Simple Temporal Network Research Articles

On Expected Value Strong Controllability

The Probabilistic Simple Temporal Network with Uncertainty (PSTNU) is a variant of the Simple Temporal Network with Uncertainty (STNU) in which known probability distributions govern the timing of uncontrollable timepoints. Previous approaches to solving PSTNUs focus mininizing risk, that is, the probability of violating constraints. These approaches are not applicable in over-constrained controllability problems, when it is certain that all constraints can’t be satisfied. We introduce the Weighted Probabilistic Simple Temporal Network with Uncertainty (WPSTNU), which extends the PSTNU by attaching a fixed value to the satisfaction of temporal constraints, and allows the schedule to violate some constraints in order to maximize the expected value of satisfying others. We study the problem of Expected Value Strong Controllability (EvSC) of WPSTNUs, which seeks a fixed-time schedule maximizing the expected value of satisfied constraints. We solve the EvSC problem using a mixed integer linear program (MILP) that bounds below the probability of satisfying constraints involving uncontrollable timepoints. While solving MILPs generally takes exponential time, we demonstrate our formulation’s effective performance using scheduling problems derived from the HEATlab and MIT ROVERS data sets. We then show how to use this MILP to reschedule during execution, after time has passed and uncertainty is reduced. We describe different fixed-period rescheduling approaches, including time-based and event-based, and report on the most successful strategies compared to the expected value of the fixed schedule produced by the MILP. All of our methods are evaluated on problems with both symmetric and asymmetric (skewed) probability distributions. We show that periodically rescheduling improves the expected value when compared to the fixed schedule, and describe how the benchmark and skewness impact the schedule value improvement. The resulting analysis shows that solving EvSC problems on WPSTNUs is a viable alternative to solving over-constrained controllability problems.

A Column Generation Approach to Correlated Simple Temporal Networks

Probabilistic Simple Temporal Networks (PSTN) represent scheduling problems under temporal uncertainty. Strong controllability (SC) of PSTNs involves finding a schedule to a PSTN that maximises the probability that all constraints are satisfied (robustness). Previous approaches to this problem assume independence of probabilistic durations, and approximate the risk by bounding it above using Boole’s inequality. This gives no guarantee of finding the schedule optimising robustness, and fails to consider correlations between probabilistic durations that frequently arise in practical applications. In this paper, we formally define the Correlated Simple Temporal Network (Corr-STN) which generalises the PSTN by removing the restriction of independence. We show that the problem of Corr-STN SC is convex for a large class of multivariate (log-concave) distributions. We then introduce an algorithm capable of finding optimal SC schedules to Corr-STNs, using the column generation method. Finally, we validate our approach on a number of Corr-STNs and find that our method offers more robust solutions when compared with prior approaches.

A faster algorithm for converting simple temporal networks with uncertainty into dispatchable form

A Simple Temporal Network with Uncertainty (STNU) is a data structure for reasoning about time constraints on actions that may have uncertain durations. An STNU is dispatchable if it can be executed in real-time with minimal computation 1) satisfying all constraints no matter how the uncertain durations play out and 2) retaining maximum flexibility. The fastest known algorithm for converting STNUs into dispatchable form runs in O(n3) time, where n is the number of timepoints. This paper presents a faster algorithm that runs in O(mn+kn2+n2log⁡n) time, where m is the number of edges and k is the number of uncertain durations. This performance is particularly meaningful in fields like Business Process Management, where sparse STNUs can represent temporal processes or plans. For sparse STNUs, our algorithm generates dispatchable forms in time O(n2log⁡n), a significant improvement over the O(n3)-time previous fastest algorithm.

Dynamic controllability of temporal networks with instantaneous reaction

A Conditional Simple Temporal Network with Uncertainty and Decisions (CSTNUD) is a formalism to model, validate, and execute temporal plans subject to controllable and uncontrollable events as well as controllable and uncontrollable choices simultaneously. Dynamic Controllability implies the existence of a strategy scheduling the events and fixing the controllable choices in real time in a way that only depends on the already executed uncontrollable events and already fixed uncontrollable choices. This paper unifies CSTNUDs with other temporal network formalisms by providing Conditional Temporal Networks with Uncertainty and Decisions (CTNUDs) and proposes a semantics for dynamic controllability modeled as a two-player game between Controller and Nature where each player can react instantaneously to the other player moves. Such a game is designed to guarantee termination with exactly one winner (i.e., the game is determined). We prove that adopting the instantaneous reaction semantics allows for modeling any possible reaction time, absorbing de facto previous proposed semantics of dynamic controllability. We provide an encoding into Timed Game Automata to synthesize an execution strategy for any dynamically controllable CTNUD. We implement our approach to synthesize C++ programs for the execution of dynamically controllable CTNUDs. We test our software on a set of randomly-generated instances.

Speeding Up the RUL¯ Dynamic-Controllability-Checking Algorithm for Simple Temporal Networks with Uncertainty

A Simple Temporal Network with Uncertainty (STNU) includes real-valued variables, called time-points; binary difference constraints on those time-points; and contingent links that represent actions with uncertain durations. STNUs have been used for robot control, web-service composition, and business processes. The most important property of an STNU is called dynamic controllability (DC); and algorithms for checking this property are called DC-checking algorithms. The DC-checking algorithm for STNUs with the best worst-case time-complexity is the RUL¯ algorithm due to Cairo, Hunsberger and Rizzi. Its complexity is O(mn + k²n + kn log n), where n is the number of time-points, m is the number of constraints, and k is the number of contingent links. It is expected that this worst-case complexity cannot be improved upon. However, this paper provides a new algorithm, called RUL2021, that improves its performance in practice by an order of magnitude, as demonstrated by a thorough empirical evaluation.

Observable Simple Temporal Network synthesis for the diagnosis of time patterns in time Petri nets

This paper presents a method for the diagnosis of time patterns in time Petri nets. This method uses a characterization of the pattern called Observable Simple Temporal Network, given in the form of a set of observable events with temporal constraints on their occurrence dates. The proposed diagnoser verifies if a part of an input timed sequence of observations is consistent with the characterization. If the pattern has not occurred, this consistency test will lead to the same conclusion. One the other hand, if the pattern has occurred, the consistency test will lead to an ambiguous diagnosis in the general case or to the conclusion that the pattern has definitely occurred if the underlying system is diagnosable.

Adding flexibility to uncertainty: Flexible Simple Temporal Networks with Uncertainty (FTNU)

A Flexible Simple Temporal Network with Uncertainty (FTNU) represents temporal constraints between time-points. Time-points are variables that must be set (executed) satisfying all the constraints. Some time-points are contingent. It means that they are set by the environment and only observed by the system executing the network. The ranges representing temporal constraints associated with contingent time-points (guarded ranges) can be shrunk during execution only to some extent to have more flexibility in the execution of the network. Subsets of time-points/constraints may be executed/considered in different contexts according to some observed conditions. The main issue here consists of determining whether all the time-points, under the control of the system, are executable in a way that all the specified constraints are satisfied for any possible occurrence of contingent time-points and any possible context. Such property is called controllability. Even though an algorithm was proposed for checking the controllability of such networks, we show that such an algorithm has a limit. Indeed, it does not determine the right bounds for guarded links, and, therefore, it doesn’t permit the system to exploit the potential flexibility of the network. We then propose a new constraint-propagation algorithm for checking controllability, prove that such a new algorithm determines the right guarded ranges, and it is sound-and-complete. Thus, it can be used also for executing the network, by leveraging its flexibility.

Mining CSTNUDs significant for a set of traces is polynomial

A Conditional Simple Temporal Network with Uncertainty and Decisions (CSTNUD) is a formalism for temporal plans that models controllable and uncontrollable durations as well as controllable and uncontrollable choices simultaneously. In the classic top-down model-based engineering approach, a designer builds CSTNUDs to model, validate and execute some temporal plans of interest. In this paper, we investigate a bottom-up approach by providing a deterministic polynomial time algorithm to mine a CSTNUD from a set of execution traces (i.e., a log). We provide a prototype implementation and we test it with a set of artificial data. Finally, we elaborate on consistency and controllability of mined networks.

Measuring and Optimizing Durability against Scheduling Disturbances

Flexibility is a useful and common metric for measuring the amount of slack in a Simple Temporal Network (STN) solution space. We extend this concept to specific schedules within an STN’s solution space, developing a related notion of durability that captures an individual schedule’s ability to withstand disturbances and still remain valid. We identify practical sources of scheduling disturbances that motivate the need for durable schedules, and create a geometricallyinspired empirical model that enables testing a given schedule’s ability to withstand these disturbances. We develop a number of durability metrics and use these to characterize and compute specific schedules that we expect to have high durability. Using our model of disturbances, we show that our durability metrics strongly predict a schedule’s resilience to practical scheduling disturbances. We also demonstrate that the schedules we identify as having high durability are up to three times more resilient to disturbances than an arbitrarily chosen schedule is.

Incrementally Solving STNs by Enforcing Partial Path Consistency

Efficient management and propagation of temporal constraints is important for temporal planning as well as for scheduling. During plan development, new events and temporal constraints are added and existing constraints may be tightened; the consistency of the whole temporal network is frequently checked; and results of constraint propagation guide further search. Recent work shows that enforcing partial path consistency provides an efficient means of propagating temporal information for the popular Simple Temporal Network (STN). We show that partial path consistency can be enforced incrementally, thus exploiting the similarities of the constraint network between subsequent edge tightenings. We prove that the worst-case time complexity of our algorithm can be bounded both by the number of edges in the chordal graph (which is better than the previous bound of the number of vertices squared), and by the degree of the chordal graph times the number of vertices incident on updated edges. We show that for many sparse graphs, the latter bound is better than that of the previously best-known approaches. In addition, our algorithm requires space only linear in the number of edges of the chordal graph, whereas earlier work uses space quadratic in the number of vertices. Finally, empirical results show that when incrementally solving sparse STNs, stemming from problems such as Hierarchical Task Network planning, our approach outperforms extant algorithms.

Privacy-Preserving Algorithm for Decoupling of Multi-Agent Plans with Uncertainty

The execution of multi-agent plans often requires communication between agents in order to synchronize their tasks. In cases where communication is unreliable or undesirable, temporal decoupling algorithms allow agents to find a distributed execution strategy beforehand without requiring perfect communication on the fly. The state-of-the-art Multi-Agent Simple Temporal Network with Uncertainty (MaSTNU) framework extends the decoupling problem for Multi-Agent Simple Temporal Network (MaSTN) to allow the modeling of uncertain durations and allow agents to communicate when certain events occur and communication is available. However, the existing approach assumes centralized knowledge of the MaSTNU, whereas in the multi-agent context, privacy is an important concern. In this paper, we propose a distributed, privacy-preserving algorithm for finding distributed execution strategies for MaSTNU. Experiments also showed significant speed-up of the proposed algorithm when the multi-agent plan is loosely coupled and mostly private.

Consistency checking of STNs with decisions: Managing temporal and access-control constraints in a seamless way

A Simple Temporal Network (STN) consists of time points modeling temporal events and constraints modeling the minimal and maximal temporal distance between them. A Simple Temporal Network with Decisions (STND) extends an STN to model temporal plans with decisions. STNDs label time points and constraints by conjunctions of literals saying for which scenarios (i.e., complete truth value assignments to the propositions) they are relevant. In this paper, we deal with the use of STNDs for modeling and synthesizing execution strategies. We propose an incremental hybrid SAT-based consistency checking algorithm for STNDs that is faster than the one previously proposed and allows for the synthesis of all consistent scenarios and related early execution schedules (offline temporal planning). We carry out an experimental evaluation with Kappa, a tool that we developed for STNDs. We also show that any STND can be easily translated into a disjunctive temporal network and vice versa.

Faster Dynamic-Consistency Checking for Conditional Simple Temporal Networks

A Conditional Simple Temporal Network (CSTN) is a structure for representing and reasoning about time in domains where temporal constraints may be conditioned on outcomes of observations made in real time. A CSTN is dynamically consistent (DC) if there is a strategy for executing its time-points such that all relevant constraints will necessarily be satisfied no matter which outcomes happen to be observed. The literature on CSTNs contains only one sound-and-complete DC-checking algorithm that has been implemented and empirically evaluated. It is a graph-based algorithm that propagates labeled constraints/edges. A second algorithm has been proposed, but not evaluated. It aims to speed up DC checking by more efficiently dealing with so-called negative q-loops.This paper presents a new two-phase approach to DC-checking for CSTNs. The first phase focuses on identifying negative q-loops and labeling key time-points within them. The second phase focuses on computing (labeled) distances from each time-point to a single sink node. The new algorithm, which is also sound and complete for DC-checking, is then empirically evaluated against both pre-existing algorithms and shown to be much faster across not only previously published benchmark problems, but also a new set of benchmark problems. The results show that, on DC instances, the new algorithm tends to be an order of magnitude faster than both existing algorithms. On all other benchmark cases, the new algorithm performs better than or equivalently to the existing algorithms.

Conditional simple temporal networks with uncertainty and decisions

A Conditional Simple Temporal Network with Uncertainty (CSTNU) is a formalism able to model temporal plans subject to both conditional constraints and uncertain durations. The combination of these two characteristics represents the uncontrollable part of the network. That is, before the network starts executing, we do not know completely which time points and constraints will be taken into consideration nor how long the uncertain durations will last. Dynamic Controllability (DC) implies the existence of a strategy scheduling the time points of the network in real time depending on how the uncontrollable part behaves. Despite all this, CSTNUs fail to model temporal plans in which a few conditional constraints are under control and may therefore influence (or be influenced by) the uncontrollable part. To bridge this gap, this paper proposes Conditional Simple Temporal Networks with Uncertainty and Decisions (CSTNUDs) which introduce decision time points into the specification in order to operate on this conditional part under control. We model the dynamic controllability checking (DC-checking) of a CSTNUD as a two-player game in which each player makes his moves in his turn at a specific time instant. We give an encoding into timed game automata for a sound and complete DC-checking. We also synthesize memoryless execution strategies for CSTNUDs proved to be DC and carry out an experimental evaluation with ▪, a tool that we have designed for CSTNUDs to make the approach fully automated.

New Perspectives on Flexibility in Simple Temporal Planning

Flexibility is generally agreed to be a desirable feature of a Simple Temporal Network (STN). However, exactly what flexibility attempts to measure has varied, making it difficult to objectively evaluate flexibility metrics. Further, past metrics tend to lose information or exhibit other undesirable properties when aggregating the flexibility measures of individual events across an entire STN. Our work is driven by the realization that the solution space of an STN is a convex polyhedron whose geometric properties convey useful information about the STN. These geometric inspirations lead to measures of an STN solution space and also motivate a set of desiderata for general flexibility metrics. We also put forth two new geometrically-inspired flexibility metrics that have some theoretical advantages over existing metrics. Finally, we comprehensively evaluate both new and existing flexibility metrics against our proposed desiderata.

Multiagent Simple Temporal Problem: The Arc-Consistency Approach

The Simple Temporal Problem (STP) is a fundamental temporal reasoning problem and has recently been extended to the Multiagent Simple Temporal Problem (MaSTP). In this paper we present a novel approach that is based on enforcing arc-consistency (AC) on the input (multiagent) simple temporal network. We show that the AC-based approach is sufficient for solving both the STP and MaSTP and provide efficient algorithms for them. As our AC-based approach does not impose new constraints between agents, it does not violate the privacy of the agents and is superior to the state-of-the-art approach to MaSTP. Empirical evaluations on diverse benchmark datasets also show that our AC-based algorithms for STP and MaSTP are significantly more efficient than existing approaches.

Coordinated Selection and Timing of Multiple Trajectories of Discretely Mobile Robots

The paper addresses the multi-agent path planning (MPP) of mobile agents with multiple goals taking into consideration the kinematic constraints of each agent. The “Swing and Dock” (SaD) robotic system being discussed uses discrete locomotion, where agents swing around fixed pins and dock with their mounting legs to realize displacement from one point to another. The system was developed as a subsystem for mobile robotic fixture (SwarmItFix). Previous work dealt with MPP for SaD agents using the concept of extended temporal graph with Integer Linear Programming (ILP) based formulations. The approach discretized time into unit steps, whereas in reality, the agents are constrained by velocity limits. Hence, a real-time schedule is required to accurately plan the agent movement in a working scenario. We utilize the concept of simple temporal network and extend our ILP formulations to model the velocity kinematic constraints. The mathematical formulations are implemented and tested using a GUROBI solver. Computational results display the effectiveness of the approach.

Checking dynamic consistency of conditional hyper temporal networks via mean payoff games: Hardness and (pseudo) singly-exponential time algorithm

Conditional Simple Temporal Network (CSTN ) is a constraint-based graph formalism for conditional temporal planning, which may be viewed as an extension of Simple Temporal Networks. Recently, STN s have been generalized into Hyper Temporal Networks (HyTN s), by considering weighted directed hypergraphs where each hyperarc models a disjunctive temporal constraint. We introduce the Conditional Hyper Temporal Network (CHyTN) model, a natural extension and generalization of both CSTN s and HyTN s, obtained by blending them together. We show that deciding whether a given CSTN is dynamically-consistent is coNP-hard, and that deciding whether a given CHyTN is dynamically-consistent is PSPACE-hard. Next, we offer the first deterministic (pseudo) singly-exponential time algorithm for checking DC in CHyTNs and CSTN s. To analyze the computational complexity of the proposed algorithm, we introduce a refined notion of DC, named ϵ-DC, presenting a sharp lower bounding analysis on the critical value of the reaction time where a conditional temporal network transits from being, to not being, dynamically-consistent.

Hierarchical task network-based emergency task planning with incomplete information, concurrency and uncertain duration

This paper focuses on the emergency task planning problem with the following characteristics: incomplete initial environment information, concurrent execution and uncertain execution durations. To address this problem, the conditional temporal hierarchical task network (HTN) planning with uncertain durations should be investigated. However, the research work on conditional HTN planning mainly concentrates on the planning domain without temporal features and pays no attention to the handling of concurrency and uncertain durations. This motivates us to propose a planning paradigm based on the conditional HTN planning. The planning paradigm incorporates a temporal reasoning technique suitable for conditional HTN planning to achieve concurrency and a temporal management approach to confirm the satisfiability of temporal constraints efficiently. For temporal reasoning, rules for generating temporal constraints are designed to avoid three types of flaws due to interactions between durative actions; a mechanism for detecting invalid temporal constraints is also presented. Regarding temporal management, Conditional Simple Temporal Network with Uncertainty (CSTNU) is utilized to represent the temporal constraints involving uncontrollable intervals and observations, and an approach for eliminating redundant temporal constraints is proposed to reduce the temporal constraint to be represented in a CSTNU to promote efficiency. Finally, an experimental study of an earthquake rescue domain demonstrates the viability of the proposed planning paradigms.

The Mathematics of Dispatchability Revisited

Dispatchability is an important property for the efficient execution of temporal plans where the temporal constraints are represented as a Simple Temporal Network (STN). It has been shown that every STN may be reformulated as a dispatchable STN, and dispatchability ensures that the temporal constraints need only be satisfied locally during execution. Recently it has also been shown that Simple Temporal Networks with Uncertainty, augmented with wait edges, are Dynamically Controllable provided every projection is dispatchable. Thus, the dispatchability property has both theoretical and practical interest. One thing that hampers further work in this area is the under-developed theory. The existing definitions are expressed in terms of algorithms, and are less suitable for mathematical proofs. In this paper, we develop a new formal theory of dispatchability in terms of execution sequences. We exploit this to prove a characterization of dispatchability involving the structural properties of the STN graph. This facilitates the potential application of the theory to uncertainty reasoning.