Two coupled Levy queues with independent input

TL;DR

This paper derives the joint workload distribution for two coupled Levy queues with independent inputs, extending classical models using Wiener-Hopf factorization and providing explicit transform formulas.

Contribution

It introduces a general framework for coupled Levy queues, deriving explicit joint workload transforms and extending classical queue analysis methods.

Findings

Explicit joint workload transform derived

Framework includes coupled processor and fluid network models

Extends classical queue theory with Levy process inputs

Abstract

We consider a pair of coupled queues driven by independent spectrally-positive Levy processes. With respect to the bi-variate workload process this framework includes both the coupled processor model and the two-server fluid network with independent Levy inputs. We identify the joint transform of the stationary workload distribution in terms of Wiener-Hopf factors corresponding to two auxiliary Levy processes with explicit Laplace exponents. We reinterpret and extend the ideas of Cohen and Boxma (1983) to provide a general and uniform result with a neat transform expression.