butools.map.RAPFromMomentsAndCorrelations¶

butools.map.RAPFromMomentsAndCorrelations()¶

Matlab:	[H0, H1] = RAPFromMomentsAndCorrelations(moms, corr)
Mathematica:	{H0, H1} = RAPFromMomentsAndCorrelations[moms, corr]
Python/Numpy:	H0, H1 = RAPFromMomentsAndCorrelations(moms, corr)

Returns a rational arrival process that has the same moments and lag autocorrelation coefficients as given.

Parameters:	moms : vector of doubles The vector of marginal moments. To obtain a RAP of size M, 2*M-1 moments are required. corr : vector of doubles The vector of lag autocorrelation coefficients. To obtain a RAP of size M, 2*M-3 coefficients are needed.
Returns:	H0 : matrix, shape (M,M) The H0 matrix of the rational arrival process H1 : matrix, shape (M,M) The H1 matrix of the rational arrival process

Notes

There is no guarantee that the returned matrices define a valid stochastic process. The joint densities may be negative.

References

[R45]

Mitchell, Kenneth, and Appie van de Liefvoort. “Approximation models of feed-forward G/G/1/N queueing networks with correlated arrivals.” Performance Evaluation 51.2 (2003): 137-152.

Examples

For Matlab:

>>> H0 = [-6.2, 2., 0; 2., -9., 1.; 1., 0, -3.];
>>> H1 = [2.2, 0, 2.; 0, 4., 2.; 0, 1., 1.];
>>> mom = MarginalMomentsFromRAP(H0, H1);
>>> disp(mom);
      0.29774      0.19284      0.19448      0.26597      0.45833
>>> corr = LagCorrelationsFromRAP(H0, H1, 3);
>>> disp(corr);
     0.012394    0.0027412   0.00072384
>>> [G0, G1] = RAPFromMomentsAndCorrelations(mom, corr);
>>> disp(G0);
      -8.9629       22.253      -18.544
     -0.99178       -4.667        2.331
      -1.2473       2.4279      -4.5701
>>> disp(G1);
       2.2027      -1.3173       4.3689
       1.2179       1.8217      0.28809
       1.0212      0.41735        1.951
>>> rmom = MarginalMomentsFromRAP(G0, G1);
>>> disp(rmom);
      0.29774      0.19284      0.19448      0.26597      0.45833
>>> rcorr = LagCorrelationsFromRAP(G0, G1, 3);
>>> disp(rcorr);
     0.012394    0.0027412   0.00072384

For Mathematica:

>>> H0 = {{-6.2, 2., 0},{2., -9., 1.},{1., 0, -3.}};
>>> H1 = {{2.2, 0, 2.},{0, 4., 2.},{0, 1., 1.}};
>>> mom = MarginalMomentsFromRAP[H0, H1];
>>> Print[mom];
{0.29774127310061604, 0.19283643304803644, 0.19448147792730758, 0.2659732553924553, 0.45833053059627116}
>>> corr = LagCorrelationsFromRAP[H0, H1, 3];
>>> Print[corr];
{0.012393574884970258, 0.0027411959690404088, 0.0007238364213571031}
>>> {G0, G1} = RAPFromMomentsAndCorrelations[mom, corr];
>>> Print[G0];
{{-8.96289388087693, 22.252570107207173, -18.544098091372838},
 {-0.9917815607047362, -4.666992249154709, 2.33103341018933},
 {-1.247298899065379, 2.4279117893845945, -4.570113869959446}}
>>> Print[G1];
{{2.2027474563394773, -1.3172514038167056, 4.368925812519816},
 {1.2179262967043782, 1.8217266419760083, 0.2880874609897277},
 {1.0211541630657368, 0.4173538177941065, 1.9509929987803876}}
>>> rmom = MarginalMomentsFromRAP[G0, G1];
>>> Print[rmom];
{0.297741273100616, 0.19283643304803638, 0.19448147792730755, 0.2659732553924553, 0.45833053059627116}
>>> rcorr = LagCorrelationsFromRAP[G0, G1, 3];
>>> Print[rcorr];
{0.012393574884970393, 0.0027411959690408086, 0.0007238364213573696}

For Python/Numpy:

>>> H0 = ml.matrix([[-6.2, 2., 0],[2., -9., 1.],[1., 0, -3.]])
>>> H1 = ml.matrix([[2.2, 0, 2.],[0, 4., 2.],[0, 1., 1.]])
>>> mom = MarginalMomentsFromRAP(H0, H1)
>>> print(mom)
[0.29774127310061604, 0.19283643304803644, 0.19448147792730755, 0.26597325539245531, 0.45833053059627116]
>>> corr = LagCorrelationsFromRAP(H0, H1, 3)
>>> print(corr)
[ 0.01239  0.00274  0.00072]
>>> G0, G1 = RAPFromMomentsAndCorrelations(mom, corr)
>>> print(G0)
[[ -8.96289  22.25257 -18.5441 ]
 [ -0.99178  -4.66699   2.33103]
 [ -1.2473    2.42791  -4.57011]]
>>> print(G1)
[[ 2.20275 -1.31725  4.36893]
 [ 1.21793  1.82173  0.28809]
 [ 1.02115  0.41735  1.95099]]
>>> rmom = MarginalMomentsFromRAP(G0, G1)
>>> print(rmom)
[0.29774127310061604, 0.19283643304803638, 0.19448147792730741, 0.26597325539245492, 0.45833053059627044]
>>> rcorr = LagCorrelationsFromRAP(G0, G1, 3)
>>> print(rcorr)
[ 0.01239  0.00274  0.00072]