Elementary Math for the Traffic Problems

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

Hi Lovers of Thinking,

Ho^m nay to^i se~ no'i chuye^.n about one simple problem ma` ca'c 
ba'c drivers (like me) ga(.p pha?i thu+o+`ng nga`y tre^n freeway 
nhu+ng i't ng` hie^?u, cu~ng nhu+ ca`ng i't ng` thu+? la`m formalize 
dda`ng hoa`ng dde^? ddi dde^'n correct statements or helpful conclusions.
DDie^?n hi`nh ga^`n dda^y nha^'t la` tu.i CNN commentators (vo^'n 
kho^ng hie^?u Math) bi`nh lua^.n "lung tung" ve^` chuye^.n ta('c 
ddu+o+`ng khi da^n ti`nh cha.y ba~o, eg. Floyd.  Ne^'u each driver 
y' thu+'c ddu+o+.c (eg. ddu+o+.c tuye^n truye^`n by the Mass media) 
la` ho. pha?i cha.y vo+'i "optimal velocity" equal bao nhie^u (dda(.c
bie^.t la` trong ca'c ti`nh huo^'ng evacuations) dde^? ddo^. tho^ng
ddu+o+`ng la` cao nha^'t, thi` theo to^i cu~ng chu+a ca^`n pha?i xa^y
the^m va`i lanes mo+'i cho ca'c tru.c ddu+o+`ng cu~.  (Xa^y mo^~i km
freeway in USA to^'n chu+`ng 2 mil. USD.   To^?ng co^.ng USA co' 
ga^`n 70.000 km freeways.)     
  DDe^? tra'nh unnecessary complicated formalism nhu+ la` ddi va`o 
serious PhD thesis to^i ta.m ga'c la.i chuye^.n formalise "crosses",
"taking over", "turn left/right/back", etc. cu~ng nhu+ chu+a ddo^.ng
to+'i va^'n dde^` optimalisation (pha^`n na`o gia?i quye^'t traffic
problems) for a given graph of roads.
  Well, for the simplicity, let imagine that you are driving on the
one-directional (long-enough) road having only one lane !

Simple Observations:
--------------------
 1) Ne^'u chi./anh cha.y xe ra^'t cha^.m thi` se~ ga^y "ta('c ddu+o+`ng" 
    cho ca'c xe sau, tu+'c la` trong fixed time T se~ co' kho^ng nhie^`u
    xe cha.y qua ddu+o+.c ddoa.n ddu+o+`ng ddo'.
 2) Ngu+o+.c la.i, ne^'u chi./anh cha.y xe ra^'t nhanh cu~ng kho^ng
    la`m ta(ng ddu+o+.c mu+'c "tho^ng ddu+o+`ng" (tu+'c la` ta(ng so^'
    xe passed in the fixed time T tre^n ddoa.n ddu+o+`ng ddo';  ta.m 
    go.i la` "road's passibility"), bo+?i vi` dde^? an toa`n khi 
    "pho'ng nhanh" khoa?ng ca'ch giu+~a 2 xe ga^`n nhau pha?i ddu+o+.c
    ta(ng le^n ra^'t dda'ng ke^?, va` do ddo' mo^~i xe cha.y nhanh se~ 
    chie^'m ra^'t nhie^`u "die^.n ti'ch" ho+n so vo+'i khi 
    "cha.y cha^.m".

Conclusion: Therefore, exists an optimal velocity (for maximal road
            passibility) !
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Problem 1 :
Design a model and calculate an optimal velocity (in this model) 
for the maximal road's passibility !
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All discussions, solutions are welcome.  
 
Cheers,
SN
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Sonnet Nguyen
Center for Meta-Jokes
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BTW. The simplest & quite funny model of mine (having only few basic 
    parameters) establishes (consider actual technical data of 
    cars) that the optimal velocity must be nearly ... 40 km/h.