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- Title
The Wei–Norman method for the infinite-server queue with phase-type arrivals.
- Authors
Löpker, Andreas
- Abstract
We will briefly demonstrate the idea with the above E HT <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mrow /><mn>2</mn></msub></math> ht /G/ HT <math xmlns="http://www.w3.org/1998/Math/MathML"><mi> </mi></math> ht example. Even if no solution can be found one might still draw conclusions regarding the generating function (1) and hence the joint distribution of HT <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>X</mi><mi>t</mi></msub></math> ht and HT <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>J</mi><mi>t</mi></msub></math> ht . However, if the commutator HT <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>A</mi><mi>B</mi><mo>:</mo><mo>=</mo><mi>A</mi><mi>B</mi><mo>-</mo><mi>B</mi><mi>A</mi></mrow></math> ht is not zero, then this is no longer true.
- Subjects
QUEUING theory; LINEAR differential equations; MARKOV processes; NONLINEAR differential equations; NONLINEAR equations; INTEGRAL calculus; RICCATI equation
- Publication
Queueing Systems, 2022, Vol 100, Issue 3/4, p221
- ISSN
0257-0130
- Publication type
Article
- DOI
10.1007/s11134-022-09784-5