Large Deviations Behavior of Counting Processes and Their Inverses
Abstract
We show, under regularity conditions, that a counting process satisfies a large deviations principle in R, a sample-path large deviations principle in the function space D, or the Gartner-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 Gartner-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. Large deviations, Gartner-Ellis theorem, Counting processes, Point processes, Cumulant generating function, Waiting-time distribution, Small- tail asymptotics.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jul 01, 1993
- Accession Number
- ADA271142
Entities
People
- Peter W. Glynn
- Ward Whitt
Organizations
- Stanford University