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 language | English |
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Pages (from-to) | 415-428 |
Number of pages | 14 |
Journal | Mathematical Methods of Operations Research |
Volume | 64 |
Issue number | 3 |
DOIs | |
State | Published - 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