Ergodic theorems for queuing systems with dependent inter-arrival times

2020/04/03 by Lovas, Attila, Rásonyi, Miklós · 1 citation
#FOS: Mathematics #Optimization and Control (math.OC) #Probability (math.PR)

paper · doi:10.48550/arxiv.2004.01475

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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