In this paper we address a seemingly simple question: Is there a universal packet scheduling algorithm? More precisely, we analyze (both theoretically and empirically) whether there is a single packet scheduling algorithm that, at a network-wide level, can match the results of any given scheduling algorithm. We find that in general the answer is “no”. However, we show theoretically that the classical Least Slack Time First (LSTF) scheduling algorithm comes closest to being universal and demonstrate empirically that LSTF can closely, though not perfectly, replay a wide range of scheduling algorithms in realistic network settings. We then evaluate whether LSTF can be used in practice to meet various network-wide objectives by looking at three popular performance metrics (mean FCT, tail packet delays, and fairness); we find that LSTF performs comparable to the state-of-the-art for each of them.