Heavy traffic analysis of a polling model with retrials and glue periods
| Autor: | Jacques Resing, J.L. Dorsman, Murtuza Ali Abidini |
|---|---|
| Přispěvatelé: | Stochastic Operations Research, Stochastics (KDV, FNWI) |
| Jazyk: | angličtina |
| Rok vydání: | 2018 |
| Předmět: |
Statistics and Probability
Exponential distribution 0211 other engineering and technologies 02 engineering and technology Heavy traffic math.PR 01 natural sciences 010104 statistics & probability Optical networking FOS: Mathematics 0101 mathematics GLUE Queue Mathematics 021103 operations research business.industry Applied Mathematics Probability (math.PR) Reservation Expression (mathematics) retrials polling model Polling system Modeling and Simulation business Mathematics - Probability Interpolation Computer network |
| Zdroj: | Stochastic Models, 34(4), 464-503. Taylor and Francis Ltd. arXiv.org, e-Print Archive, Mathematics ISSUE=1707.03876;TITLE=arXiv.org, e-Print Archive, Mathematics |
| ISSN: | 1532-6349 |
| Popis: | We present a heavy traffic analysis of a single-server polling model, with the special features of retrials and glue periods. The combination of these features in a polling model typically occurs in certain optical networking models, and in models where customers have a reservation period just before their service period. Just before the server arrives at a station there is some deterministic glue period. Customers (both new arrivals and retrials) arriving at the station during this glue period will be served during the visit of the server. Customers arriving in any other period leave immediately and will retry after an exponentially distributed time. As this model defies a closed-form expression for the queue length distributions, our main focus is on their heavy-traffic asymptotics, both at embedded time points (beginnings of glue periods, visit periods and switch periods) and at arbitrary time points. We obtain closed-form expressions for the limiting scaled joint queue length distribution in heavy traffic and use these to accurately approximate the mean number of customers in the system under different loads. Comment: 23 pages, 2 figures |
| Databáze: | OpenAIRE |
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