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离散时间服务台可修的排队系统MAP/PH(PH/PH)/1 总被引:5,自引:0,他引:5
本文研究离散时间可修排队系统,其中顾客的输入过程为离散马尔可夫到达过程(MAP),服务台的寿命,服务台的顾客的服务时间和修理时间均为离散位相型(PH)变量,首先我们考虑广义服务过程,证明它是离散MAP,然后运用阵阵几何解理论,我们给出了系统的稳态队长分布和稳态等待时间分布,同时给出了系统的稳态可用度这一可靠性指标。 相似文献
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主要研究工作休假和休假中止的M/G/1排队系统,首先将对应于此系统的数学模型转化为抽象Cauchy问题,其次证明对应于此排队模型的主算子生成正压缩C0半群T(t),然后证明T(t)是局部等距的,最后证明此模型存在唯一的非负时间依赖解。 相似文献
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V. S. Koroliuk V. V. Koroliuk N. Limnios 《Methodology and Computing in Applied Probability》2009,11(2):201-209
We study asymptotic average and diffusion approximation schemes for semi-Markov queuing systems by a random evolution approach
and using compensating operator of the corresponding extended Markov renewal process. These results generalize Markov and
renewal flow queuing systems.
相似文献
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Sandeep Jain N. R. Srinivasa Raghavan 《Central European Journal of Operations Research》2009,17(1):95-110
This paper presents stylized models for conducting performance analysis of the manufacturing supply chain network (SCN) in
a stochastic setting for batch ordering. We use queueing models to capture the behavior of SCN. The analysis is clubbed with
an inventory optimization model, which can be used for designing inventory policies . In the first case, we model one manufacturer
with one warehouse, which supplies to various retailers. We determine the optimal inventory level at the warehouse that minimizes
total expected cost of carrying inventory, back order cost associated with serving orders in the backlog queue, and ordering
cost. In the second model we impose service level constraint in terms of fill rate (probability an order is filled from stock
at warehouse), assuming that customers do not balk from the system. We present several numerical examples to illustrate the
model and to illustrate its various features. In the third case, we extend the model to a three-echelon inventory model which
explicitly considers the logistics process. 相似文献
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N. K. Bakirov M. V. Snachev V. E. Bening 《Moscow University Computational Mathematics and Cybernetics》2009,33(1):32-37
An exact formula for the mean number of claims served by a one-channel queuing system (QS) with rejections on a given time interval is obtained, which makes it possible, in particular, to calculate exactly the QS efficiency indexes on an arbitrary time interval. 相似文献
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��Recently, big data, could computing and internet of things
provide some new information technologies for organization and management of complex
systems, and they have caused multifaceted changes on organization framework and
operations mechanism of enterprises. Based on this, we first construct a new stochastic
model for a big data driven large-scale bike-sharing system, which expresses the
important role played by big data, and describes the operations mechanism of the
large-scale bike-sharing system, and specifically, the rebalancing of bikes in various
stations in terms of trucks. Then, we present a mean-field limit theory, which is
applied to analyzing the big data driven large-scale bike-sharing system, including
establishing a time-inhomogeneous queueing system by means of the mean field theory,
and setting up the mean-field equations through the time-inhomogeneous queueing system;
providing an empirical measure process by means of a nonlinear birth-death process,
giving algorithms for computing the fixed point in terms of a segmented structural
birth-death processes, and computing the average number of bikes in each station; and
providing numerical examples to analyze how the steady average number of bikes in each
station depends on some key parameters of the bike-sharing system. Using these results,
this paper analyzes physical effect of big data on performance of the large-scale
bike-sharing. Therefore, this paper gives a promising research direction of stochastic
model in the study of large-scale bike-sharing systems. 相似文献
10.
Saralees Nadarajah 《随机分析与应用》2013,31(3):526-536
Abstract Transition probabilities of embedded Markov chain for single-server queues are considered when the distribution of the inter-arrival time or that of the service time is specified. A comprehensive collection of formulas is derived for the transition probabilities, covering some seventeen flexible families. The corresponding estimation procedures are also derived by the method of moments. It is expected that this work could serve as a useful reference for the modeling of queuing systems with embedded Markov chains. 相似文献