Re: Elementary Math for the Traffic Problems

["Anh Le" <anh_t_le@hotmail.com>]

Hi ba'c Sonet,

From: Sonnet Nguyen <sonnet@white.cft.edu.pl>
>Reply-To: vnsa@list-server.net
>To: vnsa@List-Server.net
>CC: Nguyen Aiviet <aiviet2@yahoo.com>
>Subject: Re: Elementary Math for the Traffic Problems
>   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^?.

   Y nhu+ ra(`ng ba'c se~ no'i ca^u na`y-:). Ca'i model ddo' pha?i cu+.c ky` 
ddo+n gia?n thi` ca^u tru+o+'c mo+'i ddu'ng, vi' du. chi? xe't mo^~i mo^.t 
con ddu+o+`ng (kho^ng graph gi` he^'t) co' capacity l, mo^~i xe cha.y giao 
ddo^.ng trong va^.n to^'c tu+` a dde^'n b, ti`m optimal speed sao cho to^?ng 
tho+`i gian cha.y cu?a ca'c xe nga('n nha^'t-:).

   Ba`i ti`m lu+u lu+o+.ng to^'i u+u thu+.c ra la.i ra^'t lie^n quan dde^'n 
ba`i ba'c no'i, ba'c nha^`m ro^`i. Va^'n dde^` o+? cho^~ cha.y ca`ng nhanh 
thi` ca`ng bo+'t ta('c ddu+o+`ng, la.i gia?m tho+`i gian, la`m gi` co' 
chuye^.n ta('c vi` cha.y qua' nhanh. Ddu+o+`ng chi? ta('c ne^'u xe't dde^'n 
topology cu?a graph va` ca'c hu+o+'ng cha.y ta.o tha`nh loop, co' va`o ma` 
kho^ng co'/kho^ng ki.p ra, va` ne^'u vu+o+.t qua' capacity cu?a ddu+o+`ng, 
ta(ng kha? na(ng ddu+o+`ng ho?ng ga^y ra congestion. DDo' chi'nh la` "model" 
cu. the^?.
   Ddau o+? cho^~ co' model ro^`i va^~n kho^ng gia?i ddu+o+.c (vi` the^' 
ca'c ky~ su+ mo+'i pha?i ddo'ng tie^`n thue^' nuo^i cho ca'c  mathematicians 
gia?i ho^. ma` ma^'y chu.c na(m ro^`i chu+a tha^'y dda^u-:)). Ba'c BAVu~ 
no'i ddu'ng ddo', mo^~i xe co' indepedent logic, ma` ca'c model chi? xe't 
dde^'n ca'c kie^?u random distribution ddo+n gia?n (markov process, queing 
kie^?u M/M/1).
   To'm la.i ba`i toa'n cu?a ba'c va^~n co`n la^'p lu+?ng nhie^`u qua', 
kie^?u na`y "smart guys" pha?i ddoa'n mo` ba'c muo^'n gi` dda~ (tru+` Iga).
   Ddu+'ng tu+` vi. tri' central observer, vo+'i ca'c distribuion ddo+n 
gia?n, ca'c algorithms to^i no'i are quite relevant (thu+.c ra chu'ng cu~ng 
tu+` ma^'y ddi.nh lua^.t ve^` ma.ch ddie^.n ho.c tho+`i xa xu+a nhu+ 
Kirshoff, Norton...). Trong thu+.c te^' vo+'i telecom networks thi` kho^ng 
ai du`ng. Vi' du. nhu+ flow control "algorithm" cu?a TCP/IP dda^'y, mo^~i 
source co' logic rie^ng, to^'c ddo^. generate packets kha'c nhau va` kho^ng 
phu. thuo^.c va`o nhau, nhu+ng la.i la`m a?nh hu+o+?ng dde^'n toa`n bo^. 
networsk. Chu+a no'i mo^~i loa.i packets co`n co' priority rie^ng, ddu+o+.c 
ddo^'i xu+? theo ca'c logic co`n kha'c cu?a ca'c links va` routers nu+~a.
   TCP la`m gi`? No' cu+' lie^`u ma.ng ddu+a a`o a.t packets va`o ma.ng, sau 
ddo' ddo+.i acknowledment, ne^'u tho+`i gian delivery la^u qua' (xe bi. 
ta('c la^u) thi` gia?m intensity ddi (gia?m window size for ACK ddi). DDo' 
la` ca'ch la`m vie^.c hoa`n toa`n heuristics.
    Cha('c cha('n va^'n dde^` xa'c ddi.nh (vo+'i convergent time nhanh) 
optimal window size cu?a TCP pha?i lie^n quan xa^u sa dde^'n toa'n cao ca^'p 
(-:)), ie. ba'c Sonnet ca^`n gi` pha?i ddo+.i dde^'n khi ve^` hu+u, ha~y coi 
Ph.D. thesis for clever students la` ca'i ddinh! Ne^'u gia?i ddu+o+.c gio+'i 
telecom network engineers se~ coi ba'c la` the greatest mathematician in the 
history, co' the^? look down dda'm Hilbert, Tarsky... nha` ba'c ddu+o+.c 
ro^`i. Pha?i thay ddo^?i tu+ duy, thu+.c te^' ddi chu+'-:)
   (sorry, just kidding and "no^?" mo^.t chu't dde^? khi'ch ba'c Sonnet-:))

Tuan Anh.

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