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- Title
Open problems for critically loaded k-limited polling systems.
- Authors
Boon, Marko A. A.; Winands, Erik M. M.
- Abstract
Conjecture 1 Denote by HT <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>N</mi><mi>i</mi></msub></math> ht the steady-state number of customers in HT <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>Q</mi><mi>i</mi></msub></math> ht . In particular, it turns out that simply assuming that in HT the number of customers served in each cycle is always HT <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>k</mi><mn>1</mn></msub></math> ht and HT <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>k</mi><mn>2</mn></msub></math> ht , respectively, is incorrect. Let HT <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>A</mi><mi>i</mi></msub></math> ht , HT <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>B</mi><mi>i</mi></msub></math> ht , and HT <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>S</mi><mi>i</mi></msub></math> ht denote the generic interarrival, service and switch-over times for 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 , with finite variances.
- Subjects
QUEUING theory; PROBABILITY density function; BOUNDARY value problems
- Publication
Queueing Systems, 2022, Vol 100, Issue 3/4, p281
- ISSN
0257-0130
- Publication type
Article
- DOI
10.1007/s11134-022-09770-x