Synchronized L\'evy queues

TL;DR

This paper analyzes a multivariate Le9vy process with one non-decreasing component and others with no negative jumps, deriving a product form for the steady-state buffer content distribution in a parallel queue system.

Contribution

It provides a novel explicit Laplace-Stieltjes transform for the steady-state buffer content vector in a multivariate Le9vy queue model, enabling interpretation as a sum of independent vectors.

Findings

Derived the Laplace-Stieltjes transform of the buffer content vector.

Expressed the transform as a product of joint transforms.

Interpreted the buffer content as a sum of independent random vectors.

Abstract

We consider a multivariate L\'evy process where the first coordinate is a L\'evy process with no negative jumps which is not a subordinator and the others are nondecreasing. We determine the Laplace-Stieltjes transform of the steady-state buffer content vector of an associated system of parallel queues. The special structure of this transform allows us to rewrite it as a product of joint Laplace-Stieltjes transforms. We are thus able to interpret the buffer content vector as a sum of independent random vectors.