MAMSolver

M/M/1 Queue: A QBD Process

The above Markov chain is countinous time and the input of the C++ version of the tool should consist of matrixes that define its infinitesimal generator. The order of the input matrices is showed in the following. Note that the matrices in this example are simple scalars (the explanations on the right should not be included in the input file). 
1
Size of boundary portion
1
Size of repetitive portion
1
Burst size of the process
0.000000000000001
Numerical accuracy


-2.0
Local transitions in boundary portion


3.0
Backward transitions to boundary portion


2.0
Forward transitions from boundary portion




3.0
Backward transitions in the repetitive portion


-5.0
Local transitions in the repetitive portion


2.0
Forward transitions in the repetitive portion


The input to the Matlab version of the tool should be transition matrices as defined above. The input format can be found in a Matlab mat file: QBDtestcase1. To use the mat file and to use the functions of MAMSolver, see the following example. > load QBDtestcase1 > G = QBD_G_ETAQA(A); > pe = QBD_pi_ETAQA(B,A,B0,G); > meanqlen = QBD_qlen_ETAQA(B,A,B0,pe,1);

M/Cox2/1 Queue: A QBD process

Back To Top

Markov Chain for an M/Cox2/1 queue

The above Markov chain is countinous time and the input of the C++ version of the tool should consist of matrixes that define its infinitesimal generator. The order of the input matrices is showed in the following. Note that the matrices in this example are simple scalars (the explanations on the right should not be included in the input file). 
1
Size of boundary portion
2
Size of repetitive portion
1
Burst size of the process
0.000000000000001
Numerical accuracy


 -2.0
Local transitions in boundary portion


  6.0
  3.0
Backward transitions to boundary portion


  2.0    0.0
Forward transitions from boundary portion




  6.0    0.0
  3.0    0.0
Backward transitions in the repetitive portion


-12.0    4.0
   0.0   -5.0
Local transitions in the repetitive portion


  2.0    0.0
  0.0    2.0
Forward transitions in the repetitive portion



The input to the Matlab version of the tool should be transition matrices as defined above. The input format can be found in a Matlab mat file: QBDtestcase2. To use the mat file and to use the functions of MAMSolver, see the following example. > load QBDtestcase2 > G = QBD_G_ETAQA(A); > pe = QBD_pi_ETAQA(B,A,B0,G); > meanqlen = QBD_qlen_ETAQA(B,A,B0,pe,1);

GI/M/1 Queue: Bursty Service

Back To Top

The above Markov chain is countinous time and the input of the tool should consist of matrixes that define its infinitesimal generator. The burst size in this example is 3. The order of the input matrices is showed in the following (the explanations on the right should not be included in the input file):
1
Size of boundary portion
1
Size of repetitive portion
3
Burst size of the process
0.000000000000001
Numerical accuracy


 -2.0
Local transitions in boundary portion


  2.0  Forward transitions from boundary portion


  6.0
Backward transitions to boundary portion


  3.0



 1.0





-8.0
Backward transitions to the first set of the repetitive portion


 3.0



 2.0



 1.0





  2.0
Forward transitions in the repetitive portion


 -8.0
Local transitions in the repetitive portion


 3.0
Backward transitions tin the repetitive portion


 2.0



 1.0



The input to the Matlab version of the tool should be transition matrices as defined above. The input format can be found in a Matlab mat file: GIM1testcase. To use the mat file and to use the functions of MAMSolver, see the following example. > load GIM1testcase > R = GIM1_R_ETAQA(A); > pe = GIM1_pi_ETAQA(B,A,R,'Boundary',B0); > meanqlen = GIM1_qlen_ETAQA(B,A,R,pe,1,'Boundary',B0);

M/G/1 Queue

Back To Top


The above Markov chain is countinous time and the input of the tool should consist of matrixes that define its infinitesimal generator. The burst size in this example is 3. The order of the input matrices is showed in the following (the explanations on the right should not be included in the input file):
1
Size of boundary portion
2
Size of repetitive portion
3
Burst size of the process
0.000000000000001
Numerical accuracy


 -3.5
Local transitions in boundary portion


 10.0
 12.0
Backward transitions to boundary portion


  2.0    0.0
Forward transitions from boundary portion


  1.0    0.0



  0.5    0.0





 10.0    0.0
 12.0    0.0
Backward transitions in the repetitive portion


-17.5    4.0
   0.0 -15.5
Local transitions in the repetitive portion


  2.0    0.0
  0.0    2.0
Forward transitions in the repetitive portion


  1.0    0.0
  0.0    1.0



  0.5    0.0
  0.0    0.5



The input to the Matlab version of the tool should be transition matrices as defined above. The input format can be found in a Matlab mat file: MG1testcase1. To use the mat file and to use the functions of MAMSolver, see the following example. > load MG1testcase1; > G = MG1_G_ETAQA(A); > pe = MG1_pi_ETAQA(B,A,G,'Boundary',C0); > meanqlen = MG1_qlen_ETAQA(B,A,pe,1,'Boundary',C0);