We found a match
Your institution may have access to this item. Find your institution then sign in to continue.
- Title
Rates of convergence of the join the shortest queue policy for large-system heavy traffic.
- Authors
Mukherjee, Debankur
- Abstract
Since HT <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi> </mi><mo> </mo><mi>N</mi></mrow></math> ht , the above process is ergodic. Thus, the state-of-the-art understanding is on solid grounds when the number of queues I N i is very small or in the asymptotic regime when HT <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>N</mi><mo stretchy="false">-></mo><mi> </mi></mrow></math> ht . Let HT <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msup><mrow><mi mathvariant="bold">Q</mi></mrow><mi>N</mi></msup><mrow><mo stretchy="false">(</mo><mi> </mi><mo stretchy="false">)</mo></mrow></mrow></math> ht denote the steady-state random variable. However, as the traffic becomes heavier ( HT <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi> </mi><mo> </mo><mn>1</mn><mo stretchy="false">/</mo><mn>2</mn></mrow></math> ht ), the HT <math xmlns="http://www.w3.org/1998/Math/MathML"><msubsup><mi>Q</mi><mn>1</mn><mi>N</mi></msubsup></math> ht process starts to hit the state HT <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mrow><mo maxsize="1.2em" minsize="1.2em" stretchy="true">{</mo></mrow><msubsup><mi>Q</mi><mn>1</mn><mi>N</mi></msubsup><mo>=</mo><mi>N</mi><mrow><mo maxsize="1.2em" minsize="1.2em" stretchy="true">}</mo></mrow></mrow></math> ht much more frequently, thereby spending less time away from the boundary.
- Subjects
QUEUING theory; BOUNDARY value problems; POISSON processes
- Publication
Queueing Systems, 2022, Vol 100, Issue 3/4, p317
- ISSN
0257-0130
- Publication type
Article
- DOI
10.1007/s11134-022-09803-5