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We present a MAC-layer, soft real-time packet scheduling algorithm called UPA. UPA considers a message model where message packets have end-to-end timeliness requirements that are specified using Jensen's time-utility functions (TUFs). The algorithm seeks to maximize system-wide, aggregate packet utility. Since this scheduling problem is NP-hard, UPA heuristically computes schedules with a quadratic worst-case cost, faster than the previously best CMA algorithm. Our simulation studies show that UPA performs the same as or significantly better than CMA for a broad set of TUFs. Furthermore, we implement UPA and prototype a TUF-driven switched Ethernet system. The performance measurements of UPA from the implementation reveal its strong effectiveness. Finally, we derive timeliness feasibility conditions of TUF-driven switched Ethernet systems that use the UPA algorithm.