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The importance of the order two Markovian arrival process (MAP(2)) comes from its compactness, serving either as arrival or service process in applications, and from the nice properties which are not available for higher order MAPs. E.g., for order two processes the acyclic MAP(2) (AMAP(2)), the MAP(2) and the order two matrix exponential process (MEP(2)) are equivalent. Additionally, MAP(2) processes...
The adequate modeling of input processes often requires that correlation is taken into account and is a key issue in building realistic simulation models. In analytical modeling Markovian Arrival Processes (MAPs) are commonly used to describe correlated arrivals, whereas for simulation often ARMA/ARTA-based models are in use. Determining the parameters for the latter input models is well-known whereas...
Fitting of the parameters of a Phase Type (PH) distribution or a Markovian Arrival Process (MAP) according to some quantities of measured data streams is still a challenge. This paper presents a new approach which computes in two steps for a set of moments and joint moments for an acyclic PH distribution that is expanded into a MAP. In contrast to other known approaches, parameters are computed to...
Exact product form solutions have been found for several classes of stochastic models including some networks of stochastic automata or communicating Markov chains. In this paper a theory of approximate product forms is presented. The idea is to define an approximate product form solution as a Kronecker product of vectors that minimizes the Euclidean norm of the residual vector for arbitrary networks...
The representation of general distributions or measured data by phase-type distributions is an important and nontrivial task in analytical modeling. Although a large number of different methods for fitting parameters of phase-type distributions to data traces exist, many approaches lack efficiency and numerical stability. In this paper, a novel approach is presented that fits a restricted class of...
Markov models are useful in the performance and dependability assessment of systems to obtain quantitative information that helps in making design decisions. The many known analysis techniques can be partitioned into approximate and exact techniques, where the former can be usually applied with limited effort but unknown precision and the latter give exact results but for the price of a computationally...
Stochastic orders can be applied to Markov reward models and used to aggregate models, while introducing a bounded error. Aggregation reduces the number of states in a model, mitigating the effect of the state-space explosion and enabling the wider use of Markov reward models. Existing aggregation techniques based upon stochastic orders are limited by a combination of strong requirements on the structure...
Path-based techniques make the analysis of very large Markov models feasible by trading off high computational complexity for low space complexity. Often, a drawback in these techniques is that they have to evaluate many paths in order to compute reasonably tight bounds on the exact solutions of the models. In this paper, we present a path composition algorithm to speed up path evaluation significantly...
In this paper we present an algorithm of the EM-type that performs fitting of PH-distributions with a given number of states to empirical distribution. In contrast to known approaches, the algorithm first generates a discretized representation of the observed data and then performs the fitting. In this way the algorithm is more efficient than other known EM-type methods. By an appropriate discretization,...
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