NDLI: Queueing systems with pre-scheduled random arrivals

Content Provider	Springer Nature Link
Author	Guadagni, G. Ndreca, S. Scoppola, B.
Copyright Year	2010
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.
Starting Page	1
Ending Page	18
Page Count	18
File Format	PDF
ISSN	14322994
Journal	Mathematical Methods of Operations Research
Volume Number	73
Issue Number	1
e-ISSN	14325217
Language	English
Publisher	Springer-Verlag
Publisher Date	2010-09-30
Publisher Place	Berlin, Heidelberg
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Queueing system Air-traffic congestion Non Poissonian arrivals Calculus of Variations and Optimal Control; Optimization Business/Management Science Operations Research/Decision Theory
Content Type	Text
Resource Type	Article
Subject	Management Science and Operations Research Mathematics Software

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