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- Title
On level-dependent QBD processes with explosive state space.
- Authors
Takine, Tetsuya
- Abstract
The author is interested in LD-QBD processes with I explosive state space i , i.e., the cardinality HT <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>M</mi><mi>l</mi></msub></math> ht of HT <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi> </mi><mi>l</mi></msub></math> ht increases exponentially with HT <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>l</mi></math> ht . In any of them, however, the inverse of an HT <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msub><mi>M</mi><mi>l</mi></msub><mo>×</mo><msub><mi>M</mi><mi>l</mi></msub></mrow></math> ht matrix has to be computed in order to obtain HT <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mrow><mi mathvariant="bold-italic"> </mi></mrow><mi>l</mi></msub></math> ht . When HT <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>L</mi><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo><mo>=</mo><mi>l</mi></mrow></math> ht , customers arrive at rate HT <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi> </mi><mi>l</mi></msub></math> ht and occupy position HT <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>l</mi><mo>+</mo><mn>1</mn></mrow></math> ht .
- Subjects
MATRIX analytic methods; QUEUING theory; MARKOV processes; NONNEGATIVE matrices; MATRIX multiplications
- Publication
Queueing Systems, 2022, Vol 100, Issue 3/4, p353
- ISSN
0257-0130
- Publication type
Article
- DOI
10.1007/s11134-022-09796-1