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  • Sample-path analysis  (2)
  • global balance  (1)
  • 1
    Electronic Resource
    Electronic Resource
    Pathwise rate- stability for input-output processes (1996)
    Springer
    Queueing systems 22 (1996), S. 47-63 
    Details
    ISSN: 1572-9443
    Keywords: Sample-path analysis ; stability ; rate stability ; ω-rate stability ; input-output process ; queueing ; infinite-server queues
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Notes: Abstract An input-output processZ = {Z(t), t ⩾ 0} is said to beω-rate stable ifZ(t) = o(ω(t)) for some non-negative functionω(t). We prove that the processZ is ω-rate stable under weak conditions that include the assumption that input satisfies a linear burstiness condition and Z is asymptotically average stable. In many cases of interest, the conditions forω-rate-stability can be verified from input data. For example, using input information, we establishω-rate stability of the workload for multiserver queues, an ATM multiplexer, andω-rate stability of queue-length processes for infinite server queues.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01159392
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Sample-path analysis of processes with imbedded point processes (1989)
    Springer
    Queueing systems 5 (1989), S. 131-165 
    Details
    ISSN: 1572-9443
    Keywords: Sample-path analysis ; queues ; point processes ; time averages ; customer averages ; rate conservation ; global balance ; insensitivity ; LCFS-PR discipline
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Notes: 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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01149190
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    Paper (German National Licenses)
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