We found a match
Your institution may have access to this item. Find your institution then sign in to continue.
- Title
Many-server limits for service systems with dependent service and patience times.
- Authors
Moyal, Pascal; Perry, Ohad
- Abstract
Specifically, for any HT <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>t</mi><mo»=</mo><mn>0</mn></mrow></math> ht , let HT <math xmlns="http://www.w3.org/1998/Math/MathML"><msubsup><mi>W</mi><mi>t</mi><mi>n</mi></msubsup></math> ht , HT <math xmlns="http://www.w3.org/1998/Math/MathML"><msubsup><mi>S</mi><mi>t</mi><mi>n</mi></msubsup></math> ht and HT <math xmlns="http://www.w3.org/1998/Math/MathML"><msubsup><mi>X</mi><mi>t</mi><mi>n</mi></msubsup></math> ht be the number of customers in queue, in service, and in the overall system (queue + service) at time I t i . We propose employing the measure-valued approach taken in [[7]] and in [[5]] which proved FWLLNs for the I GI i / I GI i / I n i and the HT <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>G</mi><mi>I</mi><mo stretchy="false">/</mo><mi>G</mi><mi>I</mi><mo stretchy="false">/</mo><mi>n</mi><mo>+</mo><mi>G</mi><mi>I</mi></mrow></math> ht models, respectively. This representation is simpler in that it somewhat decouples the dynamics of the two processes HT <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi> </mi><mi>n</mi></msup></math> ht and HT <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi> </mi><mi>n</mi></msup></math> ht , however, it would require to adapt the framework of [[5]], by keeping track of I residual i service times (as, e.g., in [[4]]), rather than ages.
- Subjects
QUEUING theory; PATIENCE; LAW of large numbers; CENTRAL limit theorem
- Publication
Queueing Systems, 2022, Vol 100, Issue 3/4, p337
- ISSN
0257-0130
- Publication type
Article
- DOI
10.1007/s11134-022-09800-8