scholarly journals Probabilistic Temporal Networks with Ordinary Distributions: Theory, Robustness and Expected Utility

2021 ◽  
Vol 71 ◽  
pp. 1091-1136
Author(s):  
Michael Saint-Guillain ◽  
Tiago Vaquero ◽  
Steve Chien ◽  
Jagriti Agrawal ◽  
Jordan Abrahams
Keyword(s):  
Expected Utility ◽  
Probability Distributions ◽  
Dynamic Control ◽  
Success Probability ◽  
Computation Method ◽  
Temporal Networks ◽  
Fixed Parameter ◽  
Simple Temporal Networks ◽  
Strong Dynamic ◽  
Utility Measures

Most existing works in Probabilistic Simple Temporal Networks (PSTNs) base their frameworks on well-defined, parametric probability distributions. Under the operational contexts of both strong and dynamic control, this paper addresses robustness measure of PSTNs, i.e. the execution success probability, where the probability distributions of the contingent durations are ordinary, not necessarily parametric, nor symmetric (e.g. histograms, PERT), as long as these can be discretized. In practice, one would obtain ordinary distributions by considering empirical observations (compiled as histograms), or even hand-drawn by field experts. In this new realm of PSTNs, we study and formally define concepts such as degree of weak/strong/dynamic controllability, robustness under a predefined dispatching protocol, and introduce the concept of PSTN expected execution utility. We also discuss the limitation of existing controllability levels, and propose new levels within dynamic controllability, to better characterize dynamic controllable PSTNs based on based practical complexity considerations. We propose a novel fixed-parameter pseudo-polynomial time computation method to obtain both the success probability and expected utility measures. We apply our computation method to various PSTN datasets, including realistic planetary exploration scenarios in the context of the Mars 2020 rover. Moreover, we propose additional original applications of the method.

scholarly journals Robustness Computation of Dynamic Controllability in Probabilistic Temporal Networks with Ordinary Distributions

2020 ◽  
Author(s):  
Michael Saint-Guillain ◽  
Tiago Stegun Vaquero ◽  
Jagriti Agrawal ◽  
Steve Chien
Keyword(s):  
Probability Distributions ◽  
Dynamic Control ◽  
Success Probability ◽  
Polynomial Time Algorithm ◽  
Time Algorithm ◽  
Temporal Networks ◽  
Fixed Parameter ◽  
Probability Of Success ◽  
Dynamic Policy ◽  
Simple Temporal Networks

Most existing works in Probabilistic Simple Temporal Networks (PSTNs) base their frameworks on well-defined probability distributions. This paper addresses on PSTN Dynamic Controllability (DC) robustness measure, i.e. the execution success probability of a network under dynamic control. We consider PSTNs where the probability distributions of the contingent edges are ordinary distributed (e.g. non-parametric, non-symmetric). We introduce the concepts of dispatching protocol (DP) as well as DP-robustness, the probability of success under a predefined dynamic policy. We propose a fixed-parameter pseudo-polynomial time algorithm to compute the exact DP-robustness of any PSTN under NextFirst protocol, and apply to various PSTN datasets, including the real case of planetary exploration in the context of the Mars 2020 rover, and propose an original structural analysis.

scholarly journals Dynamic Control of Probabilistic Simple Temporal Networks

2020 ◽  
Vol 34 (06) ◽  
pp. 9851-9858
Author(s):  
Michael Gao ◽  
Lindsay Popowski ◽  
Jim Boerkoel
Keyword(s):  
Dynamic Scheduling ◽  
Dynamic Control ◽  
Probability Density Functions ◽  
Directed Search ◽  
Temporal Constraints ◽  
Temporal Networks ◽  
Loss Of Control ◽  
Dc Algorithm ◽  
Simple Temporal Networks ◽  
Real World Problems

The controllability of a temporal network is defined as an agent's ability to navigate around the uncertainty in its schedule and is well-studied for certain networks of temporal constraints. However, many interesting real-world problems can be better represented as Probabilistic Simple Temporal Networks (PSTNs) in which the uncertain durations are represented using potentially-unbounded probability density functions. This can make it inherently impossible to control for all eventualities. In this paper, we propose two new dynamic controllability algorithms that attempt to maximize the likelihood of successfully executing a schedule within a PSTN. The first approach, which we call Min-Loss DC, finds a dynamic scheduling strategy that minimizes loss of control by using a conflict-directed search to decide where to sacrifice the control in a way that optimizes overall success. The second approach, which we call Max-Gain DC, works in the other direction: it finds a dynamically controllable schedule and then attempts to progressively strengthen it by capturing additional uncertainty. Our approaches are the first known that work by finding maximally dynamically controllable schedules. We empirically compare our approaches against two existing PSTN offline dispatch approaches and one online approach and show that our Min-Loss DC algorithm outperforms the others in terms of maximizing execution success while maintaining competitive runtimes.

scholarly journals A Satisficing Framework for Environmental Policy Under Model Uncertainty

2021 ◽  
Author(s):  
Stergios Athanasoglou ◽  
Valentina Bosetti ◽  
Laurent Drouet
Keyword(s):  
Environmental Policy ◽  
Model Uncertainty ◽  
Probability Distributions ◽  
Success Probability ◽  
Economic Assessment ◽  
Decision Criterion ◽  
Probability Criterion ◽  
Change Context ◽  
Future Consumption ◽  
Point Of Departure

AbstractWe propose a novel framework for the economic assessment of environmental policy. Our main point of departure from existing work is the adoption of a satisficing, as opposed to optimizing, modeling approach. Along these lines, we place primary emphasis on the extent to which different policies meet a set of goals at a specific future date instead of their performance vis-a-vis some intertemporal objective function. Consistent to the nature of environmental policymaking, our model takes explicit account of model uncertainty. To this end, the decision criterion we propose is an analog of the well-known success-probability criterion adapted to settings characterized by model uncertainty. We apply our criterion to the climate-change context and the probability distributions constructed by Drouet et al. (2015) linking carbon budgets to future consumption. Insights from computational geometry facilitate computations considerably and allow for the efficient application of the model in high-dimensional settings.

scholarly journals Simpler and Faster Algorithm for Checking the Dynamic Consistency of Conditional Simple Temporal Networks

2018 ◽  
Author(s):  
Luke Hunsberger ◽  
Roberto Posenato
Keyword(s):  
Recent Work ◽  
Constraint Propagation ◽  
Dynamic Consistency ◽  
Temporal Networks ◽  
Alternative Semantics ◽  
Open Questions ◽  
Simpler Algorithm ◽  
Simple Temporal Networks ◽  
Propagation Rules

Recent work on Conditional Simple Temporal Networks (CSTNs) has focused on checking the dynamic consistency (DC) property assuming that execution strategies can react instantaneously to observations. Three alternative semantics---IR-DC, 0-DC, and π-DC---have been presented. The most practical DC-checking algorithm for CSTNs has only been analyzed with respect to the IR-DC semantics, while the 0-DC semantics was shown to have a serious flaw that the π-DC semantics fixed. Whether the IR-DC semantics had the same flaw and, if so, what the consequences would be for the DC-checking algorithm remained open questions. This paper (1) shows that the IR-DC semantics is also flawed; (2) shows that one of the constraint-propagation rules from the IR-DC-checking algorithm is not sound with respect to the IR-DC semantics; (3) presents a simpler algorithm, called the π-DC-checking algorithm; (4) proves that it is sound and complete with respect to the π-DC semantics; and (5) empirically evaluates the new algorithm.

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