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

Karol Rosen

International Journal of Mathematics in Operational Research, 2019, vol. 14, issue 2, 189-220

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. (search for similar items in EconPapers)
Date: 2019
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