A Mixed-Priority Queue with Applications to the Analysis of Real-Time Systems

Jobs arrive in a Poisson stream to a single processor. Associated with each job is a priority j = 1, 2, …. The processing time requested by a job can be partitioned into an arbitrary number of intervals of two types, (1) noninterruptible portions and (2) interruptible portions. Type 2 intervals can further be classified as preemptive-resume intervals and preemptive-repeat intervals that, in turn, can be further classified as being repeat with resampling or repeat without resampling. When a job is interrupted, a setup time (which is interruptible) must first be expended before the job can regain the processor. Steady-state moments and Laplace transforms are obtained.