We present a design of a customized crossbar scheduler for on-chip networks. The proposed scheduler arbitrates on-demand interconnects, where physical topologies are identical to logical topologies for given applications. Considering conventional fully parallel and sequential schedulers as reference designs, a comparative performance analysis is conducted. The hardware scheduler module is implemented with parameterized arbiter arrays. Experiments with practical applications show that the crossbar network with our custom scheduler realizes on-demand traffic patterns, occupies on average 52% less area, and maintains higher performance, compared to the crossbar network with a fully parallel scheduler. Additionally, our custom scheduler performs significantly better than the sequential scheduler with moderate area overheads for smallsized tokens communicated over large networks.