A time-slot based signal scheme model for fixed-time control at isolated intersections

Fixed-time signal control is widely used in the real world due to its low cost of implementation. Repeated signal cycles with the same phase structure are applied in the existing fixed-time signal control schemes. However, such signal schemes do not always achieve the best performance, especially when traffic demand is unbalanced. The inclusion of sub-cycles in one cycle provides a potential solution in this situation. This study proposes a time-slot based signal scheme model with a generalized cycle structure for fixed-time signal control at isolated intersections. The proposed signal scheme can generate sub-cycles with different phase structures. It optimizes the number of sub-cycles in one cycle as well as the phase sequence, cycle length, and green splits in each sub-cycle. Certain phases may be skipped in partial sub-cycles. Nonlinear programming models are formulated to minimize average vehicle delay and maximize intersection capacity for under- and over-saturated demand. Solution algorithms for the two nonlinear models are developed by solving a series of mixed-integer-quadratic-programming (MIQP) models and mixed-integer-linear-programming (MILP) models, respectively. The numerical studies validate the advantages of proposed signal scheme in terms of intersection capacity and average vehicle delay. The sensitivity analyses show that: 1) a long maximum green time can enable the conventional dual-ring, eight-phase structure to handle unbalanced demand from the perspective of intersection capacity; 2) the time-slot number of 6 or 7 is suggested considering both the solution optimality and the model complexity.