21
views
0
recommends
+1 Recommend
0 collections
    0
    shares
      • Record: found
      • Abstract: found
      • Article: found
      Is Open Access

      Moments of polynomial functionals in Levy-driven queues with secondary jumps

      Preprint
      , ,

      Read this article at

          There is no author summary for this article yet. Authors can add summaries to their articles on ScienceOpen to make them more accessible to a non-specialist audience.

          Abstract

          A long-standing open problem concerns the calculation of the moments of the area beneath the M/G/1 workload graph during a busy period. While expressions for the first two moments were known, no results for higher moments were available. In this paper we develop a recursive algorithm by which all moments can be expressed in terms of the model primitives. Our results extend to any storage system fed by a superposition of a drifted Brownian motion and a subordinator (nondecreasing Levy process) with a secondary jump input, yielding the moments (including joint ones) of a general class of polynomial functionals of the workload process. For the special case of the M/G/1 queue we identify the joint transform of the area and the duration of the busy period.

          Related collections

          Author and article information

          Journal
          17 October 2023
          Article
          2310.11137
          b31cec63-0e38-4c1a-a8c3-03f38e9bdb54

          http://creativecommons.org/licenses/by/4.0/

          History
          Custom metadata
          60G51, 60K25
          math.PR

          Probability
          Probability

          Comments

          Comment on this article

          Related Documents Log