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.
Bibliographical noteFunding 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
- Phase-type approximation
- Piecewise linear
ASJC Scopus subject areas
- Statistics and Probability
- Computer Science Applications
- Management Science and Operations Research
- Computational Theory and Mathematics