Even though the optical burst switching scheme is simple and cuts through data bursts without opto-electro-optic (O/E/O) conversion in core nodes, burst loss due to contention and the fairness problem in the mesh network have become intrinsically serious problems. To solve these problems, we proposed a new burst generation and fairness guaranteeing scheme in edge/core node combined mesh networks in previous researches. We showed that fairness was guaranteed among the same priority by grouping bursts according to offset times and using separate wavelength groups for each priority burst. In this paper, we propose a new scheme to improve the performance of the optical burst switching system by assigning higher priority to long traveled bursts over bursts just generated by previous nodes. We use a mathematical method to compare the proposed and conventional schemes. Our analysis results show that the proposed scheme has less blocking probability than the conventional scheme.