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 |
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Pages (from-to) | 553-564 |
Number of pages | 12 |
Journal | Stochastic Models |
Volume | 18 |
Issue number | 4 |
DOIs | |
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