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- Title
Characterisation of multivariate phase type distributions.
- Authors
Nielsen, Bo Friis
- Abstract
The I ij i 'th element of HT <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi mathvariant="bold-italic">R</mi></mrow></math> ht is multiplied on the total sojourn time of state I i i to get state I i i 's contribution to variable HT <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>Y</mi><mi>j</mi></msub></math> ht . Then, HT <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi mathvariant="bold-italic">X</mi></mrow></math> ht has a rational (multi-dimensional) Laplace transform, i.e. HT <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi mathvariant="bold-italic">X</mi></mrow></math> ht belongs to the class of Bilateral Multivariate Matrix-Exponential distributions (MVBME). Theorem 2 also holds in the strictly non-negative case where HT <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mrow><mi mathvariant="bold-italic">w</mi></mrow><mo»=</mo><mrow><mn mathvariant="bold">0</mn></mrow></mrow></math> ht .
- Subjects
POISSON processes; DISTRIBUTION (Probability theory); PROBABILITY theory; QUEUING theory; GAUSSIAN distribution; MARKOV processes
- Publication
Queueing Systems, 2022, Vol 100, Issue 3/4, p229
- ISSN
0257-0130
- Publication type
Article
- DOI
10.1007/s11134-022-09802-6