到达环境可变的M/M/1排队系统  

M/M/1 Queuing System with Variable Environment

作　　者：李冰冰 吕平 LI Bingbing;LYU Ping(School of Mathematics,Hangzhou Normal University,Hangzhou 311121,China)

机构地区：[1]杭州师范大学数学学院,浙江杭州311121

出　　处：《杭州师范大学学报（自然科学版）》2024年第2期190-196,共7页Journal of Hangzhou Normal University(Natural Science Edition)

基　　金：杭州师范大学教育学院省优势特色学科培育项目(9JYXK023);杭州师范大学附属医院院级科研基金项目(2021YN2021086).

摘　　要：文章在经典的M/M/1排队系统模型下增加了一个可变环境因素,即顾客的到达环境A、B可以相互转化,到达时间参数将与环境同变化,利用拉普拉斯变换求环境A、B的瞬时概率,再利用概率母函数得出系统的队长分布、等待队长分布和平均队长.In this paper,a variable environmental factor was added to the classic M/M/1 queuing system model.The arrival environment A and B of customers could be transformed into each other,and the parameters of arrival time could be changed with the environment.The instantaneous probability of environment A and B were calculated by Laplace Transform,and the queue length distribution,waiting queue length distribution and average queue length of the system were obtained by probability generating function.

关 键 词：可变环境 瞬时概率 平衡方程 队长 

分 类 号：O212.6[理学—概率论与数理统计]