Extended generator and associated martingales for M/G/1 retrial queue with classical retrial policy and general retrial times

A retrial queue with classical retrial policy, where each blocked customer in the orbit retries for service, and general retrial times is modeled by a piecewise deterministic Markov process (PDMP). From the extended generator of the PDMP of the retrial queue, we derive the associated martingales. These results are used to derive the conditional expected number of customers in the orbit in the transient regime.

GENERATION OF WIND-SERIES USING CUMULATIVE PROBABILITY WIND TRANSITION MATRIX-A FIRST ORDER MARKOV PROCESS

One appl ica tion ofihe cuuiulative probability wind tra ns ition matrix is 10 determine the variousprnhal"lk ....i n,1....-ries th ai mi1;\'hl occur. during the period fur which offs hore oilspil1 risk is 10 be analysed. Du ring th is;Inalpli ~ ""'t" haw to gene la te different probable "';110.1 conditions at d iff erent Instances oftime. OnC" ur lhe method s tosiumlutcthe nl lhlu m wind behaviourt hrough lime. is 10 U ~ h istorical wi nd da ta presented in the fon n of wi nd Ira n...ilion lItutrix. Th is pa per h it;hli.::hts th r- 1llC'l h(Klulog)' and use ofthe cumulat ive probability v.i nd transition matrix. in~t'lh"ral ill~ 1111' ,Iifferl:'nl proba ble wind-series.

Optimising the Preventive Maintenance Interval Using a Semi-Markov Process, Z-Transform, and Finite Planning Horizon

This chapter uses a semi-Markov process and the z transform to find the optimal preventive maintenance interval when dealing with maintenance decision making for a finite time planning horizon. The result is a method that can be easily implemented to assets for which a Weibull reliability analysis exists. The suggested preventive interval formulation is simple and practical. The requirements to apply this simple formula are related to the existence of asset´s reliability data as well as cost/rewards that the assets have when remaining or transitioning to a given state. The application of this method can be very straightforward, and the tool can become a good decision support tool allowing “what if” analysis for different time horizon and maintenance policies.

Fast reactions with non-interacting species in stochastic reaction networks

<abstract><p>We consider stochastic reaction networks modeled by continuous-time Markov chains. Such reaction networks often contain many reactions, potentially occurring at different time scales, and have unknown parameters (kinetic rates, total amounts). This makes their analysis complex. We examine stochastic reaction networks with non-interacting species that often appear in examples of interest (e.g. in the two-substrate Michaelis Menten mechanism). Non-interacting species typically appear as intermediate (or transient) chemical complexes that are depleted at a fast rate. We embed the Markov process of the reaction network into a one-parameter family under a two time-scale approach, such that molecules of non-interacting species are degraded fast. We derive simplified reaction networks where the non-interacting species are eliminated and that approximate the scaled Markov process in the limit as the parameter becomes small. Then, we derive sufficient conditions for such reductions based on the reaction network structure for both homogeneous and time-varying stochastic settings, and study examples and properties of the reduction.</p></abstract>

Comparative Analysis of Pitching Prediction Algorithms

Two algorithms are described in the paper; one of them is the Kalman filter, which is based on the use of a pitching mathematical model, and the second uses a neural network in which the model is considered unknown. The results of the algorithms sensitivity analysis to the parameters of the model and its influence on the potential accuracy of prediction are presented. A stationary narrow-band second-order Markov process is used as a model of the ship pitching, which was used to form the input signal of the algorithms. Also, the results of the algorithms simulation in predicting real data are presented.

The Kishony Mega-Plate Experiment, a Markov Process

A correct understanding of the DNA evolution of drug resistance is critical in developing strategies for suppressing and preventing this process. The Kishony Mega-Plate Experiment demonstrates this important phenomenon that occurs in the practice of medicine, that of the evolution of drug-resistance. The evolutionary process which the bacteria in this experiment are doing is called a Markov Process or Markov Chain. Understanding this process enables clinicians and researchers to predict the evolution of drug-resistance and develop strategies to prevent this process. This paper will show how to apply the Markov Chain model of DNA evolution to the Kishony Mega-Plate Experiment and why the experiment behaves the way it does by contrasting the Jukes-Cantor model of DNA evolution (a stationary model) with a modification of the JukesCantor model that makes it a non-stationary, non-equilibrium Markov Chain. The numerical behaviors of the stationary and non-stationary models are compared. What this analysis shows is that DNA evolution is a non-stationary, non-equilibrium process and that by using the correct non-stationary, non-equilibrium model that one can simulate and predict the behavior of real evolutionary examples and that these analytical tools can give the clinician guidance on how to use antimicrobial selection pressures for treating infectious diseases. This in turn can help reduce the numbers and costs of hospitalization for sepsis, pneumonia and other infectious diseases.