摘要
设外界质点按泊松过程输入于一个可数集I^0=(1,2,…),质点一旦进入I^0后各自独立地按同一马氏过程规律作随机迁移运动;在给定的条件下,本文获得:系统的状态过程是马氏过程;对固定时间t>0,质点数目按空间配置形成泊松点过程且求出其极限分布;最后给出在排队网络系统(M/M/∞)的应用。
Let I= (1,2,…). Suppose that (1)there are particles input randomly at j∈I0, their numbers in (0,t) form a poisson processes A. (y) with intensity λf>0,A. (j)(j∈I0)are mutually indepent and ∑J∈IλJ<∞; (2) once the particles enter I then they move independently through I0 according to the transition law of a known Markov chain X0 and (3)the lifetimes of all particles are i·i·d. random variable independent of X0.Let φ denote the class of all finite subset of I0 and the Y. (i)denote the number of particles at time t.In the paper,it is proved that (i) the Yc=Yc(I)= (Yt(j),j∈I0 )is a Markov process, (ii) Fix t>0, is a poisson point process on I0 and find the limit distribution of the Kt(J)(t→∞). (iii) It is applied to obtain (M/M/@)m queue network when [I0 | =m<∞.
出处
《厦门大学学报（自然科学版）》
CAS
CSCD
北大核心
1992年第3期220-224,共5页
Journal of Xiamen University：Natural Science
基金
福建省科学基金
关键词
无穷质点系统
泊松点过程
马氏链
Infinite particle systems, Poisson point process, Markov chain, Queue network system
