State-Dependent Phase-Type Queueing Networks for Urban Traffic Signal Control
- 1National Engineering Laboratory of Integrated Transportation Big Data Application Technology, National United Engineering Laboratory of Integrated and Intelligent Transportation, School of Transportation and Logistics, Southwest Jiaotong University, Chengdu 611756, China
Abstract
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.
Related
- Regret-Based Max-Pressure Traffic Signal Control under Uncertain Traffic States
- A Review of Max-Pressure Traffic Signal Control Algorithms: State of the Art and Research Opportunities
- MIXSim: A multiclass first order traffic model with composition-dependent dynamics for mixed-autonomy urban networks
- Interference Queueing Networks: A Replica Mean-Field Approach in the Symmetric Setting
- Transient Behavior of Threshold-Dependent Ruin and Queueing Models with Phase-Type Jumps
BibTeX
@article{tu2026statedependent,
title = {{State-Dependent Phase-Type Queueing Networks for Urban Traffic Signal Control}},
author = {Dan Tu and Rong Liang and Caiwen Luo and Yi Wang and Zhihong Yao and Yangsheng Jiang},
journal = {Mathematics},
year = {2026},
month = oct,
doi = {10.3390/math14203755},
url = {https://www.mdpi.com/2227-7390/14/20/3755},
note = {CC BY 4.0},
}
RIS
TY - JOUR
TI - State-Dependent Phase-Type Queueing Networks for Urban Traffic Signal Control
AU - Dan Tu
AU - Rong Liang
AU - Caiwen Luo
AU - Yi Wang
AU - Zhihong Yao
AU - Yangsheng Jiang
PY - 2026
DA - 2026/10/16
JO - Mathematics
DO - 10.3390/math14203755
UR - https://www.mdpi.com/2227-7390/14/20/3755
AB - 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.
SN - 2227-7390
ER -