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- Title
From PH/MAP to ME/RAP.
- Authors
Asmussen, Søren; Bladt, Mogens
- Abstract
Similarly, in the RAP HT <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mrow><mi mathvariant="bold-italic">A</mi></mrow><mo> </mo><msup><mrow><mi mathvariant="double-struck">R</mi></mrow><mi>p</mi></msup></mrow></math> ht is a piecewise deterministic Markov process, [[5]]. It is PH for any HT <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi> </mi><mo> </mo><mn>0</mn></mrow></math> ht , but the minimal possible I p i goes to HT <math xmlns="http://www.w3.org/1998/Math/MathML"><mi> </mi></math> ht as HT <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi> </mi><mo stretchy="false">V</mo><mn>0</mn></mrow></math> ht . From this, one immediately gets HT <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>u</mi><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo><mo>=</mo><mrow><mi mathvariant="bold-italic"> </mi></mrow><mo>exp</mo><mrow><mo maxsize="1.2em" minsize="1.2em" stretchy="true">{</mo></mrow><mo stretchy="false">(</mo><mrow><mi mathvariant="bold-italic">T</mi></mrow><mo>+</mo><mrow><mi mathvariant="bold-italic">v</mi></mrow><mrow><mi mathvariant="bold-italic"> </mi></mrow><mo stretchy="false">)</mo><mi>t</mi><mrow><mo maxsize="1.2em" minsize="1.2em" stretchy="true">}</mo></mrow><mrow><mi mathvariant="bold-italic">v</mi></mrow></mrow></math> ht .
- Subjects
CONDITIONAL expectations; LEVY processes; QUEUING theory; MARKOV processes
- Publication
Queueing Systems, 2022, Vol 100, Issue 3/4, p173
- ISSN
0257-0130
- Publication type
Article
- DOI
10.1007/s11134-022-09755-w