Queueing systems with pre-scheduled random arrivals

2008/05/29 by Gianluca Guadagni, Guadagni, G., Sokol Ndreca +3
Business, Management and Accounting · Economics, Econometrics and Finance · Engineering · #Advanced Queuing Theory Analysis #Air Traffic Management and Optimization #Aviation Industry Analysis and Trends #FOS: Mathematics #Probability (math.PR)

paper · pdf · doi:10.48550/arxiv.0805.4472

openalex publication_date 2008/05/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider a point process i+ξ_i, where i∈ \bZ and the ξ_i's are i.i.d. random variables with variance σ². This process, with a suitable rescaling of the distribution of ξ_i's, converges to the Poisson process in total variation for large σ. 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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