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

D. Perry, W. Stadje, S. Zacks

Research output: Contribution to journalArticlepeer-review


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 languageEnglish
Pages (from-to)369-379
Number of pages11
JournalQueueing Systems
Issue number4
StatePublished - 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.


  • 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


Dive into the research topics of 'Contributions to the theory of first-exit times of some compound processes in queueing theory'. Together they form a unique fingerprint.

Cite this