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arXiv · 2004.01475

Ergodic theorems for queuing systems with dependent inter-arrival times

Attila Lovas·Miklós Rásonyi
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Abstract

We study a G/GI/1 single-server queuing model with i.i.d.\ service times that are independent of a stationary process of inter-arrival times. We show that the distribution of the waiting time converges to a stationary law as time tends to infinity provided that inter-arrival times satisfy a G\"artner-Ellis type condition. A convergence rate is given and a law of large numbers established. These results provide tools for the statistical analysis of such systems, transcending the standard case with independent inter-arrival times.

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Attila Lovas, Miklós Rásonyi. 2020-04-03. Ergodic theorems for queuing systems with dependent inter-arrival times. https://arxiv.org/abs/2004.01475

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