State-Dependent Phase-Type Queueing Networks for Urban Traffic Signal Control

Fine-grained adaptive signal control requires a performance evaluator that is causally faithful and fast enough for phase-level rolling decisions. Simulation-in-the-loop optimization pays for fidelity with replication cost, while fast analytical evaluators based on store-and-forward or exponential queueing assumptions discard the stochastic structure of inter-arrival and service times or the coupling between intersections. We develop a finite-capacity queueing network evaluator in which each signalized link is a PH/PH/1/K queue with a state-dependent service rate, arrival and service-time variability is inherited from rolling-window moment fitting, and link interactions are resolved by a fixed-point decomposition in which finite-capacity blocking caps delivered throughput; the node solve is proved exact, with complete proofs of convergence, sensitivity, and cost bounds. Discrete-event checks confirm the node solution across variability regimes from near-deterministic to strongly bursty, where matched-mean exponential approximations deviate by up to 33%, network mean queues over 24 links are predicted within 12.7 vehicles, and a network evaluation completes in about 0.26 s. Embedded as the fitness kernel of a warm-started rolling hybrid metaheuristic, the evaluator reduces network vehicle-hours by 13.9% relative to uniform fixed timing and 12.4% versus a cycle-based max-pressure baseline on a nine-intersection network, making phase-level rolling optimization computationally feasible with an explicit causal chain from settings to performance.