UPPER FIRST-EXIT TIMES OF COMPOUND POISSON PROCESSES REVISITED

Authors:
W. Stadje;S. Zacks
Affiliations:
Fachbereich Mathematik/Informatik, University of Osnabrück, 49069 Osnabrück, Germany, E-mail: wolfgang@mathematik.uni-osnabrueck.de;Department of Mathematical Sciences, Binghamton University, Binghamton, New York 13902-6000, E-mail: shelly@math.binghamton.edu
Venue:
Probability in the Engineering and Informational Sciences
Year:
2003

Citing 2
Cited 1

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

Queueing Systems: Theory and Applications
Busy period analysis for M/G/1 and G/M/1 type queues with restricted accessibility

Operations Research Letters

On The Upper First-Exit Times Of Compound G/M Processes

Probability in the Engineering and Informational Sciences

Quantified Score

Hi-index	0.00

Visualization

Abstract

For a compound Poisson process (CPP) with only positive jumps, an elegant formula connects the density of the hitting time for a lower straight line with that of the process itself at time t, h(x; t), considered as a function of time and position jointly. We prove an analogous (albeit more complicated) result for the first time the CPP crosses an upper straight line. We also consider the conditional density of the CPP at time t, given that the upper line has not been reached before t. Finally, it is shown how to compute certain moment integrals of h.