This research contributes to the improvement of the optimal headway solution for the transit performance functions (e. g., minimize total cost; maximize social welfare) derived from the traffic model proposed by Hendrickson. The purpose of this paper is threefold. First, we prove that that model has a unique solution for headway. Second, we offer a formulated approximation for headway. Third, numerical examples illustrate that our formulated approximation performs more accurately than the Hendrickson’s.