Narrow Results

Decay of various quantities (return or survival probability, correlation functions) in time are the basis of a multitude of important and interesting phenomena in quantum physics, ranging from spectral properties, resonances, return and approach to equilibrium, to dynamical stability properties and irreversibility and the "arrow of time" in [Asymptotic Time Decay in Quantum Physics (World Scientific, 2013)].

In this review, we study several types of decay — decay in the average, decay in the L^p-sense, and pointwise decay — of the Fourier–Stieltjes transform of a measure, usually identified with the spectral measure, which appear naturally in different mathematical and physical settings. In particular, decay in the L^p-sense is related both to pointwise decay and to decay in the average and, from a physical standpoint, relates to a rigorous form of the time-energy uncertainty relation. Both decay on the average and in the L^p-sense are related to spectral properties, in particular, absolute continuity of the spectral measure. The study of pointwise decay for singular continuous measures (Rajchman measures) provides a bridge between ergodic theory, number theory and analysis, including the method of stationary phase. The theory is illustrated by some new results in the theory of sparse models.

Many multi-state systems settle on more than one operating levels and the elementary states having a common operating level can be treated as one. In this paper, one kind of such Markov repairable systems is introduced, which is named aggregated Markov repairable systems with multi-operating levels. In the system, the functioning states are lumped together according to their membership as a common operating level and each operating level is characterized by a performance rate. The systems degrade from a higher operating level to a lower one when no preventive maintenances (PMs) are performed. While the system is in some deteriorated operating levels that are easy to be recognized PMs are carried out. The PMs may be perfect or imperfect. If the system fails, the repairs may restore it to any of its operating levels. A multivariate semi-Markov process is build to describe performance properties of the system. Several reliability indices such as the availability, frequencies of repairs and failures are presented. Furthermore, the up time, the length of a cycle, the sojourn times in various operating levels and visiting numbers to them, the times that the system satisfies demands of customers and the output during a cycle are studied. Semi-Markov process theory, Laplace transform and matrix methods are employed in the study. A numerical example is given to illustrate the results in the paper. The impact of PM on the system is considered through the numerical illustration.

In this paper, we study a MAP/PH/1 queue with two classes of customers and discretionary priority. There are two stages of service for the low-priority customer. The server adopts the preemptive priority discipline at the first stage and adopts the nonpreemptive priority discipline at the second stage. Such a queuing system can be modeled into a quasi-birth-and-death (QBD) process. But there is no general solution for this QBD process since the generator matrix has a block structure with an infinite number of blocks and each block has infinite dimensions. We present an approach to derive the bound for the high-priority queue length. It guarantees that the probabilities of ignored states are within a given error bound, so that the system can be modeled into a QBD process where the block elements of the generator matrix have finite dimensions. The sojourn time distributions of both high and low priority customers are obtained. Some managerial insights are given after comparing the discretionary priority rule with the preemptive and nonpreemptive disciplines numerically.

In a two-state Markov chain with time periodic dynamics, we study path properties such as the sojourn time in one state between two consecutive jumps or the distribution of the first jump. This is done in order to exhibit a resonance interval and an optimal tuning rate interpreting the phenomenon of stochastic resonance through quality notions related with interspike intervals. We consider two cases representing the reduced dynamics of particles diffusing in time periodic potentials: Markov chains with piecewise constant periodic infinitesimal generators and Markov chains with time-continuous periodic generators.

This paper considers the analysis on network data flow of discrete-time queuing system. The system consists of single buffer and there serverrs with the same service function and different service rate. In the process of data transmission, when many input terminals send data to a middle note synchronously the waiting data have to queue in the buffer. We use fuzzy control theory to select suitable routes for the data so as to reduce the sojourn time and avoid network congestion. We give different simulations in terms of different conditions. Numerical examples are worked out which show the validity of the fuzzy controller.