Modeling of the Memory Management Process for Dynamic Work-Stealing Schedulers

Parallel task schedulers that use the work-stealing strategy have tasks allocation close to optimal (e.g. all processors are loaded equally). The basic idea of the strategy is as follows: if one processor runs out of tasks, it steals them from another processor. All tasks are located in queues, where deque (double-ended queue) is the most common and effective implementation of such queue. The aim of this research is to construct and analyze mathematical models of n sequential circular deques located in a shared memory. Mathematical models are built in the form of random walks on an integer lattice in n-dimensional space. Operations (with given probabilities) occur at each step of the discrete time. On the basis of aforementioned models the following problems were solved: finding the optimal partition of a shared memory between n deques and finding the optimal number of elements for stealing. The criterion of optimality is the maximum mean time to the memory overflow.