N-策略与Min(N,V)-策略的M/G/1/∞排队系统等待时间的随机分解结构

唐应辉, 兰绍军

系统工程理论与实践 ›› 2016, Vol. 36 ›› Issue (1) : 174-183.

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系统工程理论与实践 ›› 2016, Vol. 36 ›› Issue (1) : 174-183. DOI: 10.12011/1000-6788(2016)01-0174-10
论文

N-策略与Min(N,V)-策略的M/G/1/∞排队系统等待时间的随机分解结构

    唐应辉1,2, 兰绍军1
作者信息 +

The stochastic decomposition structure of the waiting time for M/G/1/∞ queue with N-policy and Min(N,V)-policy

    TANG Yinghui1,2, LAN Shaojun1
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摘要

在一些关于 N- 策略休假的 M/G/1/∞ 排队模型研究中, 由于顾客的等待时间与该顾客到达时刻以后的输入间隔时间不再独立, 因此对顾客的稳态等待时间分布的讨论较为困难, 更多是集中在系统的稳态队长和附加队长的讨论上, 很少有文献讨论顾客的稳态等待时间及其随机分解. 本文首先考虑经典 N- 策略休假的 M/G/1/∞ 排队系统, 讨论了顾客的稳态等待时间分布, 给出了顾客的稳态等待时间的随机分解结果和顾客的附加延迟时间分布的显式表达式, 同时, 指出了已有结果的错误. 其次, 我们考虑在多重休假和单重休假下具有 Min(N,V)- 策略控制的 M/G/1/∞ 排队系统, 给出了顾客的稳态等待时间的随机分解结果, 获得了顾客的平均稳态等待时间和平均附加延迟时间表达式. 特别地, 通过本文可直接获得一些特殊排队系统的相应结果.

Abstract

In some studies concerning M/G/1/∞ queueing models with N-policy, since the waiting time for a customer arriving during a server off-duty period is no longer independent of the inter-arrival times of customers arriving later, it is difficult to investigate the distribution of equilibrium waiting time, and considerable effort is devoted to study the steady-state queue length and additional queue length of queueing system, while there is relatively little work done on the stationary waiting time and its stochastic decomposition. Due to the fact, in this paper we firstly treat the classical N-policy M/G/1/∞ queueing system. We study the waiting time distribution in equilibrium, and present the stochastic decomposition result of steady-state waiting time as well as the explicit expression for the distribution of additional delay time. Meanwhile, some errors on corresponding results in existed references are pointed out. Further, we consider the M/G/1/∞ queueing systems with multiple server vacations and single server vacation under Min(N,V)-policy. By similar analytical method, we not only obtain the stochastic decomposition result of equilibrium waiting time but also derive the formulas for the mean stationary waiting time and mean additional delay time. Especially, some corresponding results for some special queueing systems can be directly obtained on the basis of the results provided in this paper.

关键词

N- 策略和 Min(N / V)- 策略 / M/G/1/∞ 排队 / 稳态等待时间 / 附加延迟时间 / 随机分解

Key words

N-policy and Min(N,V)-policy / M/G/1/∞ queue / steady-state waiting time / additional delay time / stochastic decomposition

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唐应辉 , 兰绍军. N-策略与Min(N,V)-策略的M/G/1/∞排队系统等待时间的随机分解结构. 系统工程理论与实践, 2016, 36(1): 174-183 https://doi.org/10.12011/1000-6788(2016)01-0174-10
TANG Yinghui , LAN Shaojun. The stochastic decomposition structure of the waiting time for M/G/1/∞ queue with N-policy and Min(N,V)-policy. Systems Engineering - Theory & Practice, 2016, 36(1): 174-183 https://doi.org/10.12011/1000-6788(2016)01-0174-10
中图分类号： O226    O213.2   

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基金

国家自然科学基金(71171138, 71571127)
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