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We study the behavior of packet scheduling protocols in a temporary sessions model in which sessions come and go over time. We first show that, in this setting, the standard delay bound for the well-studied generalized processor sharing (GPS) protocol can be exceeded by an arbitrary amount. In extreme cases, GPS can actually be unstable. In contrast, we then show that it is possible to choose deadlines so that the earliest-deadline-first (EDF) protocol is always stable. We illustrate our results by analysis and simulations.