Combining Decomposition and Reduction for State Space Analysis of a Self-Stabilizing System

Müllner, Nils; Theel, Oliver; Fränzle, Martin

doi:10.1109/aina.2012.127

Cited by 4 publications

(13 citation statements)

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“…Publications preceeding this paper focused on system decomposition [14] to allow for local lumping on the likely considerably smaller transition models of subsystems (i.e. sub-Markov chains).…”

Section: A Related Workmentioning

confidence: 99%

“…Similar to defining safety to demarcate legal from illegal states when determining fault tolerance properties [14], temperature bands can be used to specify comfort zones in which the thermostat should operate. Consider that the thermostat has a latency of one time step and measures the temperature at discrete evenly distributed time points utilizing a bang-bang control [15].…”

Section: B the Deadbandmentioning

confidence: 99%

“…The graph in Figure 15 indirectly shows how the computation time of adding further housings increases with each housing. Compared to decomposing hierarchical systems and otherwise mutually depending processes as discussed in [14], composing mutually independent processes is rather simple. With the households being homogeneous, one surrogate DTMC can be multiplied with the Kronecker product over and over again with the resulting matrix being lumped after each iteration.…”

Section: A Interleaving Application Of the Kronecker Product ⊗ And Lmentioning

confidence: 99%

“…Contrary, constructing hierarchically structured systems is not as easy. The example in [14] contained only |M| = 648 states and |M | = 324 states. Its computation by hand took about two weeks.…”

Section: A Interleaving Application Of the Kronecker Product ⊗ And Lmentioning

confidence: 99%

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Composing Thermostatically Controlled Loads to Determine the Reliability against Blackouts

Müllner

Theel

Fränzle

2014

2014 28th International Conference on Advanced Information Networking and Applications Workshops

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Abstract-Power grids are parallel systems in which consumers demand a shared resource independent of each other. A blackout occurs when the total demand increases or decreases too rapidly. This paper combines methods and concepts from three domains. The first one stems from estimating the power consumption based on thermostatically controlled loads via Markov chains. The second domain provides the composition of parallel systems enriched by intermediate lumping to construct a minimal aggregate transition model, in this case of a community of housings. The third domain provides reasoning about fault tolerance properties by introducing limiting window reliability as measure, suitable to account for the continuous risk of blackouts. Combined, the three methods and concepts allow to determine the risk of blackout of a community over time.

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Section: A Related Workmentioning

confidence: 99%

Section: B the Deadbandmentioning

confidence: 99%

Section: A Interleaving Application Of the Kronecker Product ⊗ And Lmentioning

confidence: 99%

Section: A Interleaving Application Of the Kronecker Product ⊗ And Lmentioning

confidence: 99%

See 2 more Smart Citations

Composing Thermostatically Controlled Loads to Determine the Reliability against Blackouts

Müllner

Theel

Fränzle

2014

2014 28th International Conference on Advanced Information Networking and Applications Workshops

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“…This paper continues our previous approach [1,2] by i) extending the method to further account for semi-hierarchically structured systems and by ii) discussing different types of execution semantics despite serial and maximal parallel execution semantics. A small example points out the issues arising with these extensions and how they can be tackled.…”

Section: A) Related Workmentioning

confidence: 99%

Combining Decomposition and Lumping to Evaluate Semi-hierarchical Systems

Müllner

Theel

Fränzle

2014

2014 IEEE 28th International Conference on Advanced Information Networking and Applications

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Abstract-Determining performance and fault tolerance properties of distributed systems is a challenging task. One common approach to quantify such properties is to construct the state space and a transition model of the distributed system that is to be evaluated. The challenge lies in the state space being exponentially large in the size of the system. One popular approach to tackle this challenge is to combine decomposition and lumping. The system is decomposed, transition models of the subsystems are constructed and minimized by lumping bisimilar states under an equivalence relation, and the intermediate marginal transition systems are composed to construct the minimal aggregate transition model. The approach allows to circumvent the necessity to construct a full transition model while preserving the ability to compute precise measures. The decomposition yet hinges on the structure of the communication within the system. When processes do not influence each other, decomposition is trivial as it is arbitrary. On the contrary, when all processes are influenced by all other processes -known as heterarchical structure -systems cannot be decomposed at all. Between systems of independent and heterarchical processes are i) hierarchically structured systems and ii) systems that are globally hierarchical, but contain locally heterarchical subsystems. The hierarchical type has been addressed elsewhere. This paper targets the second typereferred to as semi-hierarchically structured -, thus expanding the frontier from decomposing purely hierarchically structured systems to decomposing semi-hierarchically structured systems. Furthermore, this paper points out the role of different types of execution semantics regarding the decomposition.

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