摘要
本文考虑带有多级适应性休假的Geo/G/1离散时间排队系统,其中在服务员休假期间到达的顾客以概率(0<θ≤1)进入系统.运用更新过程理论和全概率分解技术,从任意初始状态出发,获得时刻n^+处队长瞬态分布的z-变换的递推表达式,并在瞬时性质分析的基础上,分别得到时刻n^+;n;n^-处队长稳态分布的递推公式,所得结果进一步表明稳态队长不再具有随机分解结构.最后通过数值实例,讨论队长稳态分布对系统参数的敏感性,并阐述了队长稳态分布的递推公式在系统容量优化设计中的重要应用价值.
This paper considers a discrete time Geo/G/1 queue with multiple adaptive vacations where the customers who arrive during server vacations enter the system with probability(0<θ≤1).Using renewal process theory and total probability decomposition technique,from the beginning of arbitrary initial state,the z-transform recursive expressions of the transient queue length distribution at time epoch n+are obtained.Based on the transient analysis,the explicit recursive formulae of the steady state queue length distribution at time epochs n^-;n and n+are derived,respectively.Furthermore,the results obtained in this paper indicate that the equilibrium queue length distribution no longer follows the stochastic decomposition structure.Finally,numerical results are offered to discuss the sensitivity of the steady state queue length distribution towards system parameters,and illustrate the significant application value of the recursive formulae for the steady state queue length distribution in the system capacity optimum design.
作者
魏瑛源
唐应辉
余玅妙
WEI Yingyuan;TANG Yinghui;YU Miaomiao(School of Mathematics&Statistics,Hexi University,Zhangye 734000,China;School of Mathematics&Software Science,Sichuan Normal University,Chengdu 610066,China;Sichuan University of Science&Engineering,Zigong 643000,China)
出处
《应用数学》
CSCD
北大核心
2020年第1期186-201,共16页
Mathematica Applicata
基金
Supported by the National Natural Science Foundation of China(71571127)
关键词
离散时间Geo/G/1排队
多级适应性休假
θ-进入规则
队长分布
全概率分解技术
系统容量的优化设计
Discrete time Geo/G/1 queue
Multiple adaptive vacation
θ-entering discipline
Queue length distribution
Total probability decomposition technique
System capacity optimum design
