Stability, which indicates that queues do not grow infinitely over time, is a key concept in control policies such as BackPressure (BP). However, its abstract nature and diverse definitions make its comparative analysis difficult both theoretically and experimentally. As a result, simulations in existing studies often use alternative metrics, such as average delay, to evaluate the performance of different control policies. Little research directly compares different stabilities through theory or experiments. In this paper, we compare seven common stability definitions and theoretically demonstrates that they are equivalent in simulations and applications. Furthermore, we propose a t-test method for identifying whether a queue is stable based on the sequence of queueing differences. This method allows us to classify any sampled demand as stable or unstable based on simulated queues for a given control policy. Therefore, if the network’s dimension, i.e., the number of movements, does not exceed three, we can directly draw the stability region (SR) for all policies and compare their sizes. To accurately reproduce various BP theories, ensure fair comparisons, and facilitate the visualization of SRs, we use simulation codes to simulate a two-movement intersection scenario and discuss its extension to networks. Six distinct types of BP policies are compared, along with analysis for fixed-time and actuated controls. We obtain many insights that are difficult to achieve through purely theoretical analysis and delay-based simulations, including: 1) variability in BP’s SR: the SR typically varies when the BP changes its queue status weight or efficiency weight; 2) size hierarchy of SR: BPs generally outperform actuated controls in terms of SR, and actuated controls tend to outperform fixed-time controls; 3) non-cyclic vs. cyclic BP: non-cyclic BP usually has a larger SR than cyclic BP; 4) effect of real-time supply information: using real-time supply increases the SR of BP, even under the assumption of fixed saturation headway; and 5) SR degradation phenomenon: longer cycle lengths in cyclic BP may cause its SR to degenerate into a rectangular shape typical of fixed-time control.
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