Partitioning of processors on a multiprocessor system involves logically dividing the system into processor partitions. Programs can be executed in the different partitions in parallel. Optimally setting the partition size can significantly improve the throughput of multiprocessor systems. The speedup characteristics of parallel programs can be defined by execution signatures. The execution signature of a parallel program on a multiprocessor system is the rate at which the program executes in the absence of other programs and depends upon the number of allocated processors, the specific architecture, and the specific program implementation. Based on the execution signatures, this paper analyzes simple Markovian models of dynamic partitioning. From the analysis, when there are at most two multiprocessor partitions, the optimal dynamic partition size can be found which maximizes throughput. Compared against other partitioning schemes, the dynamic partitioning scheme is shown to be the best in terms of throughput when thereconfiguration overhead is low. If the reconfiguration overhead is high, dynamic partitioning is to be avoided. An expression for the reconfiguration overhead threshold is derived. A general iterative partitioning technique is presented. It is shown that the technique gives maximum throughput forn partions.