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

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  • S. Zacks

    (Binghamton University)

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.

Suggested Citation

  • S. Zacks, 2007. "Review of Some Functionals of Compound Poisson Processes and Related Stopping Times," Methodology and Computing in Applied Probability, Springer, vol. 9(2), pages 343-356, June.
    • Handle: RePEc:spr:metcap:v:9:y:2007:i:2:d:10.1007_s11009-006-9015-1
    DOI: 10.1007/s11009-006-9015-1
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    References listed on IDEAS

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    1. N. Mukhopadhyay & T. Solanky, 1997. "Estimation after sequential selection and ranking," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 45(1), pages 95-106, January.
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    Cited by:

    1. Shuanming Li & Yi Lu & Can Jin, 2016. "Number of Jumps in Two-Sided First-Exit Problems for a Compound Poisson Process," Methodology and Computing in Applied Probability, Springer, vol. 18(3), pages 747-764, September.

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