This work presents timed automata as a natural tool for solving Chinese postman problems on time varying network. This study shows that the optimal Chinese tour can be equivalently casted as the shortest run in this automaton system, which can be obtained efficiently by solving a series of decision problems for reachability. A composition strategy is then proposed to adapt to the current model, such that the number of timed automaton is reduced from O(|A|+|A_R|+1) to O(1). Computational results show that the improved model can solve small-sized instances optimally, and that it can obtain a better gap between the lower bound and upper bound than the ones obtained by the cutting plane and column generation algorithms.