A 2$\times$2 random switching model and its dual risk model

TL;DR

This paper analyzes a specialized M/G/2-queue with a random switch, examining workload exceedance and ruin probabilities, especially considering heavy-tailed and light-tailed job distributions, using a dual risk model approach.

Contribution

It introduces a dual risk model for a 2x2 random switching queue and derives asymptotic behavior of workload and ruin probabilities considering heavy and light tails.

Findings

Asymptotic exceedance probabilities for workload buffers are characterized.

Ruin probabilities are determined for different tail distributions.

The dual risk model effectively captures the queue's asymptotic behavior.

Abstract

In this article a special case of an M/G/2-queue is considered, where the two servers are exposed to two types of jobs that are distributed among the servers via a random switch. In this model the asymptotic behaviour of the workload buffer exceedance probabilities for the two single servers/ both servers together/ one (unspecified) server is determined. Hereby one has to distinguish between jobs that are either heavy-tailed or light-tailed. The results are derived via the dual risk model of the studied M/G/2-queue for which the asymptotic behaviour of different ruin probabilities is determined.