16,897 research outputs found
Transient Reward Approximation for Continuous-Time Markov Chains
We are interested in the analysis of very large continuous-time Markov chains
(CTMCs) with many distinct rates. Such models arise naturally in the context of
reliability analysis, e.g., of computer network performability analysis, of
power grids, of computer virus vulnerability, and in the study of crowd
dynamics. We use abstraction techniques together with novel algorithms for the
computation of bounds on the expected final and accumulated rewards in
continuous-time Markov decision processes (CTMDPs). These ingredients are
combined in a partly symbolic and partly explicit (symblicit) analysis
approach. In particular, we circumvent the use of multi-terminal decision
diagrams, because the latter do not work well if facing a large number of
different rates. We demonstrate the practical applicability and efficiency of
the approach on two case studies.Comment: Accepted for publication in IEEE Transactions on Reliabilit
Explicit Model Checking of Very Large MDP using Partitioning and Secondary Storage
The applicability of model checking is hindered by the state space explosion
problem in combination with limited amounts of main memory. To extend its
reach, the large available capacities of secondary storage such as hard disks
can be exploited. Due to the specific performance characteristics of secondary
storage technologies, specialised algorithms are required. In this paper, we
present a technique to use secondary storage for probabilistic model checking
of Markov decision processes. It combines state space exploration based on
partitioning with a block-iterative variant of value iteration over the same
partitions for the analysis of probabilistic reachability and expected-reward
properties. A sparse matrix-like representation is used to store partitions on
secondary storage in a compact format. All file accesses are sequential, and
compression can be used without affecting runtime. The technique has been
implemented within the Modest Toolset. We evaluate its performance on several
benchmark models of up to 3.5 billion states. In the analysis of time-bounded
properties on real-time models, our method neutralises the state space
explosion induced by the time bound in its entirety.Comment: The final publication is available at Springer via
http://dx.doi.org/10.1007/978-3-319-24953-7_1
Numerical Verification of Affine Systems with up to a Billion Dimensions
Affine systems reachability is the basis of many verification methods. With
further computation, methods exist to reason about richer models with inputs,
nonlinear differential equations, and hybrid dynamics. As such, the scalability
of affine systems verification is a prerequisite to scalable analysis for more
complex systems. In this paper, we improve the scalability of affine systems
verification, in terms of the number of dimensions (variables) in the system.
The reachable states of affine systems can be written in terms of the matrix
exponential, and safety checking can be performed at specific time steps with
linear programming. Unfortunately, for large systems with many state variables,
this direct approach requires an intractable amount of memory while using an
intractable amount of computation time. We overcome these challenges by
combining several methods that leverage common problem structure. Memory is
reduced by exploiting initial states that are not full-dimensional and safety
properties (outputs) over a few linear projections of the state variables.
Computation time is saved by using numerical simulations to compute only
projections of the matrix exponential relevant for the verification problem.
Since large systems often have sparse dynamics, we use Krylov-subspace
simulation approaches based on the Arnoldi or Lanczos iterations. Our method
produces accurate counter-examples when properties are violated and, in the
extreme case with sufficient problem structure, can analyze a system with one
billion real-valued state variables
Parameterized Model Checking of Token-Passing Systems
We revisit the parameterized model checking problem for token-passing systems
and specifications in indexed .
Emerson and Namjoshi (1995, 2003) have shown that parameterized model checking
of indexed in uni-directional token
rings can be reduced to checking rings up to some \emph{cutoff} size. Clarke et
al. (2004) have shown a similar result for general topologies and indexed
, provided processes cannot choose the
directions for sending or receiving the token.
We unify and substantially extend these results by systematically exploring
fragments of indexed with respect to
general topologies. For each fragment we establish whether a cutoff exists, and
for some concrete topologies, such as rings, cliques and stars, we infer small
cutoffs. Finally, we show that the problem becomes undecidable, and thus no
cutoffs exist, if processes are allowed to choose the directions in which they
send or from which they receive the token.Comment: We had to remove an appendix until the proofs and notations there is
cleare
Implicit Decomposition for Write-Efficient Connectivity Algorithms
The future of main memory appears to lie in the direction of new technologies
that provide strong capacity-to-performance ratios, but have write operations
that are much more expensive than reads in terms of latency, bandwidth, and
energy. Motivated by this trend, we propose sequential and parallel algorithms
to solve graph connectivity problems using significantly fewer writes than
conventional algorithms. Our primary algorithmic tool is the construction of an
-sized "implicit decomposition" of a bounded-degree graph on
nodes, which combined with read-only access to enables fast answers to
connectivity and biconnectivity queries on . The construction breaks the
linear-write "barrier", resulting in costs that are asymptotically lower than
conventional algorithms while adding only a modest cost to querying time. For
general non-sparse graphs on edges, we also provide the first writes
and operations parallel algorithms for connectivity and biconnectivity.
These algorithms provide insight into how applications can efficiently process
computations on large graphs in systems with read-write asymmetry
Statistical Model Checking for Stochastic Hybrid Systems
This paper presents novel extensions and applications of the UPPAAL-SMC model
checker. The extensions allow for statistical model checking of stochastic
hybrid systems. We show how our race-based stochastic semantics extends to
networks of hybrid systems, and indicate the integration technique applied for
implementing this semantics in the UPPAAL-SMC simulation engine. We report on
two applications of the resulting tool-set coming from systems biology and
energy aware buildings.Comment: In Proceedings HSB 2012, arXiv:1208.315
On minimising the maximum expected verification time
Cyber Physical Systems (CPSs) consist of hardware and software components. To verify that the whole (i.e., software + hardware) system meets the given specifications, exhaustive simulation-based approaches (Hardware In the Loop Simulation, HILS) can be effectively used by first generating all relevant simulation scenarios (i.e., sequences of disturbances) and then actually simulating all of them (verification phase). When considering the whole verification activity, we see that the above mentioned verification phase is repeated until no error is found. Accordingly, in order to minimise the time taken by the whole verification activity, in each verification phase we should, ideally, start by simulating scenarios witnessing errors (counterexamples). Of course, to know beforehand the set of such scenarios is not feasible. In this paper we show how to select scenarios so as to minimise the Worst Case Expected Verification Tim
Formal Methods for Probabilistic Energy Models
The energy consumption that arises from the utilisation of information processing systems adds a significant contribution to environmental pollution and has a big share of operation costs. This entails that we need to find ways to reduce the energy consumption of such systems. When trying to save energy it is important to ensure that the utility (e.g., user experience) of a system is not unnecessarily degraded, requiring a careful trade-off analysis between the consumed energy and the resulting utility. Therefore, research on energy efficiency has become a very active and important research topic that concerns many different scientific areas, and is as well of interest for industrial companies.
The concept of quantiles is already well-known in mathematical statistics, but its benefits for the formal quantitative analysis of probabilistic systems have been noticed only recently. For instance, with the help of quantiles it is possible to reason about the minimal energy that is required to obtain a desired system behaviour in a satisfactory manner, e.g., a required user experience will be achieved with a sufficient probability. Quantiles also allow the determination of the maximal utility that can be achieved with a reasonable probability while staying within a given energy budget. As those examples illustrate important measures that are of interest when analysing energy-aware systems, it is clear that it is beneficial to extend formal analysis-methods with possibilities for the calculation of quantiles.
In this monograph, we will see how we can take advantage of those quantiles as an instrument for analysing the trade-off between energy and utility in the field of probabilistic model checking. Therefore, we present algorithms for their computation over Markovian models. We will further investigate different techniques in order to improve the computational performance of implementations of those algorithms. The main feature that enables those improvements takes advantage of the specific characteristics of the linear programs that need to be solved for the computation of quantiles. Those improved algorithms have been implemented and integrated into the well-known probabilistic model checker PRISM. The performance of this implementation is then demonstrated by means of different protocols with an emphasis on the trade-off between the consumed energy and the resulting utility. Since the introduced methods are not restricted to the case of an energy-utility analysis only, the proposed framework can be used for analysing the interplay of cost and its resulting benefit in general.:1 Introduction
1.1 Related work
1.2 Contribution and outline
2 Preliminaries
3 Reward-bounded reachability properties and quantiles
3.1 Essentials
3.2 Dualities
3.3 Upper-reward bounded quantiles
3.3.1 Precomputation
3.3.2 Computation scheme
3.3.3 Qualitative quantiles
3.4 Lower-reward bounded quantiles
3.4.1 Precomputation
3.4.2 Computation scheme
3.5 Energy-utility quantiles
3.6 Quantiles under side conditions
3.6.1 Upper reward bounds
3.6.2 Lower reward bounds
3.6.2.1 Maximal reachability probabilities
3.6.2.2 Minimal reachability probabilities
3.7 Reachability quantiles and continuous time
3.7.1 Dualities
4 Expectation Quantiles
4.1 Computation scheme
4.2 Arbitrary models
4.2.1 Existential expectation quantiles
4.2.2 Universal expectation quantiles
5 Implementation
5.1 Computation optimisations
5.1.1 Back propagation
5.1.2 Reward window
5.1.3 Topological sorting of zero-reward sub-MDPs
5.1.4 Parallel computations
5.1.5 Multi-thresholds
5.1.6 Multi-state solution methods
5.1.7 Storage for integer sets
5.1.8 Elimination of zero-reward self-loops
5.2 Integration in Prism
5.2.1 Computation of reward-bounded reachability probabilities
5.2.2 Computation of quantiles in CTMCs
6 Analysed Protocols
6.1 Prism Benchmark Suite
6.1.1 Self-Stabilising Protocol
6.1.2 Leader-Election Protocol
6.1.3 Randomised Consensus Shared Coin Protocol
6.2 Energy-Aware Protocols
6.2.1 Energy-Aware Job-Scheduling Protocol
6.2.1.1 Energy-Aware Job-Scheduling Protocol with side conditions
6.2.1.2 Energy-Aware Job-Scheduling Protocol and expectation quantiles
6.2.1.3 Multiple shared resources
6.2.2 Energy-Aware Bonding Network Device (eBond)
6.2.3 HAECubie Demonstrator
6.2.3.1 Operational behaviour of the protocol
6.2.3.2 Formal analysis
7 Conclusion
7.1 Classification
7.2 Future prospects
Bibliography
List of Figures
List of Table
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