In this paper, we focus on a roadside directional sensor network where sensors with directional Field Of Views (FOVs) are placed along a roadway. We study the problem of wakeup scheduling, with the objective of maximizing network lifetime under the constraint that full coverage and network connectivity are maintained at all times. First, we present centralized polynomial time algorithms to optimally solve the problems of scheduling sensor nodes with fixed sensing orientations. Moreover, an effective heuristic algorithm is proposed to solve the problem of scheduling sensor nodes with variable sensing orientations. In addition, we also present distributed algorithms for both fixed and variable cases. Simulation results based on a roadway in the Yellowstone National Park have been presented to show the performance of the proposed algorithms.