Large deviations behavior of counting processes and their inverses |
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Authors: | Peter W. Glynn Ward Whitt |
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Affiliation: | (1) Department of Operations Research, Stanford University, 94305-4022 Stanford, CA, USA;(2) AT&T Bell Laboratories, Room 2C-178, 07974-0636 Murray Hill, NJ, USA |
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Abstract: | We show, under regularity conditions, that a counting process satisfies a large deviations principle in or the Gärtner-Ellis condition (convergence of the normalized logarithmic moment generating functions) if and only if its inverse process does. We show, again under regularity conditions, that embedded regenerative structure is sufficient for the counting process or its inverse process to have exponential asymptotics, and thus satisfy the Gärtner-Ellis condition. These results help characterize the small-tail asymptotic behavior of steady-state distributions in queueing models, e.g., the waiting time, workload and queue length. |
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Keywords: | Large deviations Gä rtner-Ellis theorem counting processes point processes cumulant generating function waiting-time distribution small-tail asymptotics |
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