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 | |
| 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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