Factorization identities for reflected processes, with applications

TL;DR

This paper develops factorization identities for a broad class of reflected stochastic processes, including queueing systems and Levy processes, providing new insights and tools for analyzing their behavior.

Contribution

It introduces general factorization identities for reflected processes, encompassing queueing systems, Levy, and diffusion processes, extending classical results like Wiener-Hopf.

Findings

Derived new factorization identities for preemptive-resume queues with catastrophes.

Unified framework connecting queueing models with Levy and diffusion processes.

Simplified known identities such as Wiener-Hopf within this broader context.

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 Levy processes, diffusion processes, and certain types of growth-collapse processes; thus, all of the processes mentioned above also satisfy similar factorization identities. In the Levy case, our identities simplify to both the well-known Wiener-Hopf factorization, and another interesting factorization of reflected Levy 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.