Abstract
The purpose of this paper is to review, unify, and extend previous work on sample-path analysis of queues. Our main interest is in the asymptotic behavior of a discrete-state, continuous-time process with an imbedded point process. We present a sample-path analogue of the renewal-reward theorem, which we callY=λX. We then applyY=λX to derive several relations involving the transition rates and the asymptotic (long-run) state frequencies at an arbitrary point in time and at the points of the imbedded point process. Included are sample-path versions of the rate-conservation principle, the global-balance conditions, and the insensitivity of the asymptotic frequency distribution to the distribution of processing time in a LCFS-PR service facility. We also provide a natural sample-path characterization of the PASTA property.
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