Study on the Departure Process of Discrete-TimeGeo/G/1Queue with Randomized Vacations

This paper presents an analysis of the departure process of a discrete-timeGeo/G/1queue with randomized vacations. By using probability decomposition techniques and renewal process, the expression of expected number of departures during time interval(0+,n+]is derived. The relation among departure process, server state process, and service renewal process is obtained. The relation displays the decomposition characteristic of the departure process. Furthermore, the approximate expansion of the expected number of departures is gained. Since the departure process also often corresponds to an arrival process for a downstream queue in queueing network, it is hoped that the results obtained in this paper may provide useful information for queueing network.

ARE QUANTUM CORRELATIONS GENUINELY QUANTUM?

It is shown that the probabilities for the spin singlet can be reproduced through classical resources, with no communication between the distant parties, by using merely shared (pseudo-)randomness. If the parties are conscious beings aware of both the hidden-variables and the random mechanism, then one has a conspiracy. If the parties are aware of only the random variables, they may be induced to believe that they are able to send instantaneous information to one another. It is also possible to reproduce the correlations at the price of reducing the detection efficiency. It is further demonstrated that the same probability decomposition could be realized through action-at-a-distance, provided it existed.

A New Concept for Assessing System Reliability Based on Probability Decomposition Method

In fault tree analysis, the system failure probability and the component importance measures cannot totally include the contribution of all the component existing states to system reliability. It is for this reason that an ‘equivalent’ failure probability concept is proposed. First, the system existing states are analyzed by probability decomposition method. Then Markov chain method and the expectation theory are used to calculate the expected working number resulting in system failure. And the system equivalent failure probability is finally attained. Analysis shows that: (1) equivalent failure probability not only includes the contribution of critical states of component to system reliability, but also the non-critical states of component are considered; and (2) it may provide a thorough assessment of system reliability and is useful for reliability design.