  We study a fundamental online job admission problem where jobs with deadlines
arrive online over time at their release dates, and the task is to determine a
preemptive single-server schedule which maximizes the number of jobs that
complete on time. To circumvent known impossibility results, we make a standard
slackness assumption by which the feasible time window for scheduling a job is
at least $1+\varepsilon$ times its processing time, for some $\varepsilon>0$.
We quantify the impact that different provider commitment requirements have on
the performance of online algorithms. Our main contribution is one universal
algorithmic framework for online job admission both with and without
commitments. Without commitment, our algorithm with a competitive ratio of
$O(1/\varepsilon)$ is the best possible (deterministic) for this problem. For
commitment models, we give the first non-trivial performance bounds. If the
commitment decisions must be made before a job's slack becomes less than a
$\delta$-fraction of its size, we prove a competitive ratio of
$O(\varepsilon/((\varepsilon-\delta)\delta^2))$, for $0<\delta<\varepsilon$.
When a provider must commit upon starting a job, our bound is
$O(1/\varepsilon^2)$. Finally, we observe that for scheduling with commitment
the restriction to the `unweighted' throughput model is essential; if jobs have
individual weights, we rule out competitive deterministic algorithms.
