Analytical derivation of the optimal traffic signal timing: Minimizing delay variability and spillback probability for undersaturated intersections

•Deriving analytical formulas based on the shockwave theory for calculation of delay and queue length as a function of the time of joining the queue at the intersection.•Deriving analytical formulation of the delay variability at intersections.•Deriving the optimal signal timing for both dynamic and prefixed cycle length strategies and imposing the spillback avoidance constraint to minimize the delay variability.•Proposing several efficient algorithms to obtain the analytical global optimal solution to minimize the delay variability.