Published in Medical research archives
Aims: Accurate estimation of the three key parameters (sensitivity, time duration in disease-free state and sojourn time in preclinical state) in cancer screening are critical. Likelihood method with a new link function was applied to the Health Insurance Plan of Greater New York (HIP) breast cancer screening data, to estimate the onset age of prec...
Published in Medical research archives
Aims: The aim of this study is to provide statistical inference of the sojourn time and the transition probability from the disease free to the preclinical state of lung cancer for male and female smokers using lung cancer data from the National Lung Screening Trial (NLST). Materials and Methods: We applied a likelihood function to the lung cancer ...
Published in Automation and Remote Control
Consideration was given to the two-server queuing system with resequencing buffer and customer resequencing to which a Markov customer flow arrives. The resequencing buffer has also an infinite capacity. The time of customer servicing by each server has the same phasetype distribution. A recurrent algorithm was proposed for calculation of the joint...
Published in Annales Henri Poincaré
One manifestation of quantum resonances is a large sojourn time, or autocorrelation, for states which are initially localized. We elaborate on Lavine’s time-energy uncertainty principle and give an estimate on the sojourn time. For the case of perturbed embedded eigenstates the bound is explicit and involves Fermi’s Golden Rule. It is valid for a v...
Published in Annales Henri Poincaré
We study the aging behavior of a truncated version of the Random Energy Model evolving under Metropolis dynamics. We prove that the natural time-time correlation function defined through the overlap function converges to an arcsine law distribution function, almost surely in the random environment and in the full range of time scales and temperatur...
Published in Journal of Mathematical Sciences
This article focuses on queuing systems with doubly stochastic Poisson regenerative input flow and an infinite number of servers. Service times have the heavy-tailed distribution. The analogs of the law of large numbers and the central limit theorem for the number of occupied servers are obtained. These theorems follow from results for systems with...
Published in Distributed Computing
Hajek and Zhu (Stoch Syst 1(2):246–273, 2011) recently showed that the BitTorrent protocol can become unstable when peers depart immediately after downloading all pieces of a file. In light of this result, Zhou et al. (2011) propose bundling swarms together, allowing peers to exchange pieces across different swarms, and claim that such “universal s...
Published in Problems of Information Transmission
We consider a multiserver queueing system without buffer, with customers of two types, operating in a random environment. The system is fed by a marked Markovian arrival process which depends on the environment state. Customers of the first type have absolute priority over customers of the second type. Instantaneous service rates are piecewise cons...
Published in Automation and Remote Control
We consider an exponential queueing network with single-line nodes that differs from a Jackson network only in that the time claims sojourn in the system (waiting time for the servicing) at the network’s nodes is limited by an exponentially distributed random value. Claims serviced at nodes and claims that have not finished servicing (that exceeded...
Published in Journal of Mathematical Sciences
It is known that the occupation time random field for a homogeneous Markov chain has the Markov property. We study the possibility of generalizing this result for inhomogeneous chains. Consider a process that is a homogeneous Markov chain with transition probability density Q1 up to time T and with density Q2 after T, where Q1 ≠ Q2. It turns out th...
