This paper introduces an analytical method for approximating the performance of a two-class
priority M=M=1 system. The prioritized class-1 jobs are real-time, served either with the
preemptive or non-preemptive Earliest-Deadline-First (EDF) policy and can preempt the non
real-time class-2 jobs. The preempted service of the class-2 job is resumed from the time in
instances where no class-1 job is in the system. The service discipline of class-2 jobs is FCFS.
The required mean service times may depend on the class of the jobs. The real-time jobs have
exponentially distributed relative deadlines until the end of service. The system is approximated
by a Markovian model in the long run, which can be solved numerically, using standard Markovian
solution techniques. The performance measures of the system are the loss probability of the
class-1 jobs and the mean sojourn (waiting) time of the class-2 jobs. Comparing numerical and
simulation results, it is found that the existing errors are relatively small.