We present a simple Markovian framework for modeling packet traffic with variability over several time scales. fitting procedure matching second-order properties of counts to that self-similar process. Our models essentially consist superpositions two-state Markov modulated Poisson processes (MMPPs). illustrate superposition four MMPPs suffices model behavior approach allows us fit additional descriptors while maintaining the counting use this match interarrival correlations.

K -means clustering is employed to identify recurrent delay patterns on a high traffic railway line north of Copenhagen, Denmark. The clusters behavioral in the very large (“big data”) datasets generated automatically and continuously by signal system. results reveal conditions where corrective actions are necessary, showing cases take place. Delay profiles change from timestamps compare different train runs partition set observations into groups similar elements. can discriminate affecting...

Abstract Decisions about the development of new marketed technologies or products invariably come with consequences for economy, society and environment. Environmental health risk assessment on one hand sustainability other are tools that offer different but complementary information such consequences. Conflicts synergies between two may arise when there trade-offs considerations specific risks safety versus long-term sustainability. There is a compelling case combined both risks, also in...

AbstractKnowing passenger numbers is important for the planning and operation of urban rail systems. Manual electronic counting systems (typically infrared or video) are expensive therefore entail small sample sizes. They usually count boarding alighting passengers, which means that errors in estimates total passengers propagate along train runs. Counting manual typically flow-dependent, making uncertainty a function volume. This paper presents new technique exploits weighing installed most...

This paper introduces the concept of a Quasi-Birth-and-Death process (QBD) with Rational Arrival Process (RAP) components. We use physical interpretation prediction RAP, developed by Asmussen and Bladt, develop an analysis that parallels traditional QBD. Further, we present algorithm for numerical evaluation matrix G. As example, consider two queues where arrival sequence service times are taken from dependent RAPs, not Markovian Processes.

In this paper, we propose a class of infinite-dimensional phase-type distributions with finitely many parameters as models for heavy tailed distributions. The finite-dimensional is dense in the on positive reals and may hence approximate any such distribution. We prove that formulas from renewal theory, particular attention to ruin probabilities, which are true common also hold case. provide algorithms calculating functionals interest density probability. It might be given distribution some...

We present an overview of predictive maintenance (PdM) in industrial operations, highlighting its evolution, benefits, challenges, and potential economic impact. It is assessed that there are considerable benefits associated with PdM but also practical implementation can prove difficult due to the uncertain application, need for advanced IT infrastructure as well expert personnel, and, perhaps most importantly, a lack failure-related data model training. conclude three case studies elaborate...

Abstract This paper characterizes irreducible phase-type representations for exponential distributions. Bean and Green (2000) gave a set of necessary sufficient conditions distribution with an generator matrix to be exponential. We extend these representations, we thus give characterization all consider the results in relation time-reversal distributions, PH-simplicity, algebraic degree distribution, applications results. In particular under which Coxian becomes exponential, construct...

Abstract In this article we consider the distributions of non-negative random vectors with a joint rational Laplace transform, i.e., fraction between two multi-dimensional polynomials. These are in univariate case known as matrix-exponential distributions, since their densities can be written linear combinations elements exponential matrix. For reason shall refer to multivariate transform (MVME). The marginal an MVME distributions. We prove characterization that states distribution is if and...

We present a modelling framework and fitting method for second order self-similar behaviour with the Markovian arrival process (MAP). The is based on to autocorrelation function of counts process. It shown that this algorithm it possible closely match over 3-5 time-scales 8-16 state MAPs very simple structure, i.e. superposition 3 4 interrupted Poisson processes (IPP) respectively seems work well entire range Hurst (1951) parameter.

In this article we use the concept of multivariate phase-type distributions to define a class bivariate exponential distributions. This has following three appealing properties. Firstly, may construct pair exponentially distributed random variables with any feasible correlation coefficient (also negative). Secondly, satisfies that linear combination (projection) marginal is distribution. The latter property partially important for development hypothesis testing in models. Finally, it easy...

Motivated by service levels in terms of the waiting-time distribution seen, for instance, call centers, we consider two models systems with a discipline that depends on waiting time. The first model deals single server continuously adapts its rate based time customer line. In second model, one queue is served primary which supplemented secondary when line exceeds threshold. Using level crossings process line, derive steady-state distributions both models. results are illustrated numerical examples.

This paper is concerned with statistical inference for both continuous and discrete phase-type distributions. We consider maximum likelihood estimation, where traditionally the expectation-maximization (EM) algorithm has been employed. Certain numerical aspects of this method are revised we provide an alternative dealing E-step. also compare EM to a direct Newton–Raphson optimization function. As one main contributions paper, formulae calculating Fisher information matrix approach. The...

We introduce a new approach to modelling queueing systems where the priority or routing of customers depends on time first customer has waited in queue. This past waiting line, W FIL , is used as primary variable for our approach. A Markov chain system states represent both number free servers and discrete approximation . allows us obtain distributions complex systems, such N-design scheme widely used, e.g., call centers with dynamic priorities.