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As a natural multi-class generalization of the well-known (egalitarian) processor sharing (PS) service discipline, discriminatory processor sharing (DPS) is of great interest in many application areas, including telecommunications. Under DPS, the mean response time conditional on the service requirement is only known in closed form when all classes have exponential service requirement distributions. For generally distributed service requirements, Fayolle et al. (1980) showed that the expected conditional response times satisfy a system of integro-differential equations. In this paper, we exploit that result to prove that, provided the system is stable, for each class the expected unconditional response time is finite and that the expected conditional response time has an asymptote. The asymptotic bias of each class is found in closed form, involving the mean service requirements of all classes and the second moments …