TY - JOUR

T1 - Estimating the probability of meeting a deadline in schedules and plans

AU - Cohen, Liat

AU - Shimony, Solomon Eyal

AU - Weiss, Gera

N1 - Funding Information:
This research was supported by the ROBIL project, by the Lynne and William Frankel Center for Computer Science at Ben-Gurion University, and by the Israel Science Foundation , grant number 856/16 .
Publisher Copyright:
© 2019 Elsevier B.V.

PY - 2019/10/1

Y1 - 2019/10/1

N2 - Given a plan (or schedule) with uncertain task times, we propose a deterministic polynomial (time and memory) algorithm for estimating the probability that it meets a deadline, or, equivalently, that its makespan is less than a given duration. Approximation is needed as it is known that this problem is NP-hard even for sequential plans (sum of random variables). In addition, we show two new complexity results: (1) Counting the number of events that do not cross the deadline is #P-hard; (2) Computing the expected makespan of a hierarchical plan is NP-hard. For the proposed approximation algorithm, we establish formal approximation bounds and show that the time and memory complexities grow polynomially with the required accuracy, the number of nodes in the plan, and with the size of the support of the random variables that represent the durations of the primitive tasks. We examine these approximation bounds empirically and demonstrate, using task networks taken from the literature, how our scheme outperforms sampling techniques and exact computation in terms of accuracy and run-time. As the empirical data shows much better error bounds than guaranteed, we also suggest a method for tightening the bounds in some cases.

AB - Given a plan (or schedule) with uncertain task times, we propose a deterministic polynomial (time and memory) algorithm for estimating the probability that it meets a deadline, or, equivalently, that its makespan is less than a given duration. Approximation is needed as it is known that this problem is NP-hard even for sequential plans (sum of random variables). In addition, we show two new complexity results: (1) Counting the number of events that do not cross the deadline is #P-hard; (2) Computing the expected makespan of a hierarchical plan is NP-hard. For the proposed approximation algorithm, we establish formal approximation bounds and show that the time and memory complexities grow polynomially with the required accuracy, the number of nodes in the plan, and with the size of the support of the random variables that represent the durations of the primitive tasks. We examine these approximation bounds empirically and demonstrate, using task networks taken from the literature, how our scheme outperforms sampling techniques and exact computation in terms of accuracy and run-time. As the empirical data shows much better error bounds than guaranteed, we also suggest a method for tightening the bounds in some cases.

KW - Approximation

KW - Deadline

KW - Makespan

KW - Plan

KW - Random variables

KW - Schedule

UR - http://www.scopus.com/inward/record.url?scp=85068364434&partnerID=8YFLogxK

U2 - 10.1016/j.artint.2019.06.009

DO - 10.1016/j.artint.2019.06.009

M3 - Article

AN - SCOPUS:85068364434

VL - 275

SP - 329

EP - 355

JO - Artificial Intelligence

JF - Artificial Intelligence

SN - 0004-3702

ER -