随机数生成

本文讨论最有用的给定概率密度函数情形下的随机数生成问题,借助几何概率描述舍选法。     

Optimal backup of data bases: A statistical investigation

A stochastic model is defined for the occurrence for catastrophic errors in the maintenance of a data base. Under the assumption that backup copies are taken at regular intervals, a function is defined giving the cost of maintaining the data base at an operative level. Dependent upon the exogeneous parameters of the model, the spacing between dumps that gives the least expected cost per time unit is derived.     

均匀递归树的去点问题(英文)

本文研究了均匀递归树的去点过程.对于任意给定的点i,利用矩母函数,给出了对应子树顶点数的准确分布,推广了A.Panholzer所做的工作.     

A 3-queue polling system with join the shortest-serve the longest policy

In 1987, J.W. Cohen analyzed the so-called Serve the Longest Queue (SLQ) queueing system, where a single server attends two non-symmetric $M/G/1$-type queues, exercising a non-preemptive priority switching policy. Cohen further analyzed in 1998 a non-symmetric 2-queue Markovian system, where newly arriving customers follow the Join the Shortest Queue (JSQ) discipline. The current paper generalizes and extends Cohen’s works by studying a combined JSQ–SLQ model, and by broadening the scope of analysis to a non-symmetric 3-queue system, where arriving customers follow the JSQ strategy and a single server exercises the preemptive priority SLQ discipline. The system states’ multi-dimensional probability distribution function is derived while applying a non-conventional representation of the underlying process’s state-space. The analysis combines both Probability Generating Functions and Matrix Geometric methodologies. It is shown that the joint JSQ–SLQ operating policy achieves extremely well the goal of balancing between queue sizes. This is emphasized when calculating the Gini Index associated with the differences between mean queue sizes: the value of the coefficient is close to zero. Extensive numerical results are presented.     

On binomial thinning and mixing

In this paper we consider the notions of binomial thinning, binomial mixing, their generalizations, certain interplay between them, associated limit theorems and provide various examples.