We consider queuing systems where customers are not allowed to queue, instead of that they make repeated attempts, or retrials, in order to enter service after some time. We obtain the distribution of the number of retrials produced by a tagged customer, until he finds an available server. 相似文献
We propose a minimum mean absolute error linear interpolator (MMAELI), based on theL1 approach. A linear functional of the observed time series due to non-normal innovations is derived. The solution equation
for the coefficients of this linear functional is established in terms of the innovation series. It is found that information
implied in the innovation series is useful for the interpolation of missing values. The MMAELIs of the AR(1) model with innovations
following mixed normal andt distributions are studied in detail. The MMAELI also approximates the minimum mean squared error linear interpolator (MMSELI)
well in mean squared error but outperforms the MMSELI in mean absolute error. An application to a real series is presented.
Extensions to the general ARMA model and other time series models are discussed.
This research was supported by a CityU Research Grant and Natural Science Foundation of China. 相似文献
In this paper, we consider the weighted local polynomial calibration estimation and imputation estimation of a non-parametric function when the data are right censored and the censoring indicators are missing at random, and establish the asymptotic normality of these estimators. As their applications, we derive the weighted local linear calibration estimators and imputation estimations of the conditional distribution function, the conditional density function and the conditional quantile function, and investigate the asymptotic normality of these estimators. Finally, the simulation studies are conducted to illustrate the finite sample performance of the estimators. 相似文献
Let Ui = (Xi, Yi), i = 1, 2,…, n, be a random sample from a bivariate normal distribution with mean μ = (μx, μy) and covariance matrix . Let Xi, i = n + 1,…, N represent additional independent observations on the X population. Consider the hypothesis testing problem H0 : μ = 0 vs. H1 : μ ≠ 0. We prove that Hotelling's T2 test, which uses (Xi, Yi), i = 1, 2,…, n (and discards Xi, i = n + 1,…, N) is an admissible test. In addition, and from a practical point of view, the proof will enable us to identify the region of the parameter space where the T2-test cannot be beaten. A similar result is also proved for the problem of testing μx ? μy = 0. A Bayes test and other competitors which are similar tests are discussed. 相似文献
A fundamental principle of queueing theory isL=W (Little's law), which states that the time-average or expected time-stationary number of customers in a system is equal to the product of the arrival rate and the customer-average or expected customer-stationary time each customer spends in the system. This principle is now well known and frequently applied. However, in recent years there have been extensions, such as H=G and the continuous, distributional, ordinal and central-limit-theorem versions, which show that theL=W relation, when viewed properly, has much more power than was previously realized. Moreover, connections have been established between H=G and other fundamental relations, such as the rate conservation law and PASTA (Poisson arrivals see time averages), which show that there is a much greater unity in the overall theory than was previously realized. This paper provides a review.This paper is dedicated to the memory of our colleague Professor Peter Franken (1937–1989), who contributed greatly to the subject of this paper and to queueing theory more generally. 相似文献