Queueing systems with pre-scheduled random arrivals

G. Guadagni (), S. Ndreca () and B. Scoppola ()

Mathematical Methods of Operations Research, 2011, vol. 73, issue 1, 18 pages

Abstract: We consider a point process i + ξ i , where $${i\in \mathbb{Z}}$$ 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. Copyright Springer-Verlag 2011

Keywords: Queueing system; Air-traffic congestion; Non Poissonian arrivals (search for similar items in EconPapers)
Date: 2011
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Citations: View citations in EconPapers (7)

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DOI: 10.1007/s00186-010-0330-5

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