Importance of verifying queue model assumptions before planning with simulation software

This case study uses empirical data gathered at an Australian refinery to verify the assumptions for queue distributions before using special-purpose software to plan the off-road-truck hauling of titanium dioxide to a refinery (n = 773). Easy-to-use spreadsheet software is utilized to verify assumptions for queue models. Managers are able to make decisions based on economic implications of queue models to avoid making costly planning mistakes. Analysts can use nonparametric hypothesis-testing techniques to verify distribution assumptions for optimization without having to write hard-to-maintain and complex algebraic linear equations or nonlinear search routines.     

带启动时间的N-策略Geo/G/1排队系统的队长分布及容量的优化设计

考虑带启动时间的N-策略离散时间Geo/G/1排队系统,使用全概率分解技术,从任意初始状态出发,研究了队长的瞬态和稳态性质,推导出了在任意时刻n瞬态队长分布的z -变换的递推表达式、稳态队长分布的递推表达式和附加队长分布的表达式,并获得稳态队长的随机分解结果.最后,通过数值实例,讨论了稳态队长分布对系统参数的敏感性,并阐述了获得便于计算的稳态队长分布的表达式在系统容量的优化设计中的重要应用价值.     

GI/G/1排队系统队长的强大数定律和中心极限定理

本文首先证明当服务强度小于1时,GI/G/1排队系统的队长是一个特殊的马尔可夫骨架过程——正常返的Doob骨架过程,然后运用马尔可夫骨架过程的强大数定律和中心极限定理等重要结果,给出了队长的累积过程的期望和方差,并给出了该累积过程满足强大数定律和中心极限定理的充分条件。     

多通道Assembly-like排队系统的强逼近

借助于强逼近理论和修正系统，本文较为详细地研究了多路到达、多服务台Ａｓｓｅｍｂｌｙ－ｌｉｋｅ排队系统，得到了队长过程、离去过程、负荷和虚等待时间过程的强逼近定理。     

Admission control of a service station when the arrivals are internal

All studies in the admission control of a service station make decisions at arrival epochs. When arrivals are internal and are rejected from a queue, the rejected jobs have to be routed to other stations in the system. However the system will not know whether a job will be admitted to a queue or not until its arrival epoch to that queue. Thus, the system has to react dynamically and agilely to the decisions made at a specific queue and may try several queues before finding a queue that admits the job. This paper remedies these difficulties by changing the decision epochs of the admission control from arrival epochs to departure epochs with the actions of switching (keeping) the arrival stream on or off. Thus upstream stations will have information on the admission status of their downstream stations all the time. It is proved that the optimal policy for this revised admission control system is of control limit type for an M/G/1 queue. Comparisons of the optimal values and optimal policies for the admission controls made at arrival epochs and at departure epochs are included in the paper.     

Logarithmic asymptotics for a single-server processing distinguishable sources

We consider a single-server first-in-first-out queue fed by a finite number of distinct sources of jobs. For a large class of short-range dependent and light-tailed distributed job processes, using functional large deviation techniques we prove a large deviation principle and logarithmic asymptotics for the joint waiting time and queue lengths distribution. We identify the paths that are most likely to lead to the rare events of large waiting times and long queue lengths. A number of examples are presented to illustrate salient features of the results.      

N-策略单重休假M/G/1排队系统的队长分布

本文考虑N-策略单重休假M/G/1排队系统,通过引进"服务员忙期"和使用全概率分解技术,从任意初始状态出发,研究了队长的瞬态分布和稳态分布,首次导出了在任意时刻t瞬态队长分布的L变换的递推表达式和稳态队长分布的递推表达式,以及平稳队长的随机分解.特别地,通过本文可直接获得一些特殊排队系统相应的结果.     

Analysis of cyclic queueing networks with parallelism and vacation

The aim of this paper is to improve the machine interference model with vacation to deal with more recent problems of the communication area. To this scope the model is extended to include parallelism in the vacation station. The underlying Markov process is analyzed and a state arrangement is found that yields an efficient matrix-analytic technique that substantially lowers down the time- and space-complexity of standard methods. A numerical example of the method effectiveness is presented, and an example of resource allocation is introduced that finds applications in the QoS management of wireless networks. The author is thankful to the anonymous referees for the improvements their comments have earned to the quality of the presentation and to the completeness of the paper. The author is thankful to Giuseppe Iazeolla, whose careful reading of the original draft of this paper led to significant improvements in its overall quality. This work was partially supported by funds from the FIRB project “Performance Evaluation of Complex Systems: Techniques Methodologies and Tools” and by the University of Roma TorVergata project on High Performance ICT Platforms.     

一个具有随机丢弃分组机制且分组成批到达的GI~X/M/1/N排队系统

利用排队论中输入流稀疏化的方法,在标准的GIX/M/1/N排队系统中嵌入网络交换设备随机丢弃分组的机制,建立了一个具有随机丢弃分组机制的扩充的GIX/M/1/N排队系统,并讨论了该排队系统的分组丢失率、系统利用率、队列长度的均值/方差、平均等待时间等性能评价指标.