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EnglishWe consider a point process i + ξ i , where i Î \mathbbZiZ and the ξ i ’s are i.i.d. random variables with compact support and variance σ 2. This process, with a suitable rescaling of the distribution of ξ i ’s, is well known to converge weakly, for large σ, to the Poisson process. We then study a simple queueing system with this process as arrival process. If the variance σ 2 of the random translations ξ i is large but finite, the resulting queue is very different from the Poisson case. We provide the complete description of the system for traffic intensity ϱ = 1, where the average length of the queue is proved to be finite, and for ϱ < 1 we propose a very effective approximated description of the system as a superposition of a fast process and a slow, birth and death, one. We found interesting connections of this model with the statistical mechanics of Fermi particles. This model is motivated by air traffic systems.
Guadagni, G., Ndreca, S., & Scoppola, B. (2011). Queueing systems with pre-scheduled random arrivals. MATHEMATICAL METHODS OF OPERATIONS RESEARCH, 73(1), 1-18.
| Tipologia: | Articolo su rivista |
| Citazione: | Guadagni, G., Ndreca, S., & Scoppola, B. (2011). Queueing systems with pre-scheduled random arrivals. MATHEMATICAL METHODS OF OPERATIONS RESEARCH, 73(1), 1-18. |
| IF: | Con Impact Factor ISI |
| Lingua: | English |
| Settore Scientifico Disciplinare: | Settore MAT/07 - Fisica Matematica |
| Revisione (peer review): | Sì, ma tipo non specificato |
| Tipo: | Articolo |
| Rilevanza: | Rilevanza internazionale |
| Digital Object Identifier (DOI): | http://dx.doi.org/10.1007/s00186-010-0330-5 |
| Stato di pubblicazione: | Pubblicato |
| Data di pubblicazione: | 2011 |
| Titolo: | Queueing systems with pre-scheduled random arrivals |
| Autori: | |
| Autori: | Guadagni, G; Ndreca, S; Scoppola, B |
| Appare nelle tipologie: | 01 - Articolo su rivista |
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