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In this paper, we present a MAC-layer packet scheduling algorithm, called BPA, for real-time switched Ethernet networks. BPA considers a message model where trans-node application-level messages have end-to-end timeliness requirements that are specified using Jensen's benefit functions. The objective of BPA is to maximize the aggregate message-level benefit. The algorithm reasons that this objective can be achieved by maximizing aggregate packet-level benefit, where packets of messages are allowed to inherit benefit functions of their parent messages. BPA thus solves a non-preemptive packet scheduling problem. Since this problem is NP-hard, BPA heuristically computes packet schedules to maximize aggregate benefit, incurring a worst-case computational complexity of O(n2). This is better than the O(n3) complexity of the previously known best algorithm (called CMA) for the same problem. Further, our experimental studies show that BPA performs as good as CMA for a broad set of benefit functions, and significantly outperforms CMA for some benefit functions. Furthermore, we observe that BPA yields lower missed-deadline ratio than CMA when message arrival density increases.