Bandwidth Maximization Using Vehicle Arrival Functions

We revisit the offset optimization problem for maximization of two-way progression bands. A new formulation is proposed relying on the concepts of relative offset and vehicle arrival functions. Vehicle arrival functions represent the probability that a vehicle reaches a given intersection at a given time. Relative offsets are the displacement of the arrival functions with respect to a moving coordinate frame. An explicit formula for the bandwidth is derived based on these two quantities. The bandwidth maximization problem is then formulated as an unconstrained nonlinear program. The cases of pulse and Gaussian arrivals are considered in detail. Numerical techniques are proposed for both that return globally optimal solutions with small computational cost.