# Stability of Fluid Queuing Systems with Parallel Servers and Stochastic Capacities

arXiv: https://arxiv.org/abs/1604.02008 · HTML: https://mlsanity.com/paper/1604.02008/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 Apr 2016.

## Built on by (most cited first, 2 of 2)

- [Interpretable Machine Learning Models for Modal Split Prediction in Transportation Systems](https://mlsanity.com/paper/2203.14191/) (2022)
- [Semi-Gradient SARSA Routing with Theoretical Guarantee on Traffic Stability and Weight Convergence](https://mlsanity.com/paper/2503.14927/) (2025)

## Abstract (arXiv)

This note introduces a piecewise-deterministic queueing (PDQ) model to study the stability of traffic queues in parallel-link transportation systems facing stochastic capacity fluctuations. The saturation rate (capacity) of the PDQ model switches between a finite set of modes according to a Markov chain, and link inflows are controlled by a state-feedback policy. A PDQ system is stable only if a lower bound on the time-average link inflows does not exceed the corresponding time-average saturation rate. Furthermore, a PDQ system is stable if the following two conditions hold: the nominal mode's saturation rate is high enough that all queues vanish in this mode, and a bilinear matrix inequality (BMI) involving an underestimate of the discharge rates of the PDQ in individual modes is feasible. The stability conditions can be strengthened for two-mode PDQs. These results can be used for design of routing policies that guarantee stability of traffic queues under stochastic capacity fluctuations.