AbstractA single bus tightly coupled multiprocessor is a distributed computing system characterized by a single data highway, physically e10se juxtaposition of the processors, and a globally accessible memory that is used for interprocessor communication. We present a prioritized hier rchical Markovian queueing model for such a computer organization. This multiprocessor model consists of a set of processing elemelltg (PEs) and single queue/server pair representing the shared memory. Our model takes into count not only global system behavior, but also behavior of tasks on each processing clement and probabilistic tMk migration among the PEs. We show that the prioritization can be masked by reducing each PE submodel to an equivalent queue/server pair whose scrvice rale depends on the numbcr of tMks in this queue; furthermore, under the Msumption of heavy load, this service rate becomes independent of the number of tasks in the server' queue. 8Med on this reduction, an equivalent multiprocessor model is constructed. Global throughput (both exact and limiting) is then obtained based on this reduction.