# Metastability of Queuing Networks with Mobile Servers

## TL;DR

This paper investigates the metastability phenomena in symmetric queuing networks with mobile servers, revealing unexpected transient behaviors in large finite networks and multiple stationary solutions in the mean-field limit.

## Contribution

It introduces a novel analysis of metastability in queuing networks with moving servers, combining martingale techniques and mean-field limits to uncover transient dynamics.

## Key findings

- Large finite networks are transient for small inflow rates
- Mean-field limit has multiple stationary solutions
- Unexpected metastable behavior observed in the dynamics

## Abstract

We study symmetric queuing networks with moving servers and FIFO service discipline. The mean-field limit dynamics demonstrates unexpected behavior which we attribute to the meta-stability phenomenon. Large enough finite symmetric networks on regular graphs are proved to be transient for arbitrarily small inflow rates. However, the limiting non-linear Markov process possesses at least two stationary solutions. The proof of transience is based on martingale techniques.