Factorization identities for reflected processes, with applications

Research output: Contribution to journalArticleAcademicpeer-review

2 Citations (Scopus)

Abstract

We derive factorization identities for a class of preemptive-resume queueing systems, with batch arrivals and catastrophes that, whenever they occur, eliminate multiple customers present in the system. These processes are quite general, as they can be used to approximate Lévy processes, diffusion processes, and certain types of growth¿collapse processes; thus, all of the processes mentioned above also satisfy similar factorization identities. In the Lévy case, our identities simplify to both the well-known Wiener¿Hopf factorization, and another interesting factorization of reflected Lévy processes starting at an arbitrary initial state. We also show how the ideas can be used to derive transforms for some well-known state-dependent/inhomogeneous birth¿death processes and diffusion processes. Keywords: Lévy process; Palm distribution; random walk; time-dependent behavior; Wiener¿Hopf factorization
Original languageEnglish
Pages (from-to)632-653
Number of pages22
JournalJournal of Applied Probability
Volume50
Issue number3
DOIs
Publication statusPublished - 2013

Fingerprint

Dive into the research topics of 'Factorization identities for reflected processes, with applications'. Together they form a unique fingerprint.

Cite this