Re: Elementary Math for the Traffic Problems

[Sonnet Nguyen <sonnet@white.cft.edu.pl>]

Hi Tuan Anh and everybody,

On Mon, 25 Oct 1999, Anh Le wrote:

> Trong CS co' ba`i tu+o+ng tu+. - algorithm Ford-Fulkerson. Cho graph vo+'i 
> ca'c egde ha.n che^' ve^` capacity, ti`m pha^n bo^' sao cho to^?ng lu+u 
> lu+o+.ng ca'c do`ng cha?y giu+~a 2 ddie^?m la` lo+'n nha^'t.

To^i kho^ng tha^'y any close links between 2 ba`i toa'n "to^?ng lu+u
lu+o+.ng ca'c do`ng cha?y" trong Graph Theory va` "determine optimal
velocity" in Freeway ma` to^i no'i dde^'n.   Ba`i toa'n cha.y xe tre^n
Freeway dda~ ddu+o+.c nghi~ ra nho+` bie^'t idealized (and simplified)
dde^'n mu+'c to^'i dda 1 ba`i toa'n thu+.c te^' ra^'t phu+'c ta.p, va`
nho+` va^.y no' tro+? tha`nh very interesting elementary problem, kho^ng
co`n di'nh gi` dde^'n graph.  Ne^'u quay la.i the original, very difficult  
problem: optimalization traffic capacity for given graph of Roads (ddu?
kie^?u optimalizations) thi` to^i chu+a co' algorithm gia?i no', cha('c
pha?i ddo+.i dde^'n lu'c nghi? hu+u se~ nghi~ tie^'p :-) Ma` tho^i pha?i
dde^? la.i i't unsolved problems dde^? clever students co`n co' dde^` ta`i
ma` vie^'t PhD thesis chu+' :-) 
   Anyway, intelligence dda^u pha?i chuye^.n bie^'t du`ng complicated
algorithms hay ho.c qua Graph Theory :-)

> Gio?ng tai nghe model cu?a ba'c dda^y.

Cu+' tu+` tu+`, trong Forum co' ra^'t nhie^`u ng` smart vo+'i tu+ duy
ra^'t to^'t, va^.y cu+' dde^? ca'c ba'c cu`ng suy nghi~ the^m i't la^u
cu`ng hie^?u the^m educational, pedagogic values of the problem I posted. 
Cu`ng la('m thi` ca'c ba'c la.i nho+` chi. Iga to^'t bu.ng dde^? chi. 
a^'y gia?i ho^. :-))    
  To^i dda~ post simple observation, which illustrates (heuristic) 
proof: there must exist the universal optimal velocity, more over,
almost independent of the models !  Co`n muo^'n determine the optimal
velocity thi` ca^`n pha?i co' model cu. the^?.  Muo^'n co' model
dda`ng hoa`ng thi` dda^`u tie^n pha?i xa'c ddi.nh ca'c attributes,
variables, parameters ma` no' se~ pha?i chu+'a, cu~ng nhu+ pha?i
thu+? hi`nh dung xem passibility se~ phu. thuo^.c va`o ca'c variables 
& parameters trong model ddo' ra sao.  La`m gi` co' chuye^.n pha?i 
cho sa(~n one table including mo.i thu+' data co^.ng the^m ca'c 
formulas se~ pha?i du`ng. Ne^'u nhu+ va^.y chi? vie^.c  ngo^`i la`m 
"co^.ng tru+` nha^n chia" la` xong, co`n de^~ ho+n ca? TV Quizes :-) 
Go+.i y' nhu+ va^.y la` ddu? dde^? cho ca'c ba.n tre? vo^'n clever 
gia?i no' de^~ da`ng :-))
  Just kidding.  DDa^y cu~ng chi? la` bu+o+'c dda^`u tie^n cu?a 
necessary process nha(`m chuye^?n xu hu+o+'ng VN tu+` lo^'i chuye^n 
solve given problems o+? mu+'c tha^'p le^n tho'i quen design projects,
design models (solving a class of problems) o+? mu+'c cao ho+n.     
 
Cheers,
SN