Group-based hierarchical adaptive traffic-signal control part I: Formulation

- A multi-resolution strategy is developed to simultaneously determine the global parameters (such as the cycle length and the cycle-structure) at a coarse-resolution level, and to allow for local adjustments in factors such as the stage-switching times in response to real-time-traffic information at the fine-resolution level.
- The mathematical framework of the proactive global optimization scheme involves the procedures for maximizing the reserve capacity and minimizing the control delay to identify the most appropriate cycle-structure for minimizing the control delay on cycle-by-cycle for the given predicted traffic conditions.
- The cycle-structure of green phases, established on the global optimization scheme, are reactively adjusted with respect to transient fluctuations in the traffic flows in a second by the local reactive control scheme based on the max-pressure control policy.

A group-based adaptive traffic-control method for isolated signalized junctions is developed that includes a hierarchical structure comprising tactical and local levels of signal timing optimization. The control method optimizes the signal timings in adaptive traffic-control systems, and takes full advantage of flexible new technologies to incorporate the most up-to-date traffic information, as collected in real time. The definitions, combinations, and sequencing of the cycle structure stages are generated automatically using a procedure for optimizing the signal-timing plans in response to online data from traffic detectors. This new method provides a wider search space and improves the efficiency of the signal-control systems, thus improving the junction performance, minimizing delays, and maximizing capacity in real time. A multi-resolution strategy is proposed for updating the elements of the signal plans cycle-by-cycle and adjusting the current green signal timing second-by-second. The group-based variables and parameters for the proactive global-optimization method utilize lane-based predictive traffic-flow information, such as arrival and discharge rates, expressed as the slopes of polygonal delay formulas. Therefore, there is a high degree of flexibility in the tactical identification of the optimal signal plan in response to the real-time predicted traffic information, the objective function of the polygonal delay formula, and the direct differential equations for the adaptive group-based variables. The reactive local signal-control policy, which is formed based on the max-pressure strategy, is developed to locally adjust the current green signal time and to accommodate delicate demand fluctuations second-by-second at the fine-resolution level. The most appropriate cycle-structure for the tactical level of control is identified using a group-based global-optimization procedure that takes advantage of the latest available information. In part II of this study (Lee et al. 2017), the effectiveness of the proposed methods is validated based on the actualized mathematical frameworks, computer simulations, and a case study, using the appropriate computer programs.