Factorization Identities for Reflected Processes, with Applications. (30th January 2018)

• Record Type: Journal Article
• Authors: Fralix, Brian H.; van Leeuwaarden, Johan S. H.; Boxma, Onno J.
• Is Part Of: Journal of applied probability. Volume 50:Number 3(2013)
• Page Start: 632
• Page End: 653
• Publication Date: 2018-01-30
• Subjects: Lévy process, -- Palm distribution, -- random walk, -- time-dependent behavior, -- Wiener‒Hopf factorization; 60G50, -- 60G51, -- 60G55, -- 60K25; 519.2
• DOI: 10.1239/jap/1378401227
• Languages: English
• ISSNs: 0021-9002

Abstract

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.