Queueing systems with pre-scheduled random arrivals

Details Queueing systems with pre-scheduled random arrivals Queueing systems with pre-scheduled random arrivals

2008-05-29

arxiv.org/abs/0805.4472v4

Mathematics

Probability

21 pages, 5 figures, new section on correlated arrivals, version 4

Scientific paper

We consider a point process $i+\xi_i$, where $i\in \bZ$ and the $\xi_{i}$'s are i.i.d. random variables with variance $\sigma^{2}$. This process, with a suitable rescaling of the distribution of $\xi_i$'s, converges to the Poisson process in total variation for large $\sigma$. We then study a simple queueing system with our process as arrival process, and we provide a complete analytical description of the system. Although the arrival process is very similar to the Poisson process, due to negative autocorrelation the resulting queue is very different from the Poisson case. We found interesting connections of this model with the statistical mechanics of Fermi particles. This model is motivated by air traffic systems.

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