Large deviations for the overflow level of G/G/1 queues in series
by Karol Rosen
International Journal of Mathematics in Operational Research (IJMOR), Vol. 14, No. 2, 2019

Abstract: We present a result characterising the large deviations behaviour of the total overflow level in a cycle starting with zero customers for a system of G/G/1 queues in series. We also present large deviations results for the total overflow level as seen by a random customer and in stationarity. We prove that the large deviations behaviour of the total overflow level for all three distributions, in a cycle, as seen by a random customer and in stationarity, have the same decay rate. We find the most likely path to have overflow in the system. Based on those results we propose a state-independent importance sampling algorithm. We also give conditions under which that algorithm is asymptotically efficient. By means of numerical simulation, we provide evidence of the advantages of this algorithm.

Online publication date: Thu, 07-Feb-2019

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