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Review of Some Functionals of Compound Poisson Processes and Related Stopping Times

  • S. ZacksEmail author
Article

Abstract

The paper reviews recent results of D. Perry, W. Stadje and S. Zacks, on functionals of stopping times and the associated compound Poisson process with lower and upper linear boundaries. In particular, formulae of these functionals are explicitly developed for the total expected discounted cost of discarded service in an M/G/1 queue with restricted accessibility; for the expected total discounted waiting cost in an M/G/1 restricted queue; for the shortage, holding and clearing costs in an inventory system with continuous input; for the risk in sequential estimation and for the transform of the busy period when the upper boundary is random.

Keywords

Compound Poisson process M/G/1 queue with restricted accessibility Expected cost functionals Stopping times Production/Inventory systems Sequential estimation Random boundaries 

AMS 2000 Subject Classification

60G17 60G40 60K25 60J75 90B05 

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Copyright information

© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  1. 1.Department of Mathematical SciencesBinghamton UniversityBinghamtonUSA

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