A controlled M / G / 1 workload process with an application to perishable inventory systems

D. Perry, W. Stadje

Research output: Contribution to journalArticlepeer-review

Abstract

We derive the stationary distribution of the regenerative process W(t), t ≥ 0, whose cycles behave like an M / G / 1 workload process terminating at the end of its first busy period or when it reaches or exceeds level 1, and restarting with some fixed workload a ε (0,1). The result is used to obtain the overflow distribution of this controlled workload process; we derive double struck E sign-αW(T) and double struck E sign[e αW(T) | W(T) ≥ 1], where T is the duration of the first cycle. W(t) can be linked to a certain perishable inventory model, and we use our results to determine the distribution of the duration of an empty period.

Original languageEnglish
Pages (from-to)415-428
Number of pages14
JournalMathematical Methods of Operations Research
Volume64
Issue number3
DOIs
StatePublished - Dec 2006

Keywords

  • Controlled workload process
  • M / G / 1
  • Overflow
  • Perishable inventory system
  • Stationary distribution

ASJC Scopus subject areas

  • Software
  • Mathematics (all)
  • Management Science and Operations Research

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