Local stability in a transient Markov chain

TL;DR

This paper establishes conditions under which transient Markov chains exhibit local stability, with applications to overloaded queueing systems and networks, providing theoretical insights into their behavior.

Contribution

It introduces new propositions that identify conditions for local stability in systems modeled by transient Markov chains, extending understanding of such systems.

Findings

Proves conditions for local stability in transient Markov chains

Applies results to overloaded queueing networks and systems

Provides theoretical framework for analyzing stability in complex systems

Abstract

We prove two propositions with conditions that a system, which is described by a transient Markov chain, will display local stability. Examples of such systems include partly overloaded Jackson networks, partly overloaded polling systems, and overloaded multi-server queues with skill based service, under first come first served policy.