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We address the problem of scheduling concurrent periodic real-time transactions on Multidomain Ring Bus (MDRB). The problem is challenging because although the bus allows multiple nonoverlapping transactions to be executed concurrently, the degree of concurrency depends on the topology of the bus and of executed transactions. To solve this problem, first, we propose two novel efficient scheduling algorithms for topographically acyclic transaction sets. The first algorithm is optimal for transaction sets under restrictive assumptions while the second one induces a good sufficient schedulable utilization bound for more general transaction sets. Then, we extend these two algorithms for the scheduling of topographically cyclic transaction sets. Extensive simulations show that the proposed algorithm can schedule transaction sets with high bus utilization and is better than that of related works in most practical settings. The implementation of the algorithms in a real testbed shows that they have relatively low execution-time overhead.