Path-Based Dynamic User Equilibrium Model with Applications to Strategic Transportation Planning

تخصیص ترافیک دینامیکی چندکلاسی با محدودیت‌های ظرفیت کمانی

“…'C}iQ_ C}OwOLt '|UqmOvJ '|m}t=v}O l}i=QD X}YND %|O}rm u=oS=w "u= QyD QyW |xm@W 'OvtWwy pkvwptL |=ysDU}U u}W}B |=yVywSB QwQt w xtOkt "1 |m}t=v}O l}i=QD X}YND |xrUt |wQ Q@ |at=H QwQt [7] TwrwBwmU=}r}R w =D}B 6 |R=Ux}@W |x}=BQ@ w 5 |r}rLD |xDUO wO x@ = Q xrUt u}= =yv; "Ov=xO=O s=Hv= |x}=B Q@ |=ypOt QO "Ov=xOQm EL@ l} Qy Cwk \=kv w CqmWt OQwt QO w s}UkD &OwW|t xO=iDU= xm@W QO u=}QH `} RwD |= Q@ |m}i=QD R=Ux}@W l} R= |R=Ux}@W QO u=}QH QovOQN |m}t=v}O |Q=PoQ=@ pOt l} R= |r}rLD |=ypOt xm |r=L QO |wQ Q@ `t=H |QwQt |= Q@ "OvQ@|t xQy@ l}i=QD u=}QH VNB |= Q@ 7 DNL xm@W |v=wH ' [8] |v=wH VywSB x@ |m}t=v}O l}i=QD X}YND |=ysD}Qwor= w =ypOt xaH=Qt [12] u=}qW w wQJ=m w [11] nvww w wDR ' [10] xO= R=@=@ w |v=wH ' [9] u= Q=mty w "OwW s=Hv= xm@W QO ATIS R= xO=iDU= `i=vt uO=O u=Wv |= Q@ |Q=}U@ C=ar=]t x@ RyHt u=oOvv= Q Q}Ut ?=NDv= Q=DiQ |wQ Q@ C=ar=]t u}= |rY= RmQtD "Ov=xOW ?re= [1513] "CU= xOw@ u; x@ RyHtQ}e u=oOvv= Q w C=aq]= Ci=} QO sDU}U |xrUt |UQQ@ |= Q@ |m}D=DU= l}i=QD X}YND |=ypOt R= 'C=ar=]t u}= QO Q_v OQwt |xrUt xm|r=L QO 'Ov=xOQm xO=iDU= xm@W |wQ Q@ ATIS Q}F -=D w =vW} Qm q=@ ' [17] wDR w wr ' [16] |vUtyt "CU= |m}t=v}O |xrUt l} C=P u; <RH [21] nv=wy w w=o ' [20] u= Q=mty w |v ' [19] u= Q=mty w wDR ' [18] u= Q=mty l}i=QD X}YND |=ypOt R= xO=iDU= =@ = Q Q_v OQwt |xrUt xm OvDUy |O= Qi= [23] u= Q=mty w T}m =UD}t ' [22] u= Q=mty w |y R}v , = Q}N= "Ov=xOQm |UQQ@ |m}t=v}O u= Qi=Ut C=aq]= |xDiQW}B |=ysDU}U |=yOQ@Q=m |@=} RQ= x@ [24] =D}B w s}m w "Ov=xDN=OQB |=ysDU}U|rY=|= RH= R=|m} 1 ATISu= Qi=Ut C=aq]=|xDiQW}B|=ysDU}U \}=QW p}rLD w |Q}os}tYD QO u=oOvv= Q x@ xm OvDUy 2 ITS OvtWwy pkvwptL |DL=Q w |}=Q=m =yv; =@ xiQ]wO =} xiQ]l} \=@DQ= j} Q] R= w Ovvm|t ltm l}i=QD CqwLD |wQ Q@ ITS C= QF= |wQ `t=H |QwQt |= Q@ "OvyO|t V}=Ri= = Q QiU |=y|Ov@xDUO w =yOQ@ Q=m w [1] u= Q=mty w u= Q VywSB x@ pkvwptL |=ypOt |xty |RmQt |xDUy "OwW `wHQ [2] u= Q=mty w w}oQwo =B=B VywSB x@ ITS |wor= xm CU= 3 DTA |m}t=v}O l}i=QD X}YND |=ypOt '=ysDU}U u}= XwYN u}= QO "Ovvm|t |v}@V}B xm@W QO = Q u=tR x@ xDU@=w l}i=QD u=}QH 4 STA |m}D=DU= l}i=QD X}YND pwtat |=ypOt R= xm OQm xQ=W= O}=@ =ypOt u}= = Q} R &OQm xO=iDU= ITS |=yCU=}U |@=} RQ= |= Q@ QFwt Qw] x@ u=wD|tv |wQ Q@ `t=H |QwQt |= Q@ "OvQ}o|tv Q_v QO = Q l}i=QD u=}QH |m}t=v}O |=y|oO}J}B xaH=Qt [4] u= Q=mty w xO= R=@=@ w [3] xO= R=@=@ w |v=wH VywSB x@ STA |=ysD}Qwor= "OwW X}YND |xrUt |OH CQwY x@ Q=@ u}rw= |= Q@ [6 w 5] QRw=ytv w Cv=JQt \U...…”

“…}DQD u}O@ "Ovvm C}a@D xOvvmxO=iDU= pO=aD |=yQ}Ut R= =@ u= QyD QyW |xm@W |OQmrta |=yQDt= Q=B 'xOW R} wHD |=yQ}Ut VQ}PB w Pwiv Oy=wN xU}=kt |m}t=v}O w |m}D=DU= Cr=L wO |= Q@ xOvvmxO=iDU= Tqm wO ZQi sD} Qwor= l} R= |Q}oxQy@ =@ 'p=L x@ =D xm OwW xQ=W= O}=@ R}v =Hu}= QO "OW |wQ Q@ |}=y|UQQ@ w =yp}rLD u}vJ ' |= Q@ |m}t=v}O |xOvvmxO=iDU= pO=aD \QW "Ovm|t x@ QHD = Q OwN x@ \w@Qt QiU |xR=@ Qy 'OYkt --=O@t GwR Qy |= Q@ %Ow@ Oy=wN Q} R CQwY x@ xUqmOvJ Cr=L |xOW xO=iDU= |=yQ}Ut xDi=}s}taD QiU u=tR 'xOvvmxO=iDU= Tqm Qy w Ct} Ra xOWv xO=iDU= |=yQ}Ut |xDi=}s}taD QiU u=tR =@ |w=Ut =} R= QDtm w Q@=Q@ sy =@ "CU= |m}t=v}O |xOvvmxO=iDU= pO=aD \}=QW , =k}kO 3 =D 1 CqO=at xm OQm xQ=W= O}=@ x@ 5 w 4 \@=wQ [26] |iW w [25] |v=}DW; x@ OwW `wHQ Ovvm|t u=}@ = Q xOW xO=OKQW "OvDUy =yv; uOw@ |ivt=v u}vJty w =yQ}Ut u=}QH |=k@ \QW |xOvvmu=}@ ? }DQD |=yC}OwOLt "OyO|t u=Wv = Q =yQ}Ut w =yu=tm u=}QH u}@ |x]@= Q R}v 6 |xrO=at u=tR '10 |x]@= Q "OvwW|t Q= QkQ@ 9 =D 7 \@=wQ \UwD R}v u=tm QO u=}QH C}iQ_ x@U=Lt n xQo =D -=O@t R= = Q d Ct} Ra |xR=@ w w Tqm x@ \w@Qt p Q}Ut QiU `wv R= dtw pa Q}Ut -u=tm `wkw |=yQ}eDt xm OyO|t u=Wv 11 |x]@= Q "Ovm|t |= Q@ 14 =D 12 \@=wQ "QiY Q@=Q@ =} Ow@ Ovy=wN l} Q@=Q@ w OvDUy K}LY O=Oa= 16 w 15 \@=wQ "Ov=xOW xi=[= pOt x@ =yQ}Ut u=}QH |v=tR |oDUw}B |Q= QkQ@ u=tm l} |wQ OwN QiU pqN QO Q}Ut u=}QH xm = Q |v=tR |xR=@ Qy syU R}v x@ \w@Qt s}y=it XwYN QO QDW}@ C=L}[wD |= Q@ "Ovvm|t u}}aD 'Ovm|t x@ QHD w |v=wH w [9] u= Q=mty w |v=wH ' [8] |v=wH x@ Q}Ut -u=tm s}yUD `wkw |=yQ}eDt |OvwQ u=wD|t R}v ?=wH |}=Dm} w OwHw C=@F= |= Q@ u}vJty "OwW `wHQ [10] xO= R=@=@ "OQm x=Q= = Q `H=Qt u}= QO xOW O=yvW}B VwQ x@=Wt %R= CU= CQ=@a dw p xDi=}s}taD QiU u=tR 'pOt u}= QO T=U= Q@ Q_v OQwt Q}Ut |rwtat QiU u=tR |xOvyOu=Wv pw= CQ=@a 'u; QO xm t a |=yQ}eDt x@ \w@Qt CQ=@a "CU= u; |wQ |=yu=tm f tw a (x t a ) QiU u=tR `@=wD C@Ft |v=tR \ki w Ovm|t pta 15 xt} QH QDt=Q=B l} CQwY x@ q=@ |x]@= Q QO OW=@ xDW=O Q= Qk `=@W= C}a[w QO |v=tR |xR=@ l} QO u=tm l} xm Ow@ Oy=wN R= |W=v Q}N -=D u=wva x@ = Q CQ=@a u}= u=wD|t u}=Q@=v@ "9 =D 7 \@=wQ T=U= Q@ |=yDv= QO hY QO xOW x@ QHD Q=_Dv= u=tR u=ty xm OQm Q}@aD pO=aD Cr=L QO hY [27] "u= Q=mty w QByW CU= u=tm l} |m}t=v}O l}i=QD X}YND |xrUt pL sD} Qwor= "3 |xR=@ QO xm w Tqm x@ \w@Qt p Q}Ut u=}QH %h dw p Ct} Ra d |xR=@ QO xm w Tqm x@ \w@Qt p Q}Ut 12 xDi=}s}taD QiU u=tR % dw p 'Ov=xOQm w Tqm x@ \w@Qt i OYkt -=O@t GwR u}@ xDi=}s}taD QiU u=tR u} QDx=Dwm %u dw i 'd Ct} Ra |xR=@ w x@ \w@Qt n 2 N p xQo =D r -=O@t R= w Tqm x@ \w@Qt p Q}Ut QiU u=tR %T dw pn 'Ov=xOQm Ct} Ra d |xR=@ QO xm A pn QO |=yu=tm 't |v=tR |xR=@ QO a u=tm u=}QH %x t a 'w Tqm x@ \w@Qt t |v=tR |xR=@ QO a u=tm u=}QH %x tw a 'w Tqm x@ \w@Qt t |v=tR |xR=@ QO a u=tm QiU u=tR `@=D %f tw a (x t a )…”

“…'xm@W OYkt -=O@t |=yGwR |xty |xawtHt %I 'w Tqm x@ \w@Qt i OYkt -=O@t GwR u}@ |=yQ}Ut xty |xawtHt %P w i d 2 D |xR=@ QO xm w Tqm x@ \w@Qt i OYkt -=O@t GwR u}@ |=[=kD MQv %q dw i 'Ov=xOQm CtRa QO a 2 A p u=tm QiU u=tR R= |D@Uv xm ' 13 Q}Ut u=tm s}yUD Q}eDt % dtw pa xOQm Ct} Ra d |xR=@ QO xm 'w Tqm x@ \w@Qt p Q}Ut |wQ xm t |v=tR |xR=@ 'OwW|t x@ QHD 'CU= x@ \w@Qt p Q}Ut u=}QH Qo = CU= 1 Q@=Q@ xm ' 14 Q}Ut u=tm `wkw Q}eDt % dtw pa QO w OUQ@ a u=tm x@ t |v=tR |xR=@ QO Ov=xOQm Ct} Ra d |xR=@ QO xm w Tqm 'CU= QiY Q@=Q@ CQwYu}= Q}e 't |v=tR |xR=@ QO a u=tm C}iQ_ %c t a "t |v=tR |xR=@ QO a u=tm =@ Q_=vDt |mtm Q}eDt % t a C}OwOLt =@ |UqmOvJ |m}t=v}O l}i=QD X}YND |xrUtDTA-MCpOt u=tR Tqm Qy u; QO xm Ovm|t u=}@ = Q xOvvmxO=iDU= pO=aD |x}=B Q@ u=}QH C}iQ_ [10] |xR=@ w u=tm Qy |= Q@ t a Q}O=kt |v=UQRwQx@ =@ w |Q= QmD CQwY x@ xrUt 'u}= Q@=v@ |xwLv R= `q]= |= Q@ "OW Oy=wN pL p@k Q= QmD QO =yv; Q}O=kt T=U= Q@ |v=tR [10] xO= R=@=@ w |v=wH VywSB x@ |Q= QmD pL VwQ u}= u}vJty w xt} QH `@=wD ?=NDv= "OwW `wHQ C@=F OwN |rai Q=Okt QO dt pa w dt pa |=yQ}eDt xm |Dkw '22 =D 19 |xrUt Q=}U@ 'OwW xOQ@ Q=m x@ u; |= Q@ =yxt} QH |v=UQRwQx@ |Q= QmD OvwQ w OvwW xDW=O xov "Ow@ Oy=wN C}iQ_ C}OwOLt uwO@ |m}D=DU= l}i=QD X}YND |xrUt x@ x}@W w dt pa |=yQ}eDt w |v=tR |xR=@ w u=tm Qy |= Q@ t a Q}O=kt uDW=Oxov C@=F =@ TB X}YND |xrUt pwtat sD} [3] xO= R=@=@ w |v=wH ODFWTQP 16 pL OvwQ OQwt QO O}=@ =OD@= 'OW K} QWD SP1 xrUtQ} R pL OvwQ xm p=L l} R= V}@ =@ Cr=L |= Q@ pL VwQ TBU w OwW C@LY SP2 |xrUtQ}R |x@U=Lt |= Q@ 16 =D 10 \@=wQ s}kDUt pL "OwW xO=O \U@ xOvvmxO=iDU= Tqm |rai Q=Okt QO =yu=tm u=}QH xmu; R= TB Q}Ut -u=tm s}yUD w `wkw |=yQ}eDt Oy=wN Q=wWO Q=}U@ |D=@U=Lt ^=Lr R= T=}kt nQR@ |=yxm@W QO OvOW C@=F OwN |xQ}NP =t= "CU= O=}R Q=}U@ =yQ}Ut w OYkt --=O@t |=yGwR O=OaD = Q} R &Ow@ xO=iDU= =@ u=wD@ =D OwW|t Ea=@ RAM Ckwt | x_i=L QO =yQ}Ut C=aq]= VwQ "OQm |v=UQRwQx@ = Q QwmPt |=yQ}eDt '=yQ}Ut |wQ CmQL xO=U VwQ l} R= [10] xO= R=@=@ w |v=wH w [8] |v=wH `H=Qt QO pYit CQwY x@ SP2 |xrUtQ}R pL pL VwQ K} QWD x@ xt=O= QO "OQm `wHQ =yv; x@ u=wD|t xm CU= xOW xO=O K}[wD "s}R=OQB|t |O=yvW}B sD} Qwor= |=ys=o TBU w |UqmOvJ Cr=L |= Q@ xrUt p=@vO x@ xm Ov=xm@W |O=a u=oOvvmxO=iDU= pt=W 1 Tqm u=oOvv= Q xm OW xDio |=yQ}Ut w C=aq]= R= R}v 2 Tqm u=oOvv= Q w OvDUy OwN QiU u=tR uOQm xv}tm DTA-MC |xrUt |Q= QmD pL 'h}YwD u}= =@ "Ovvm|t |wQ}B xOW x}YwD |R=Uxv}tm pt=W xm DTA-MC 1 |R=Uxv}tm |xrUt pL R= Ow@ Oy=wN CQ=@a xov C@=F =@ w w=1 |= Q@ 16 =D 10 w 7 =D 4 |=yC}OwOLt CLD Q} R hOy `@=D "CU= t 2 D w a 2 A Qy |= Q@ 'x t2 a '2 Tqm x@ \w@Qt |=yu=}QH uDW=O…”

“…xO=iDU= 'DTA-MC |UqmOvJ |m}t=v}O l}i=QD X}YND |xrUt pL |= Q@ xOvvmxO=iDU= Tqm l} |= Q@ \ki xrUt Q=@ Qy u; QO xm CU= |Q= QmD OvwQ l} R= xt=O= QO TB "OwW|t pL Qo}O |=yTqm x@ \w@Qt u=}QH uOw@ C@=F ZQi =@ w l} OwHw ZQi =@ 16 =D 1 pOt pL VwQ 'xrUt pL OvwQ QDxO=U syi |= Q@ \@=wQ QO w T}Ov= OwHw R= ? }DQD u}O@ xm OwW|t xO=O K}[wD xOvvmxO=iDU= Tqm "OwW|t K} QWD |Uqm OvJ Cr=L |= Q@ pL VwQ u; R= Oa@ w OwW|t Q_v hQY w dt pa |=yQ}eDt uOQm ZQi C@=F =@ 'pOt QO xOvvmxO=iDU= Tqm l} ZQi =@ l}i=QD X}YND |xrUt x@=Wt |OL =D 16 =D 10 \@=wQ uwO@ 16 =D 1 pOt ' dt pa =yQ}Ut w =yu=tm u=}QH ?UL Q@ xm Ow@ Oy=wN C}iQ_ C}OwOLt =@ |m}D=DU= x@ u=wD|t '=yu=}QH uOQm ZQi C@=F =@ R}v 16 =D 10 \@=wQ R= "CU= pL p@=k CUO x@ = Q Q}Ut -u=tm s}yUD w Q}Ut -u=tm `wkw |=yQ}eDt Q=Okt =Dm} CQwY OQm xO=iDU= pOt pL |= Q@ |Q= QmD OvwQ l} R= u=wD|t T=U= u}ty Q@ [10] "OQw; KqY= |r@k Q= QmD |=y?=wH R= xO=iDU= =@ , = QQmt dt pa w dt pa |=yQ}eDt u; QO xm Q_=vDt ? }DQD x@ SP2 w SP1 |xrUt Q} R wO x@ = Q pOt 'QDxO=U u=@R x@ "OvwW|t R= xawtHt l} =@ =OD@= pL sD} Qwor= "O}vm s}UkD 16 =D 10 w 9 =D 1 \@=wQ =@ wO pt=W sD} Qwor= |rY= Q= QmD Qy "Ovm|t `wQW dt pa w dt pa Q}PBu=mt= |=yQ}eDt |=yQ}eDt xmu; R= TB =yu=} QH uDi=} |= Q@ SP1 |xrUtQ}R pL "1 %CU= xrLQt SP2 |xrUtQ}R pL "2 w OvOW xDW=O xov C@=F OwN |rai Q=Okt QO dt pa w dt pa xm OwN |rai Q=Okt QO =yu=} QH uDW=Oxov C@=F =@ dt pa w dt pa |=yQ}eDt uDi=} |= Q@ C@=F R= Oa@ SP1 |xrUtQ}R "OW Oy=wN Q= QmD hkwD \QW x@ uO}UQ =D OvwQ u}= |m}D=DU= l}i=QD X}YND |xrUt R= |OL =D ' dt pa w dt pa |=yQ}eDt uDW=Oxov "Ow@ Oy=wN Cw=iDt C}iQ_ C}OwOLt =@ uDW=Oxov C@=F R= Oa@ SP1 |xrUtQ}R xm s}yO u=Wv s}y=wN|t p=L xm O=O u=Wv u=wD|t |DL=Q x@ "OW Oy=wN pL xvwoJ dt pa w dt pa |=yQ}eDt Q} R |R=Uxv}y@ |xrUt pO=at xOvvmxO=iDU= Tqm l} ZQi =@ 9 =D 1 |=yxrUt %CU= 7 =D 4 \@=wQ C}OwOLt CLD min Z…”

“…"OW Ovy=wN Q}@aD Sv=Qo q ? }=Q[ u=wva x@ t a w u d i |=yQ}eDt xH}Dv QO xm |=yC}OwOLt OwHw p}rO x@ u; pO=at |R=Uxv}y@ xrUt =} 9 =D 1 pOt pL |xt}QH `@=wD VwQ R= =Hu}= QO 'xH}Dv QO "Ow@ Oy=wN pmWt |OL =D 'C}iQ_ l}i=QD X}YND |xrUt pL |= Q@ pY= QO xm [27] u= Q=mty w QByW |m}t=v}O Cr=L |= Q@ [10] xO= R=@=@ w |v=wH \UwD w xOw@ C}iQ_ C}OwOLt =@ |m}D=DU= xrUt |R=UO= R; |= Q@ 'CU= xOW xO=O \U@ |m}t=v}O l}i=QD X}YND |xrUt |xt}QH `@=D p=L "OW Oy=wN xDiQo xQy@ C}iQ_ C}OwOLt uwO@ CQwY x@ t 2 D w a 2 A Qy |= Q@ t a 2 (0; 1) =@ = Q t a (:; t a ) : [0; 1) ! [0; 1)…”