Ross's second conjecture and supermodular stochastic ordering

TL;DR

This paper explores open problems and partial solutions concerning Ross's second conjecture about the behavior of single server queues with randomly varying arrival rates, aiming to advance understanding in stochastic queue modeling.

Contribution

It provides new insights and partial solutions to Ross's second conjecture, addressing the stochastic ordering in queues with time-varying arrival rates.

Findings

Identifies key open problems in the conjecture.

Proposes partial solutions and approaches to the conjecture.

Highlights the complexity of stochastic ordering in variable-rate queues.

Abstract

This short note discusses open problems and partial solutions related to Sheldon M Ross's second conjecture about the classical single server queue subject to a randomly time-varying rate arrival rate.