Optimal scheduling for constant-rate multi-mode systems

Alur, Rajeev; Trivedi, Ashutosh; Wojtczak, Dominik

doi:10.1145/2185632.2185647

Cited by 15 publications

(47 citation statements)

References 19 publications

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“…We extend the results of [5] by recovering decidability for WSHA by showing that the reachability problem and schedulability problems are NP-Complete for this model. We also define LTL and CTL model-checking problems for weak singular hybrid automata, and show that while the complexity of LTL modelchecking stays the same as LTL model checking for finite state-transition graphs (Pspace-Complete), the CTL model-checking is already PSPACE-hard.…”

Section: Introductionmentioning

confidence: 75%

“…Our definition of weak singular hybrid automata is inspired by the definition of constant-rate multi-mode systems (CMS) [5], that are hybrid systems that can switch freely between a finite set of modes (or states) and whose dynamics are specified by a finite set of variables with mode-dependent constant rates. The schedulability problem for CMS is to decide-for a given initial state and convex and bounded safety set-whether there exists a non-Zeno mode-switching schedule such that the system stays within the safety set.…”

Section: Introductionmentioning

confidence: 99%

“…On the other hand, the reachability problem is to decide whether there is a schedule that steers the system from a given initial configuration to the target configuration while staying within a specified bounded and convex safety set. Since the system is allowed to switch freely between the enabled modes, the reachability and schedulability problems can be solved in polynomial time [5] by reducing them to a linear program. We say that a singular hybrid automaton is weak if there exists an ordering among the states such that the transition to a lower order state is disallowed, and the states with the same ordering form a CMS, i.e.…”

Section: Introductionmentioning

confidence: 99%

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Weak Singular Hybrid Automata

Krishna

Mathur

Trivedi

2014

Lecture Notes in Computer Science

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Abstract. The framework of Hybrid automata-introduced by Alur, Courcourbetis, Henzinger, and Ho-provides a formal modeling and analysis environment to analyze the interaction between the discrete and the continuous parts of hybrid systems. Hybrid automata can be considered as generalizations of finite state automata augmented with a finite set of real-valued variables whose dynamics in each state is governed by a system of ordinary differential equations. Moreover, the discrete transitions of hybrid automata are guarded by constraints over the values of these real-valued variables, and enable discontinuous jumps in the evolution of these variables. Singular hybrid automata are a subclass of hybrid automata where dynamics is specified by state-dependent constant vectors. Henzinger, Kopke, Puri, and Varaiya showed that for even very restricted subclasses of singular hybrid automata, the fundamental verification questions, like reachability and schedulability, are undecidable. Recently, Alur, Wojtczak, and Trivedi studied an interesting class of hybrid systems, called constant-rate multi-mode systems, where schedulability and reachability analysis can be performed in polynomial time. Inspired by the definition of constant-rate multi-mode systems, in this paper we introduce weak singular hybrid automata (WSHA), a previously unexplored subclass of singular hybrid automata, and show the decidability (and the exact complexity) of various verification questions for this class including reachability (NP-Complete) and LTL modelchecking (Pspace-Complete). We further show that extending WSHA with a single unrestricted clock or with unrestricted variable updates lead to undecidability of reachability problem.

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Section: Introductionmentioning

confidence: 75%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Weak Singular Hybrid Automata

Krishna

Mathur

Trivedi

2014

Lecture Notes in Computer Science

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“…From 2007 to till date, various approaches in uniprocessor scheduling and multiprocessor scheduling are realized with realistic models and formal methods [17]. A mixed criticality system has two or more distinct levels like safety critical, mission critical and low critical [18]. In this model, the parameter worst case execution time is dependent on the criticality level.…”

Section: Need For the Next Level Of Schedulingmentioning

confidence: 99%

“…The mode change protocols are required for the system to move between modes. These protocols are dealt and studied by various researchers in their study [18], [19], [20]. Mixed criticality system addresses on two levels such as high criticality level and low criticality level.…”

Section: Need For the Next Level Of Schedulingmentioning

confidence: 99%

Intelligent Real-Time Systems for Managing Catastrophe through Scenario Shift Paradigm

Nair¹,

Persya²

2015

IJCA

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The intelligent real-time system design needs to incorporate autonomic features in their operations to achieve the unexpected criticalities of systems and its environment. Catastrophic scenarios can emerge in systems, challenging the traditional role of real-time systems where the temporal rigidity is the essential design feature. The priorities and its management scheme given for a normal operation by the conventional real-time systems need not be the ultimate format to meet the requirements of a catastrophic environment. Hence, usual real-time system is supplemented with a layer of intelligence to deal with the emerging catastrophic environment. Intelligent real-time systems can have hybrid schedulers with some additional features that can guarantee risk mitigation performance even with the occurrence of extreme, unusual variations of external conditions. This approach addresses intelligence in systems by making a real-time system schedule itself to adapt meaningfully even if the environment changes, by assigning intelligent priorities. This paper introduces the design of Intelligent Real-Time System (IRTS) that keep shifting the boundaries of the original hybrid scheduler with cognitive features aiding the intelligence by increasing the possibility to make a dynamically reconfigured system while increasing the fairness of the scheduling. Intelligent scheduler can be used in embedded critical systems in order to cope with the unexpected problems like nuclear power plants and hazardous installations. Theoretical analysis shows that the proposed design performs the operation of IRTS, which can be advantageously applied to pragmatic systems and show how intelligence works with priority.

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Optimal Control for Multi-mode Systems with Discrete Costs

Mouśa

Schewe

Wojtczak

2017

Lecture Notes in Computer Science

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Abstract. This paper studies optimal time-bounded control in multi-mode systems with discrete costs. Multi-mode systems are an important subclass of linear hybrid systems, in which there are no guards on transitions and all invariants are global. Each state has a continuous cost attached to it, which is linear in the sojourn time, while a discrete cost is attached to each transition taken. We show that an optimal control for this model can be computed in NEXPTIME and approximated in PSPACE. We also show that the one-dimensional case is simpler: although the problem is NP-complete (and in LOGSPACE for an infinite time horizon), we develop an FPTAS for finding an approximate solution.

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Optimal scheduling for constant-rate multi-mode systems

Cited by 15 publications

References 19 publications

Weak Singular Hybrid Automata

Weak Singular Hybrid Automata

Intelligent Real-Time Systems for Managing Catastrophe through Scenario Shift Paradigm

Optimal Control for Multi-mode Systems with Discrete Costs

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