Scheduling and stability aspects of a general class of parallel processing systems

In this paper we study the following general class of concurrent processing systems. There are several different classes of processors (servers) and many identical processors within each class. There is also a continuous random flow of jobs, arriving for processing at the system. Each job needs to engage concurrently several processors from various classes in order to be processed. After acquiring the needed processors the job begins to be executed. Processing is done non-preemptively, lasts for a random amount of time, and then all the processors are released simultaneously. Each job is specified by its arrival time, its processing time, and the list of processors that it needs to access simultaneously. The random flow (sequence) of jobs has a stationary and ergodic structure. There are several possible policies for scheduling the jobs on the processors for execution; it is up to the system designer to choose the scheduling policy to achieve certain objectives. We focus on the effect that the choice of scheduling policy has on the asymptotic behavior of the system at large times and especially on its stability, under general stationary and ergocic input flows.