arXiv:2610.32280v1 Announce Type: new Abstract: Max-pressure (MP) control adapts signal phases to prevailing traffic states, but its decision timescale is typically fixed a priori. This paper treats the decision timescale as an explicit dimension of MP control. We first characterize the trade-off between responsiveness and switching efficiency by quantifying how an equivalent switching loss reduces service capacity over a finite decision interval. This yields a load-dependent critical timescale determined by switching loss and normalized traffic load, together with a performance-oriented operating range above the stability boundary. Building on this result, we propose Variable-Timescale Max-Pressure (VT-MP), in which each intersection selects its decision interval according to local operating conditions, allowing the control timescale to vary across time and space. We establish strong stability of the resulting asynchronous heterogeneous controller under uniformly admissible local loads and bounded decision intervals, and introduce a downstream receiving-supply correction for finite-storage implementation. Three experiments provide mechanism validation and network-level evaluation. A single-intersection experiment confirms that the preferred decision interval increases systematically with traffic load and follows the derived characteristic timescales. In a store-and-forward network, heterogeneous VT-MP reduces total queueing time by 31.0% relative to the best fixed-interval benchmark. In a microscopic 5x5 SUMO network, it reduces mean trip delay by 24.3%, from 213.3 s to 161.5 s, and peak network accumulation by 12.3%. These findings show that the MP decision timescale should be treated as a traffic-state-dependent control variable rather than a fixed implementation parameter.