A necessary and sufficient condition for stability of queuing networks with state-dependent departure rates

Speaker : Pierre Popineau
Date: 26/04/2023
Time: 3:00 pm - 4:00 pm
Location: Room 4B01


Reaching stability conditions for Markovian queueing networks is a problem for which many methods have been developed, depending on the queueing policies, laws for arrivals and departure of users in the system, but obtaining instability or transience is a problem known to be harder.
In this talk, we will focus on a type of queuing networks where the departure rate in a given queue is a decreasing function of the other queue lengths, and increasing in its queue length. This type of queuing networks can be encountered in wireless communication systems, where the departure rate depends on the interference in the system.
We first obtain a stability condition for the system using fluid limits, and prove instability using stochastic domination arguments. This stability condition is interesting as it allows us to study systems for which the fluid models are not defined near 0.

The talk is based on the results of these papers :
– S. Shneer and A. Stolyar, Stability conditions for a decentralised medium access algorithm: single- and multi-hop networks, Queuing Systems, vol. 94, pp. 109–128, 2020, https://link.springer.com/article/10.1007/s11134-019-09635-w
– P. Popineau and S. Shneer, An instability condition for queuing systems with state-dependent departure rates, 2023, https://arxiv.org/abs/2304.08853