Hitting and ruin probabilities for compound Poisson processes and the cycle maximum of the M/G/1 queue

D. Perry; W. Stadje; S. Zacks

doi:10.1081/STM-120016444

Hitting and ruin probabilities for compound Poisson processes and the cycle maximum of the M/G/1 queue

D. Perry, W. Stadje, S. Zacks

Department of Statistics

Research output: Contribution to journal › Article › peer-review

Abstract

We derive a new formula for the probability that a compound Poisson process with positive jumps hits a lower straight line before it crosses a parallel upper line. This yields a new approach to determine the distribution of the cycle maximum of the M/G/1 queue. Moreover, we express the hitting probabilities in terms of the corresponding ruin probabilities.

Original language	English
Pages (from-to)	553-564
Number of pages	12
Journal	Stochastic Models
Volume	18
Issue number	4
DOIs	https://doi.org/10.1081/STM-120016444
State	Published - 2002

Keywords

Compound Poisson process
Cycle maximum
Hitting probability
Ruin
Single-server queue
Two-sided first-exit time
Workload

ASJC Scopus subject areas

Statistics and Probability
Modeling and Simulation
Applied Mathematics

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10.1081/STM-120016444

Cite this

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abstract = "We derive a new formula for the probability that a compound Poisson process with positive jumps hits a lower straight line before it crosses a parallel upper line. This yields a new approach to determine the distribution of the cycle maximum of the M/G/1 queue. Moreover, we express the hitting probabilities in terms of the corresponding ruin probabilities.",

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AU - Perry, D.

AU - Stadje, W.

AU - Zacks, S.

PY - 2002

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N2 - We derive a new formula for the probability that a compound Poisson process with positive jumps hits a lower straight line before it crosses a parallel upper line. This yields a new approach to determine the distribution of the cycle maximum of the M/G/1 queue. Moreover, we express the hitting probabilities in terms of the corresponding ruin probabilities.

AB - We derive a new formula for the probability that a compound Poisson process with positive jumps hits a lower straight line before it crosses a parallel upper line. This yields a new approach to determine the distribution of the cycle maximum of the M/G/1 queue. Moreover, we express the hitting probabilities in terms of the corresponding ruin probabilities.

KW - Compound Poisson process

KW - Cycle maximum

KW - Hitting probability

KW - Ruin

KW - Single-server queue

KW - Two-sided first-exit time

KW - Workload

UR - https://www.scopus.com/pages/publications/0036969178

U2 - 10.1081/STM-120016444

DO - 10.1081/STM-120016444

M3 - Article

AN - SCOPUS:0036969178

SN - 1532-6349

VL - 18

SP - 553

EP - 564

JO - Stochastic Models

JF - Stochastic Models

IS - 4

ER -

Hitting and ruin probabilities for compound Poisson processes and the cycle maximum of the M/G/1 queue

Abstract

Keywords

ASJC Scopus subject areas

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