǀŴ- +ĢĝȧȷɉȡßȅODƑĦĢĝȧȷɉȡßȅODǀŴ ¦I³ȺɈɄɐȯ• ĢĝȅODȺȯɐɎȆ5Ȅ9Ģ!

xa = ∑∑∑ f kr sδ ar,sk– ɅȴɊȅĢĝ9Ģ³ȘǌȍȔȁǨǩǃ/ȃ#õȘlƪ!
– ǹǺǳɔY<ȅ|NȃȂȆĔȄXȓƛȍ
ȃǨ!

r

s

k

ɉɎȣȤȩȵƸÓɉɎȣƠƱf kr sŗƕƠƱ

• Incremental!vȅĔPk =pk0 exp(Vk − Vk0 )∑ p0j exp(V j − V j0 )f krs = qrsǔǕj<ÆƮ<ř_vĻġĮBĦŢuŮɅȴɊǏ(Nested!Logit!SUE)

ǀŴȦȜȶǛ
BĦŢŬL
ÁþAŗƕƠƱ

f

rs
m, k

= q Pr(k | m, rs)exp(−θ cmrs,k )rs
m,k∑ exp(−θ c )krsmq = qrs Pr(m | rs )Pr(m | rs) =ÁþAɉɎȣƠƱÁþAɉɎȣȤȩ
ȵƸÓ

exp(−η Sm )∑ exp(−η Sm )mÁþƩÄĻġa

LogitǟvǏSUE!

0

1

∑ f
θ

rs
m,k

log f mrs,kr , s ,m,k

Nested!Logit!SUE!
xam

1

0

θ r , s ,m,k m,kmin.Z (x(f ), q) = ∑ ∫ tam (ω )dω +m,ars
cmr s,k = ∑ tamδ ma,k46!

ɅȴɊȁŉ'ȃäƨNiǈm,atam ( xam )ckr s = ∑ taδ ar,skk

0 <η <θm,aÁþAODƠƱŗƕȤȩȵ

xamr , s ,m,kÁþAŗƕƩÄĻġexp(−θ ckrs ) ɌȨȲȵvŗƕƩÄ∑ exp(−θ ckrs )min .Z (x(f )) = ∑ ∫ tam (ω )dω +xam = ∑ f mr,sk δ mr s,a ,krsm

Pr(k | m, rs) =ÁþȸȲȵɍɐȣǛďƽĢƎta ( xa )

∑ f

rs

$1 1%
log f mrs,k + ' − ( ∑ qmrs log qmrs
) η θ * r , s ,mȁǨǩíȀĲĮƸÓȆğŠ:ƸÓȄȃǼǿǨȔǛ:Ÿȅ¸³ǭžÜǲȕȔǏ(c.f.!NLɅȴɊȅRUMȁȅÔ_³í)

ÁþAŗƕȤȩȵ1
Sm = − log ∑ exp(−θ cmrs,k )θkÁþAè«äƑĦ

47!

s.t. ∑ qmrs = qrs , ∑ f krs = qrsm , xam = ∑∑ δ mrs,a ,k f mrs,k ,m

rsm

q ≥ 0, f

k

rs
m,k

m
a

≥ 0, x ≥ 0

rs m , k48!

îƭqȄǫǰȔř_vȸȲȵɍɐȣuŮɅȴɊ%
ɗÁþȸȲȵɍɐȣȀȅďƽĢƎBĦŢŬL
ȵɉȲȾǧȓ

m,a

Ɩ

道路交通
量

(m)

均衡


1

2

s

0

r ,s,m,k

リンクコスト関数"1 1#+ ∑ % i − i & )+Ori ln Ori + Ori 0 ln Ori 0 *,
θ3 (i , r ' θ4i , rs im+ ∑ qm Vs + ∑ OrimVmir + ∑ Ori [Vi r + Vi (t )]i,r ,s,m

混雑不効用

i,r ,ms.t. Ori + Ori 0 = N ri

i,r

im
r

i
r

Nested Logit モデル

2k∑ qmi,rs = qmrs

鉄道
交通量

i

m
a

x ≥ 0, f

49!

rs
m, k

i , rsm= Orim∑O = O∑q∑ fmrs,k = qmrs

xam = ∑ δ am,k,rs f mrs,k

i ,rs
m

im
r

m


1

1 rs
f m , k ln f mrs, k
θ1m

"1
" 1
1 #
1 #
+ ∑ % im − m & qmi , rs ln qmi , rs + ∑ % i − im & Orim ln Orimθθθ
θi,r ,s,m ' 2
i,r ,m ' 3
1 (
2 (

ȃǳ


ƳƦ

xam

min .Z (x(f ), q, O) = ∑ ∫ tam (ω ) dω + ∑

所要
時間



ŉ'äƨNiǈk≥ 0, qrsms

r , s ,k

≥ 0, q ≥ 0, O ≥ 0, Ori ≥ 0, Ori 0 ≥ 050!

ODůǟȅŀLȅȴɐȯȅƈð

ǕǑ

Ǖǒ

ùêÓȅă¤㧔㧟㧕⺞ᩏᣇᴺߦߟ޿ߡ٨ㇷㅍ㈩Ꮣㇷㅍ࿁෼ᣇᑼ㧔㨃㧱㧮࿁╵ࠍ૬↪㧕٨ᐔᚑ  ᐕ  ᦬  ᣣᤨὐߩบᏭࠃࠅή૞ὑ᛽಴㧔਎Ꮺਥ߇ᄖ࿖ੱߩ႐ว‫ޔ‬᛽಴ኻ⽎߆ࠄ㒰ᄖ㧕٨࿁෼₸ะ਄ࠍ⋡⊛ߣߒ‫ޔ‬ኻ⽎⠪એᄖߩ࿁╵Ꮧᦸ⠪ߦߟ޿ߡ߽ኻᔕ
‫ޣ‬ㄭᐕߩ⺞ᩏᣇᴺ‫ޤ‬‫⺖ޣ‬㗴‫ޤ‬٨දജ₸ߩૐਅ‫⺞ޔ‬ᩏല₸ߩᖡൻߥߤߦࠃࠅ‫ޔ‬ᓥ᧪ߩ⸰໧㈩Ꮣ࿁෼ᣇᑼߢߪࠦࠬ࠻Ⴧ
‫⸃ޣ‬᳿╷‫ޤ‬٨ㇷㅍ㈩Ꮣ࿁෼ᣇᑼߦࠃࠆࠦࠬ࠻❗ᷫߩขࠅ⚵ߺ߇ㄭᐕჇട
٨࿁෼₸ߪ㧞㧜㧑એ਄‫ޔ‬࿾ᣇㇺᏒ࿤ߢߪ㧟㧜㧑⏕଻ߐࠇߡ޿ࠆ଀߽
‫ޣ‬ㇷㅍ㈩Ꮣ࿁෼ᣇᑼߩ⇐ᗧὐ‫ޤ‬

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٨࿁෼₸ߦࠃࠅ⺞ᩏ⚿ᨐ߇Ꮐฝߐࠇࠆ
ψ࿁෼₸ࠍ㜞߼ࠆߚ߼‫ޔ‬ಽ߆ࠅ߿ߔߊ⽶ᜂᗵߩዋߥ޿⺞ᩏ␿ߩᎿᄦ
‫ޔ‬ψ㚂㐳ฬߦࠃࠆଐ㗬ᢥ‫ޔ‬ᐢႎ㧼㧾‫ޔ‬දജߦኻߔࠆ⻢␞㧔ࡏ࡯࡞ࡍࡦኽ౉ߥߤ㧕
٨⸰໧㈩Ꮣ࿁෼ߦᲧߴ‫ୃ࡮⿷⵬ޔ‬ᱜ߇ⴕ߃ߥ޿ߚ߼᦭ല␿߇ᷫዋߔࠆᕟࠇ

ψಽ߆ࠅ߿ߔ޿⸥౉଀ߩᎿᄦ‫ޔ‬໧޿วࠊߖ㔚⹤ኻᔕߩᒝൻ

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