Nihal Pekergin

An Algorithmic Approach to Stochastic Bounds

We present a new methodology based on the stochastic ordering, algorithmic derivation of simpler Markov chains and numerical analysis of these chains. The performance indices defined by reward functions are stochastically bounded by reward functions computed on much simpler or smaller Markov chains. This leads to an important reduction on numerical complexity. Stochastic bounds are a promising method to analyze QoS requirements. Indeed it is sufficient to prove that a bound of the real performance satisfies the guarantee.

COSMOS: A Statistical Model Checker for the Hybrid Automata Stochastic Logic

This tool paper introduces \cosmos, a statistical model checker for the Hybrid Automata Stochastic Logic (HASL). HASL employs Linear Hybrid Automata (LHA), a generalization of Deterministic Timed Automata (DTA), to describe relevant execution paths of a Discrete Event Stochastic Process (DESP), a class of stochastic models which includes, but is not limited to, Markov chains. As a result HASL verification turns out to be a unifying framework where sophisticated temporal reasoning is naturally blended with elaborate reward-based analysis. COSMOS takes as input a DESP (described in terms of a Generalized Stochastic Petri Net), an LHA and an expression

An open tool to compute stochastic bounds on steady-state distributions and rewards

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Stochastic performance bounds by state space reduction

representing the quantity to be estimated. It returns a confidence interval estimation of

Model Checking of Continuous-Time Markov Chains by Closed-Form Bounding Distributions

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TRANSFORMING STOCHASTIC MATRICES FOR STOCHASTIC COMPARISON WITH THE ST-ORDER

. COSMOS is written in C++ and is freely available to the research community.

Conditional steady-state bounds for a subset of states in Markov chains

We present X-Bounds, a new tool to implement a methodology based on stochastic ordering, algorithmic derivation of simpler Markov chains and numerical analysis of these chains. The performance indices defined by reward functions are stochastically bounded by reward functions computed on much simpler or smaller Markov chains obtained after aggregation or simplification. This leads to an important reduction on numerical complexity. Typically, chains are ten times smaller and the accuracy may be good enough.

Stochastic model checking with stochastic comparison

In this work, we present a methodology to derive stochastic bounds on discrete-time Markov chains. It is well known that the state space explosion problem of Markovian models may make them numerically intractable. We propose to evaluate bounding models with reduced size state spaces, in order to be able to analyze considered systems for larger values of parameters. Moreover, these bounding models are comparable in the sense of sample-path (strong) ordering with the underlying model. Obviously, this method does not provide exact values, however, it has the following advantages: the errors are stochastically bounded, and it is suitable to analyze transient behaviors, and the stationary ones, as well. We present how this methodology may be applied to evaluate cell loss rates in ATM switches.

CLOSED-FORM STOCHASTIC BOUNDS ON THE STATIONARY DISTRIBUTION OF MARKOV CHAINS

Continuous-time Markov chains (CTMCs) have been largely applied with combination of high-level model specification techniques as performance evaluation and dependability, reliability analysis models for computer and communication systems. These models can be complemented by probabilistic model checking formalisms based on temporal logic to specify the guarantees on the measures of interest. We consider in this paper continuous stochastic logic (CSL) which lets to express real-time probabilistic properties on CTMCs. It has been shown that the CSL operators can be checked by means of transient or steady-state analysis of the underlying CTMC. Since models are checked to see if the considered measures are guaranteed or not, bounding techniques are useful in probabilistic model checking. We propose to apply stochastic comparison technique to construct bounding models having a special structure which provides closed-form solutions to compute both transient and steady-state distributions. We present an algorithm to provide rapid model checking by means of these closed-form bounding distributions. Obviously, bounding distributions may not let to decide if the underlying model meets the probability thresholds or not. However in the case where the model can be checked by the proposed method, we gain significantly in time and memory complexity

Stochastic bounds and histograms for network performance analysis

We present a transformation for stochastic matrices and analyze the effects of using it in stochastic comparison with the strong stochastic (st) order. We show that unless the given stochastic matrix is row diagonally dominant, the transformed matrix provides better st bounds on the steady state probability distribution.