Ergodic theorems for queuing systems with dependent inter-arrival times |
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Institution: | 1. Alfréd Rényi Institute of Mathematics, Reáltanoda utca 13-15, 1053 Budapest, Hungary;2. Budapest University of Technology and Economics, Egry József utca 1, 1111 Budapest, Hungary |
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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 Gärtner-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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Keywords: | Queuing G/GI/1 queue Dependent random variables Inter-arrival times Limit theorem Law of large numbers |
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