Traffic-toolbox Function lpf - Travel time functions
Calling Sequence
- [ta,dta,cta]=lpf(F,lpp,nf)
Parameters
- F
: row vector of flows in each arc
- lpp
: parameters of the travel time functions (ttf) for each arc
- nf
: model for the ttf
- ta
: travel time of each arc for the given flow
- dta
: derivate of the ttf for the given arc flow
- cta
: integral of the ttf for the given arc flow
Description
Computes the travel time of each arc for the given flow using the travel time
functions with parameters lpp and formula nf. Each colum of lpp is of the form
[t0;ca;ma;ba] where the coefficients t0 and ca have the meanings:
t0
: free-flow travel time
ca
: practical capacity of the link
The different formulae for the ttf are:
nf=0 -> c=t0+ma/ca*F+ma*(max(0,F-ca))^ba, with ba>=1
nf=1 -> c=t0*exp((F/ca)-1), with ca>0
nf=2 -> c=t0*2^((F/ca)-1), with ca>0
nf=3 -> c=t0*(1+0.15*(F/ca)^ma), with ma>=1 and ca>0
nf=4 -> c=t0+log(ca)-log(ca-F), with ca>0
nf=5 -> c=ba-ca*(t0-ba)/(F-ca), with ca>0
nf=6 -> c=t0+ca*F+ma*F^ba, with ba>1
EXAMPLES
net=TrafficExample('Small');
[g,d,lpp,nf]=Net2Par(net);
F=rand(1,9);
[ta,dta,cta]=lpf(F,lpp,nf)
// shows the function with the different parameters
dlpf(0.1,.01,5,lpp,6);
See Also