ON SOME PROPERTIES OF POISSON PROCESSES

The Poisson process,i.e.,the simple stream,is defined by Khintchine as a stationary,orderlyand finite stream without after-effects.A necessary and sufficient condition for a stream to be asimple stream is that the interarrival times are independent random variables with identicalexponential distributions.This paper gives a simple and rigorous proof of the necessary and sufficientcondition,and discusses the other necessary and sufficient conditions for a renewal process to be aPoisson process.     

MATCHED QUEUEING SYSTEMS WITH A DOUBLE INPUT

In this paper, we study the matched queueing system with a double input, MoM/PH/1,where the two inputs are two independent Poisson processes, and the service time is of PH-distribution.The L.S. transforms and the expectations of the distributions of occupation time and virtual waiting time of the type-Ⅰ customer are derived.The probability that the server is working, the mean non-idle period, and the mean busy period are also derived. The related algorithms are given with numerical results.     

广义标准系统的比较与连续性

本文讨论了不同随机服务系统的队长、等待时间、忙期内服务的顾客数等数量指标的比较问题,并利用这些比较的结果研究了随机服务系统的某种类型的连续性。