Asymptotics of joint orderings of compound Poisson fields

TL;DR

This paper introduces a new analytical method for queuing systems with complex, heterogeneous compound Poisson inputs, using limit theorems for partial sums of marks ordered by field points.

Contribution

It develops a novel approach embedding the input flow in higher-dimensional space and proves limit theorems for ordered partial sums of marks.

Findings

Established limit theorems for partial sums of marks

Embedded heterogeneous inputs in higher-dimensional homogeneous fields

Provided a new framework for analyzing complex queuing systems

Abstract

We are developing a new method for the analysis of queuing systems with heterogeneous in time and space compound (marked) Poisson input flow. The state space of the input flow is embedded in a higher-dimensional space with a homogeneous marked Poisson field on it. We prove limit theorems for partial sums of marks under the ordering of field points by coordinates.