Title: Large deviations for the overflow level of G/G/1 queues in series

Authors: Karol Rosen

Addresses: Arbolillo 120, Tlalpan 14390, Mexico City, Mexico

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.

Keywords: large deviations; G/G/1 queues in series; rare event simulation; importance sampling; exponential twist; palm distribution; overflow level; asymptotic efficiency; stationary distribution; cycle.

DOI: 10.1504/IJMOR.2019.097755

International Journal of Mathematics in Operational Research, 2019 Vol.14 No.2, pp.189 - 220

Received: 12 Nov 2016
Accepted: 29 Aug 2017
Published online: 07 Feb 2019 *

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