Contributions to the theory of first-exit times of some compound processes in queueing theory

D. Perry; W. Stadje; S. Zacks

doi:10.1023/A:1019140616021

Contributions to the theory of first-exit times of some compound processes in queueing theory

D. Perry, W. Stadje, S. Zacks

Department of Statistics

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

Abstract

We consider compound processes that are linear with constant slope between i.i.d. jumps at time points forming a renewal process. These processes are basic in queueing, dam and risk theory. For positive and for negative slope we derive the distribution of the first crossing time of a prespecified level. The related problem of busy periods of single-server queueing systems is also studied.

Original language	English
Pages (from-to)	369-379
Number of pages	11
Journal	Queueing Systems
Volume	33
Issue number	4
DOIs	https://doi.org/10.1023/A:1019140616021
State	Published - Jan 2000

Bibliographical note

Funding Information:
This research was carried out while the first author (D. Perry) was a visiting professor at the University of Osnabrück. The support by the Deutsche Forschungs-gemeinschaft is gratefully acknowledged.

Keywords

Busy period
Compound process
Excess over the boundary
First-exit time
G/M/1.M/G/1
Phase-type approximation
Piecewise linear

ASJC Scopus subject areas

Statistics and Probability
Computer Science Applications
Management Science and Operations Research
Computational Theory and Mathematics

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abstract = "We consider compound processes that are linear with constant slope between i.i.d. jumps at time points forming a renewal process. These processes are basic in queueing, dam and risk theory. For positive and for negative slope we derive the distribution of the first crossing time of a prespecified level. The related problem of busy periods of single-server queueing systems is also studied.",

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AU - Stadje, W.

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AB - We consider compound processes that are linear with constant slope between i.i.d. jumps at time points forming a renewal process. These processes are basic in queueing, dam and risk theory. For positive and for negative slope we derive the distribution of the first crossing time of a prespecified level. The related problem of busy periods of single-server queueing systems is also studied.

KW - Busy period

KW - Compound process

KW - Excess over the boundary

KW - First-exit time

KW - G/M/1.M/G/1

KW - Phase-type approximation

KW - Piecewise linear

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ER -

Contributions to the theory of first-exit times of some compound processes in queueing theory

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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