traffic.gms : Traffic Assignment Model
A simple traffic assignment problem:
- Move 5 units of stuff from A to B as quickly as possible, using one or more
of the N paths p1..pN between A and B.
- The delay d on each path is a function of the volume of traffic on
the path:
d(p) = a(p) + x(p) + x(p)**1.5
This is a simple example showing how VI can be used to compute
effective delay*, i.e. the maximum delay over all paths with nonzero
flow, or the time it takes for all the stuff to reach the
destination. For an example involving a nontrivial network see the
traffic2 model in this library.
Contributor: Steven Dirkse, January 2009
Small Model of Type: VI
<![CDATA[
$title Traffic Assignment Model (TRAFFIC,SEQ=3)
$ontext
A simple traffic assignment problem:
- Move 5 units of stuff from A to B as quickly as possible, using one or more
of the N paths p1..pN between A and B.
- The delay d on each path is a function of the volume of traffic on
the path:
d(p) = a(p) + x(p) + x(p)**1.5
This is a simple example showing how VI can be used to compute
*effective delay*, i.e. the maximum delay over all paths with nonzero
flow, or the time it takes for all the stuff to reach the
destination. For an example involving a nontrivial network see the
traffic2 model in this library.
Contributor: Steven Dirkse, January 2009
$offtext
set
p 'paths from A to B' / p1 * p4 /;
scalar
b 'volume of stuff to move' / 5 /;
parameter
a(p);
execseed = 1;
a(p) = uniform(0,100);
positive variable
x(p) 'path flows';
equation
d(p), demand;
d(p).. a(p) + x(p) + x(p)**1.5 =N= 0;
demand.. sum{p, x(p)} =G= b;
model vi / d, demand /;
* define the complementary pairs for vi
file myinfo / '%emp.info%' /;
putclose myinfo 'vi d x';
solve vi using emp;
abort$[vi.modelstat <> %MODELSTAT.LOCALLY OPTIMAL%] 'bad modelstat for vi';
abort$[vi.solvestat <> %SOLVESTAT.NORMAL COMPLETION%] 'bad solvestat for vi';
* for the report labels, ed = effective delay
parameters
report(*)
report2(p,*);
report2(p,'flow') = x.l(p);
report2(p,'delay') = d.l(p);
report('ed_marg') = demand.m;
report('ed_calc') = smax(p$[x.l(p) > 1e-8], report2(p,'delay'));
report('ed_diff') = abs(report('ed_calc')-report('ed_marg'));
display report, report2;
abort$[report('ed_diff') > 1e-6] 'bad ed';
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