Performance Evaluation of Schedulers in a Probabilistic Setting

Abstract

Abstract. We show how to evaluate the performance of solutions to finite-horizon scheduling problems where task durations are specified by bounded uniform distributions. Our computational technique, based on computing the volumes of zones, constitutes a contribution to the computational study of scheduling under uncertainty and stochastic systems in general.

As Soon as Probable: Optimal Scheduling under Stochastic Uncertainty

“…2. Implementation and experimentation: we currently have a prototype implementation building upon the infra-structure developed in [12] for computing integrals over zones. Once completed, we intend to compare cost/quality tradeoffs of our algorithm with statistical methods such as [8,13] that evaluate and synthesize schedulers based on sampling the duration space.…”

“…A scheduler selects one action in any state and then the only nondeterminism that remains is due to the probabilistic task durations. A discussion on different types of schedulers can be found in [12]. Definition 9 (Scheduler).…”

“…In [12] we developed a method to compute the expected termination time under a given scheduler by computing volumes in the duration space. We now show how to optimally synthesize such schedulers from an uncontrolled DPA description.…”

“…This approach refines the successor operator used in the verification of timed automata [9,15] from a zone transformer into a density transformer and can compute, for example, the time distribution of reaching the final state and hence the expected termination time under a given scheduler. In [12] we developed an alternative clock-free procedure for evaluating the performance of schedulers by computing volumes of zones in the duration space.…”

“…Such problems can be modeled as duration probabilistic automata (DPA), a well-structured class of acyclic timed automata where temporal uncertainty is interpreted as a bounded uniform distribution of task durations [18]. In [12] we have developed a framework for computing the expected performance of a given scheduling policy. In the present paper we move from analysis to controller synthesis and develop a dynamicprogramming style procedure for automatically synthesizing (or approximating) expected time optimal schedulers, using an iterative computation of a stochastic time-to-go function over the state and clock space of the automaton.…”