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- Title
First exit time for a discrete-time parallel queue.
- Authors
Palmowski, Zbigniew
- Abstract
To get exponential asymptotics for general distributions of HT <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msub><mi>A</mi><mi>n</mi></msub><mo>,</mo><msubsup><mi>S</mi><mi>n</mi><mi>i</mi></msubsup></mrow></math> ht , HT <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>i</mi><mo>=</mo><mn>1</mn><mo>,</mo><mn>2</mn></mrow></math> ht (for example geometric ones), one can follow [[3], [6], [12]]. At the beginning of the I n i th time slot, HT <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>A</mi><mi>n</mi></msub></math> ht customers arrive to both queues. Let HT <math xmlns="http://www.w3.org/1998/Math/MathML"><msubsup><mi>Q</mi><mi>n</mi><mi>i</mi></msubsup></math> ht with HT <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>i</mi><mo>=</mo><mn>1</mn><mo>,</mo><mn>2</mn></mrow></math> ht be the queue length after the service HT <math xmlns="http://www.w3.org/1998/Math/MathML"><msubsup><mi>S</mi><mrow><mi>n</mi><mo>-</mo><mn>1</mn></mrow><mi>i</mi></msubsup></math> ht and before the arrival HT <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>A</mi><mi>n</mi></msub></math> ht .
- Subjects
QUEUEING networks; BOUNDARY value problems; RIEMANN-Hilbert problems; RANDOM walks
- Publication
Queueing Systems, 2022, Vol 100, Issue 3/4, p329
- ISSN
0257-0130
- Publication type
Article
- DOI
10.1007/s11134-022-09744-z