Space-Efficient Scheduling of Stochastically Generated Tasks

Abstract

Abstract. We study the problem of scheduling tasks for execution by a processor when the tasks can stochastically generate new tasks. Tasks can be of different types, and each type has a fixed, known probability of generating other tasks. We present results on the random variable S σ modeling the maximal space needed by the processor to store the currently active tasks when acting under the scheduler σ. We obtain tail bounds for the distribution of S σ for both offline and online schedulers, and investigate the expected value E[S σ ].

A Brief History of Strahler Numbers

“…The connection between Newton approximants and Strahler numbers has several interesting consequences. In particular, one can use results on the convergence speed of Newton iteration [3] to derive information on the distribution of the Strahler number in randomly generated trees. Consider for instance random trees generated according to the following rule.…”

“…This is not a coincidence. The function f (X) satisfies µf < 1, and a theorem of [3] shows that for every f satisfying this property, there exist numbers c > 0 and 0…”

Analysis of Probabilistic Basic Parallel Processes

“…The MDP version of pBPPs was studied before under the name task systems [2]. There, the scheduler aims at a "space-efficient" scheduling, which is one where the maximal number of processes is minimised.…”