there could you please solve the question in

typed text(cause hand writing is sometimes

hard to read) using the knowledge in

Mathmathical modeling ?

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01.Use the fundamental diagram V(p)=v*f [1-p/p max] in the traffic conservation law and simplifyas much as possible

Q2.Write down the differentcial equations for

the GHR model.

Solve: use Fundamental diagram vip est [ 1 - Pro in the traffic Conservation liw and simplity. much as possible 05 Write down the differenca equations for GHR mochel the One such od O Simph of the M=0 ad Care ad wo dv. (t)- Cox Car-following model is Called the GHR mocht (Gazis- Herman - Rothery) Stimulus- Response model These models use the following equation? An(t)= CUM(4) A61E-T). where C, micul l AXLt-The modhe parasuetes, EX! Consider the GHR model with a lader with velverty Valth and another car following [xolt-1) - X,14-1)] di (t) = Volt-) - CV, (t-1) Budh this ODE is be solved lineur methods, through the chlaged aspect should considred. prob ans may albo be soend efficiently using namical sinnlation. Cers, dt first order liner These Microscopic . Modeling of Traffic Flows Maroscopic modelling of traffic flow involves but at individual drivers and how they interact. To model these microscopic internetions, we differenca equations, which involve relations betuan iterates of a variable To Consich Car-following models, which are that describe longitudinal interactions of velocles, Connich th diagram use models Lo Lng ART Carn - X One - Lor, Ln hangths of Corsfonicles on respectively. xn (t), Xalt) and the prisons of the respective vehicks at trimet Uni(t), S.Lt) are the velouties of haspective vehichs at trimet ans (6), Onlt) are the accelvations of the respection vehicles at the 6 Ax (t) = xn-4) - Xolt) is the space had way between trehicle noi and n at time t Dutt) Uni (t) - Vult) is the velouty different kekenen vehicles hot and in of vehich no the rear end of vehich nl T is the readon tome. Macroscopis Modeling of Traffic Flows Macroscopic models of "buds-eye now pressena of Vehicles traffic cornier or the agregate . One such car-following model in called the GHR muchy (Gerir. Herman - Ruthery) at stimules. Response Model following guntuni antu) CASTLD) when com cull AYLE-1) will EX with GHR model MO with wonty volti ad author ar felluring 2.4) trt) () -25,6-1) dit.c.1) - cuit-) But this ad may to solved Bir moths, danged asped shimler proto lins may also be solved efficently uring namical whntetion of w Conservation laws are valuable comandathe guitly property of gran fault) - foxt) dx blot rett to a tu diperhat Intely # ( sans foren du) 13 1 f60) 4 - de favorite = $**$.$(fog) 4x *S' [ + 3(fwandes Ja- S[$3,6005) when the weled Now consider Afsat) = 0, which is syng that a Property of the that is being conserved through time. >> S 3(Pu] ex=0 se + 22 (16)=0) by the Paynild Lemone Continuity Equitton Macroscopis Modeling of Traffic Flows Macroscopic models of "buds-eye now pressena of Vehicles traffic cornier or the agregate . One such car-following model in called the GHR muchy (Gerir. Herman - Ruthery) at stimules. Response Model following guntuni antu) CASTLD) when com cull AYLE-1) will EX with GHR model MO with wonty volti ad author ar felluring 2.4) trt) () -25,6-1) dit.c.1) - cuit-) But this ad may to solved Bir moths, danged asped shimler proto lins may also be solved efficently uring namical whntetion of w Conservation laws are valuable comandathe guitly property of gran fault) - foxt) dx blot rett to a tu diperhat Intely # ( sans foren du) 13 1 f60) 4 - de favorite = $**$.$(fog) 4x *S' [ + 3(fwandes Ja- S[$3,6005) when the weled Now consider Afsat) = 0, which is syng that a Property of the that is being conserved through time. >> S 3(Pu] ex=0 se + 22 (16)=0) by the Paynild Lemone Continuity Equitton - One macroscopice model of traffic for called ti Lighthili - when - Richards (LWR) M The LWR model sonoply takes 564 V (put) px - Q (pixel This the continuity equation gives! atent) 3 () sonas $(penes Vytvov)) An interesting phasemman to consiar about macroscopie discontinmties, and Chled propagation of these discontinuities which br wil are M Shaw Now at pixit) traffic Saridy (veluchs/lam) sixit) average seed (hu/1) flyt) traffic flow (ven) fixth- pexit es (xit) Hydrodymmic Equation But24X) - Consortion Low The relation that gives flow relative called th Finterest Trapreno Qlplats), to dorty ww.st wish Qlolto al mare) o delo po is the critical censity [very/an] med pass to the Jam andy gant alport called the capacity. Velouty may also be as a fraction of cannty Vyoo) satisfy Vlo) est, Vlp.o. de de called the free flas pad tams] An exsuph of singh Q ad vfunction (plot)) = vt [ 1 - Mix] 2 p= f pro [ Q(P4, 2) a pastron [i - Art gat de porn other publities for vi Vip-exol) Gips-puse (9) vipof[i - flean) exploput (1 - 1 Pfennedy inn what p(x,0) = P(x-SP where Using entups amonth solutions to this Plemon Problen! (11 If prapt, se do le dagen San pocelo If xent vf x > at wned a-00-00 Flas Trasgou pela 1. fo Plate & Playan] we hallo a nuxefactive yap (2012.) + except v> Wah IT By 4 2P Solve: use Fundamental diagram vip est [ 1 - Pro in the traffic Conservation liw and simplity. much as possible 05 Write down the differenca equations for GHR mochel the One such od O Simph of the M=0 ad Care ad wo dv. (t)- Cox Car-following model is Called the GHR mocht (Gazis- Herman - Rothery) Stimulus- Response model These models use the following equation? An(t)= CUM(4) A61E-T). where C, micul l AXLt-The modhe parasuetes, EX! Consider the GHR model with a lader with velverty Valth and another car following [xolt-1) - X,14-1)] di (t) = Volt-) - CV, (t-1) Budh this ODE is be solved lineur methods, through the chlaged aspect should considred. prob ans may albo be soend efficiently using namical sinnlation. Cers, dt first order liner These Microscopic . Modeling of Traffic Flows Maroscopic modelling of traffic flow involves but at individual drivers and how they interact. To model these microscopic internetions, we differenca equations, which involve relations betuan iterates of a variable To Consich Car-following models, which are that describe longitudinal interactions of velocles, Connich th diagram use models Lo Lng ART Carn - X One - Lor, Ln hangths of Corsfonicles on respectively. xn (t), Xalt) and the prisons of the respective vehicks at trimet Uni(t), S.Lt) are the velouties of haspective vehichs at trimet ans (6), Onlt) are the accelvations of the respection vehicles at the 6 Ax (t) = xn-4) - Xolt) is the space had way between trehicle noi and n at time t Dutt) Uni (t) - Vult) is the velouty different kekenen vehicles hot and in of vehich no the rear end of vehich nl T is the readon tome. Macroscopis Modeling of Traffic Flows Macroscopic models of "buds-eye now pressena of Vehicles traffic cornier or the agregate . One such car-following model in called the GHR muchy (Gerir. Herman - Ruthery) at stimules. Response Model following guntuni antu) CASTLD) when com cull AYLE-1) will EX with GHR model MO with wonty volti ad author ar felluring 2.4) trt) () -25,6-1) dit.c.1) - cuit-) But this ad may to solved Bir moths, danged asped shimler proto lins may also be solved efficently uring namical whntetion of w Conservation laws are valuable comandathe guitly property of gran fault) - foxt) dx blot rett to a tu diperhat Intely # ( sans foren du) 13 1 f60) 4 - de favorite = $**$.$(fog) 4x *S' [ + 3(fwandes Ja- S[$3,6005) when the weled Now consider Afsat) = 0, which is syng that a Property of the that is being conserved through time. >> S 3(Pu] ex=0 se + 22 (16)=0) by the Paynild Lemone Continuity Equitton Macroscopis Modeling of Traffic Flows Macroscopic models of "buds-eye now pressena of Vehicles traffic cornier or the agregate . One such car-following model in called the GHR muchy (Gerir. Herman - Ruthery) at stimules. Response Model following guntuni antu) CASTLD) when com cull AYLE-1) will EX with GHR model MO with wonty volti ad author ar felluring 2.4) trt) () -25,6-1) dit.c.1) - cuit-) But this ad may to solved Bir moths, danged asped shimler proto lins may also be solved efficently uring namical whntetion of w Conservation laws are valuable comandathe guitly property of gran fault) - foxt) dx blot rett to a tu diperhat Intely # ( sans foren du) 13 1 f60) 4 - de favorite = $**$.$(fog) 4x *S' [ + 3(fwandes Ja- S[$3,6005) when the weled Now consider Afsat) = 0, which is syng that a Property of the that is being conserved through time. >> S 3(Pu] ex=0 se + 22 (16)=0) by the Paynild Lemone Continuity Equitton - One macroscopice model of traffic for called ti Lighthili - when - Richards (LWR) M The LWR model sonoply takes 564 V (put) px - Q (pixel This the continuity equation gives! atent) 3 () sonas $(penes Vytvov)) An interesting phasemman to consiar about macroscopie discontinmties, and Chled propagation of these discontinuities which br wil are M Shaw Now at pixit) traffic Saridy (veluchs/lam) sixit) average seed (hu/1) flyt) traffic flow (ven) fixth- pexit es (xit) Hydrodymmic Equation But24X) - Consortion Low The relation that gives flow relative called th Finterest Trapreno Qlplats), to dorty ww.st wish Qlolto al mare) o delo po is the critical censity [very/an] med pass to the Jam andy gant alport called the capacity. Velouty may also be as a fraction of cannty Vyoo) satisfy Vlo) est, Vlp.o. de de called the free flas pad tams] An exsuph of singh Q ad vfunction (plot)) = vt [ 1 - Mix] 2 p= f pro [ Q(P4, 2) a pastron [i - Art gat de porn other publities for vi Vip-exol) Gips-puse (9) vipof[i - flean) exploput (1 - 1 Pfennedy inn what p(x,0) = P(x-SP where Using entups amonth solutions to this Plemon Problen! (11 If prapt, se do le dagen San pocelo If xent vf x > at wned a-00-00 Flas Trasgou pela 1. fo Plate & Playan] we hallo a nuxefactive yap (2012.) + except v> Wah IT By 4 2P