butools.dmap.DMMAPFromDMRAP¶

butools.dmap.DMMAPFromDMRAP()¶

Matlab:	D = DMMAPFromDMRAP(H, precision)
Mathematica:	D = DMMAPFromDMRAP[H, precision]
Python/Numpy:	D = DMMAPFromDMRAP(H, precision)

Obtains a Markovian representation of a discrete rational arrival process of the same size, if possible, using the procedure published in [R8].

Parameters:	H : list/cell of matrices of shape(M,M), length(N) The H0...HN matrices of the DMRAP to transform precision : double, optional A representation is considered to be a Markovian one if it is closer to it than this precision
Returns:	D : list/cell of matrices of shape(M,M), length(N) The D0...DN matrices of the DMMAP (if found)

References

[R8]	(1, 2) András Horváth, Gábor Horváth, Miklós Telek, “A traffic based decomposition of two-class queueing networks with priority service”. COMPUTER NETWORKS 53:(8) pp. 1235-1248. (2009)

Examples

For Matlab:

>>> H0 = [0.15, 0.2, 0.18; -0.20, 0.17, 0.22; 0.19, 0.15, 0.16];
>>> H1 = [0.01, 0.08, 0.16; 0.02, 0.2, 0.07; 0.02, 0.15, 0.17];
>>> H2 = [0.14, 0.07, 0.01; 0.19, 0.02, 0.31; 0.06, 0.1, 0.];
>>> H = {H0, H1, H2};
>>> moms = MarginalMomentsFromDMRAP(H);
>>> disp(moms);
       1.6264       3.6055       10.991       43.903       218.08
>>> jmom = LagkJointMomentsFromDMRAP(H, 3, 1);
>>> G = DMMAPFromDMRAP(H);
>>> disp(G{1});
      0.12149      0.28833      0.11968
   5.6441e-06      0.17495     0.068392
      0.14667      0.12596      0.18355
>>> disp(G{2});
     0.026095    5.788e-06      0.13053
     0.069062      0.26926   1.1436e-05
     0.073725      0.21205     0.084643
>>> disp(G{3});
      0.14939    0.0019471      0.16253
      0.12377     0.010576      0.28397
     0.047622      0.12573   3.4639e-05
>>> rmoms = MarginalMomentsFromDMMAP(G);
>>> disp(rmoms);
       1.6264       3.6055       10.991       43.903       218.08
>>> rjmom = LagkJointMomentsFromDMMAP(G, 3, 1);
>>> err = norm(rjmom{1}-jmom{1})+norm(rjmom{2}-jmom{2});
>>> disp(err);
   7.8933e-13

For Mathematica:

>>> H0 = {{0.15, 0.2, 0.18},{-0.20, 0.17, 0.22},{0.19, 0.15, 0.16}};
>>> H1 = {{0.01, 0.08, 0.16},{0.02, 0.2, 0.07},{0.02, 0.15, 0.17}};
>>> H2 = {{0.14, 0.07, 0.01},{0.19, 0.02, 0.31},{0.06, 0.1, 0.}};
>>> H = {H0, H1, H2};
>>> moms = MarginalMomentsFromDMRAP[H];
>>> Print[moms];
{1.6263896740154515, 3.6054695734649638, 10.991320699229345, 43.90287088124943, 218.07910677758852}
>>> jmom = LagkJointMomentsFromDMRAP[H, 3, 1];
>>> G = DMMAPFromDMRAP[H];
>>> Print[G[[1]]];
{{0.12149271422840599, 0.288331581363331, 0.11967700564930148},
 {5.644084212797836*^-6, 0.17495249080494266, 0.06839214007006354},
 {0.14666783363741778, 0.12596472732550704, 0.1835547949666508}}
>>> Print[G[[2]]];
{{0.026094910703667897, 5.787995863058259*^-6, 0.1305322742733941},
 {0.06906174782798843, 0.269261673646175, 0.000011436233267865314},
 {0.07372525075569406, 0.21205253223976755, 0.08464341565015684}}
>>> Print[G[[3]]];
{{0.14938972761188077, 0.0019470730142651345, 0.16252892515988945},
 {0.12377266142377177, 0.010575633044980423, 0.2839665728645965},
 {0.047621973820317604, 0.1257348322613494, 0.000034639343138560594}}
>>> rmoms = MarginalMomentsFromDMMAP[G];
>>> Print[rmoms];
{1.6263896740154504, 3.6054695734649584, 10.991320699229316, 43.902870881249264, 218.0791067775875}
>>> rjmom = LagkJointMomentsFromDMMAP[G, 3, 1];
>>> err = Norm[rjmom[[1]]-jmom[[1]]]+Norm[rjmom[[2]]-jmom[[2]]];
>>> Print[err];
8.133031677833887*^-13

For Python/Numpy:

>>> H0 = ml.matrix([[0.15, 0.2, 0.18],[-0.20, 0.17, 0.22],[0.19, 0.15, 0.16]])
>>> H1 = ml.matrix([[0.01, 0.08, 0.16],[0.02, 0.2, 0.07],[0.02, 0.15, 0.17]])
>>> H2 = ml.matrix([[0.14, 0.07, 0.01],[0.19, 0.02, 0.31],[0.06, 0.1, 0.]])
>>> H = [H0, H1, H2]
>>> moms = MarginalMomentsFromDMRAP(H)
>>> print(moms)
[1.6263896740154515, 3.6054695734649633, 10.991320699229343, 43.902870881249427, 218.07910677758866]
>>> jmom = LagkJointMomentsFromDMRAP(H, 3, 1)
>>> G = DMMAPFromDMRAP(H)
>>> print(G[0])
[[ 0.15737  0.31966  0.07273]
 [ 0.01095  0.22961  0.06546]
 [ 0.16355  0.1105   0.09302]]
>>> print(G[1])
[[ 0.08443  0.03798  0.09227]
 [ 0.01529  0.2798   0.01004]
 [ 0.02635  0.39383  0.01577]]
>>> print(G[2])
[[ 0.12909  0.09375  0.01271]
 [ 0.22947  0.01525  0.14412]
 [ 0.01002  0.1713   0.01567]]
>>> rmoms = MarginalMomentsFromDMMAP(G)
>>> print(rmoms)
[1.6263896740154513, 3.6054695734649629, 10.991320699229343, 43.902870881249434, 218.07910677758866]
>>> rjmom = LagkJointMomentsFromDMMAP(G, 3, 1)
>>> err = la.norm(rjmom[0]-jmom[0])+la.norm(rjmom[1]-jmom[1])
>>> print(err)
6.76975985004e-14