  We consider a single server queueing system with two classes of jobs: eager
jobs with small sizes that require service to begin almost immediately upon
arrival, and tolerant jobs with larger sizes that can wait for service. While
blocking probability is the relevant performance metric for the eager class,
the tolerant class seeks to minimize its mean sojourn time. In this paper, we
discuss the performance of each class under dynamic scheduling policies, where
the scheduling of both classes depends on the instantaneous state of the
system. This analysis is carried out under a certain fluid limit, where the
arrival rate and service rate of the eager class are scaled to infinity,
holding the offered load constant. Our performance characterizations reveal a
(dynamic) pseudo-conservation law that ties the performance of both the classes
to the standalone blocking probabilities of the eager class. Further, the
performance is robust to other specifics of the scheduling policies. We also
characterize the Pareto frontier of the achievable region of performance
vectors under the same fluid limit, and identify a (two-parameter) class of
Pareto-complete scheduling policies.
