Tables for M/G/c queuing systems with phase-type service

Currently much research is done on the development of simple approximations for complex queuing systems. This practically important research is usually hampered by the fact that no exact results are available for a thorough testing of the approximations. In this paper we give for several M/G/c queuing systems with phase-type service the exact values for both the delay probability and the first two moments of the queuing time. These tables considerably extend the widely used Hillier-Lo tables which only consider Erlangian service and small values for the number of servers. The aim of the publication of our tables is to supply much needed test material to the research community and in this way to contribute to further progress in the research on queuing approximations. We present the result of the testing of several existing approximations. Also, the tables provide the practitioner with numerical results useful to design queuing systems.     

Die nicht signalgesteuerte Nebenstraßenzufahrt als verallgemeinertes M/G/1-Warteschlangensystem

This paper deals with the queuing of side-street vehicles at high-priority traffic streams of unsignalized intersections. Among other results there are obtained the solutions for the mean delay of a low-priority vehicle and the probability of the waiting system being empty. In doing so, the system under study is reduced to a M/G/1 queuing system, where the service times of those vehicles that have to queue are different from the service times of those cars that arrive to find the system empty. The exact solutions are compared with commonly used approximate solutions and evaluated numerically. Thereby important information on the quality of those approximate solutions is obtained.     

带有优先权、不耐烦顾客及负顾客的$M_1,M_2/G_1,G_2/1$可修重试排队系统

研究了带有优先权,不耐烦顾客及负顾客的M1,M2/G1,G2/1可修重试排队系统.假设两类顾客的优先级不同且各自的到达过程分别服从独立的泊松过程.有优先权的顾客到达系统时如服务器忙,则以概率H1排队等候服务,以概率1-H1离开系统;而没有优先权的顾客只能一定的概率进入Orbit中进行重试,直到重试成功.此外,假设有服从Poisson过程的负顾客到达:当负顾客到达系统时,若发现服务台忙,将带走正在接受服务的顾客并使机器处于修理状态;若服务台空闲或已经处于失效状态,则负顾客立即消失,对系统没有任何影响.应用补充变量及母函数法给出了该模型的系统指标稳态解的拉氏变换表达式,并得到了此模型主要的排队指标及可靠性指标.     

全渠道服务商在线上自助服务技术背景下的定价策略研究

在线上自助服务技术兴起的背景下,研究餐饮业服务商整合全渠道的定价策略。分析归纳了三种提供服务的渠道(线下取号排队、线上取号排队、线上预定);利用排队论以及依据消费者效用对服务系统进行理论建模,并结合数值分析,为服务商如何应对不同的消费者与市场环境指明了方向。研究发现:(1)给出了三种服务渠道的最优定价模型表示,并结合市场情况分析不同的定价策略,如在服务高峰期可以采取歧视定价策略;(2)指明了线上取号与线上预定两种渠道不宜同时提供,并给出了最优的线上预定的预留容量比例,对商家设计渠道具有指导意义;(3)发现了不管线下消费者比例如何,服务商营收曲线必定经过同一点,对服务商采取措施引流具有启发意义。本文对服务商全渠道理论建模具有启发意义。     

基于排队论的专项汽修厂维修台配置数量研究

为了解决因维修台配置不合理而导致的专项汽修厂排队等待的问题,运用排队论等理论和方法,采用先到先修理与维修台带有优先权相结合的排队规则,将维修台配置数量问题转化为两类型服务台排队问题,建立了单队列M/M/s1+s2/K/∞/FCFS+PS排队模型.通过对某专项汽修厂相关的数据采集和分析,得到了模型所需的变量和参数,运用边际效益法进行优化,得到了节假日和非节假日客流高峰期的最优维修台配置数量.通过对系统服务强度、系统资源限制和服务时间段等因素的分析,既能保证排队系统可以在不同时间段内对维修台配置数量进行调整,又能缩小最优值的求解范围.     

带RCE抵消策略的负顾客M/M/1工作休假排队系统

考虑服务员在休假期间不是完全停止工作,而是以相对于正常工作时低些的速率服务顾客的M/M/1工作休假排队模型.在此模型基础上,笔者针对现实的M/M/1排队模型中可能出现的外来干扰因素,提出了带RCE(Removal of Customers at the End)抵消策略的负顾客M/M/1工作休假排队这一新的模型.服务规则为先到先服务.工作休假策略为空竭服务多重工作休假.抵消原则为负顾客一对一抵消队尾的正顾客,若系统中无正顾客时,到达的负顾客自动消失,负顾客不接受服务.使用拟生灭过程和矩阵几何解方法给出了系统队长的稳态分布,证明了系统队长和等待时间的随机分解结果并给出稳态下系统中正顾客的平均队长和顾客在系统中的平均等待时间.     

Analysis of a busy period queuing system with balking,reneging and motivating

Queuing model is widely applied in production, inventory and service industries. It is fundamental to improve the performance of queuing model by characterizing the practical queuing characteristics. In this paper, we consider impatient behaviors of customers who possibly balk and renege in a multi-server busy period queuing system, and study strategic behavior of the service provider who attempts to improve service rate when the system is busy. The piecewise curves with threshold structure are used to construct the dynamic inputting probability, dynamic service degree and dynamic reneging rate, and they are introduced to model the balking, motivating and reneging behaviors of the busy queue. The steady-state probabilities and the performance measures of the proposed model are derived. Finally, an empirical example is given to show the effectiveness of the proposed model by comparing it with the queuing model in literature.     

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Concerning the problem that network congestion risk of computer network service system for some data frames having a full priority of transmission, a method about nonpreemptive limited-priority M/M/n/m queuing system model was proposed. Firstly, as the parameter r of limited-priority was introduced into the model, the data frame with full priority was converted to the one with limited priority. Secondly, in order to lower the risk of computer network service system and stabilize the network system further, the fairness among different priorities was studied in the model. Moreover, by making use of Total Probability Theorem, three results of the models, the average waiting time, the average dwelling time and the average queue length were obtained.     

带有止步和状态相依的M/Ej/1/N排队系统的矩阵解法

研究了带有止步和服务率依赖于状态的M/Ej/1/N排队系统.顾客到达系统时,以一定的概率选择进入系统或止步(不进入系统).顾客接受服务的服务率依赖于系统中的顾客数,当系统中的顾客数不超过临界值k时,服务员慢速服务;否则,服务员快速服务.利用分块矩阵的方法,推出了稳态概率向量所满足的矩阵形式的迭代公式,给出了稳态概率的表达式和计算过程.作为特例,考虑了N=4时系统稳态概率的计算.在此基础上,还求出了系统的一些性能指标,并建立了以临界值k为控制变量的费用模型.通过数值分析,求出了使费用函数最小的最优临界值k*,并进一步研究了模型参数对最优临界值和最优费用的影响.     

基于LSTM-GA混合模型的患者预约排队策略优化

在医疗运作管理领域,合理的资源分配能够帮助更多的患者尽早就医,降低患者病情恶化和死亡的风险。本文设计了预约排队策略对患者占有资源的顺序进行分配,建立了基于长短时记忆(Long Short Term-Memory, LSTM)神经网络和遗传算法(Genetic Algorithm, GA)的混合模型以优化排队策略。首先利用大数据和深度学习分析患者到达和医院服务情况,建立LSTM神经网络学习数据特征并预测未来数据,相比于排队论常用的随机分布方法取得了更好的效果.其次设计了基于排队系统仿真的排队策略优化算法,利用改进GA得到最优排队策略。实证研究表明,文本的方法可以明显降低患者的等待时间,最高可达59%。最后对排队策略进行敏感性分析,结果表明排队策略有效作用于仿真的各个时段。     

制造企业成品出入库两级排队协同服务模型

优化企业成品出入库协同服务水平、平衡工作负荷,从而提高企业仓储服务效率、降低物流成本,是现代制造企业亟待解决的一个重要的管理细节问题。针对这个问题,本研究以仓储入库和出库两个排队过程为研究对象,建立出入库等待时间溢出情景下的两级排队协同服务模型,分析了在排队等待时间控制目标下,出入库员工优化配置方案。该模型引入溢出和串联两个协同服务机制,分三种情景即前方与后方服务台都有空闲,前方繁忙与后方空闲,前方空闲(或繁忙)与后方繁忙,建立了各情景下的系统状态转移方程,求解系统状态的概率,并进而推算出反映系统表现的各项指标,如员工使用率,队列长度,等待时间,以及等待时间超过溢出界值的概率。用制造企业成品出入库管理案例进行验证分析,对企业目前采用的M/M/S出入库排队系统与两级排队协同服务系统进行了数值计算对比。结果表明后者能有效提升出入库服务效率,减少出入库排队系统平均等待时间,降低由于入库和出库两个服务过程效率不均衡而产生的企业内部物流成本,是提升企业内部物流协同管理水平的一个重要方法。其应用可以服务于仓储出入库协同管理的信息化与自动化水平的提高。     

无阻塞概率下的排队效率分析

排队在日常生活当中屡见不鲜,为了使顾客排队等待的时间尽可能减少,除了合理安排工作人员的服务质量及服务设备外,还应该考虑如何安排排队更有效。本文在通讯系统排队问题分析的基础上,在假设阻塞概率趋近于零的情况下,比较了不同排队方式下的效率,得出结论：排成一个大队要优于排成几个小队。     

基于排队的库存服务系统最优控制策略

研究一个连续盘点的(s,Q)补货的库存服务系统。基于排队理论建立库存水平状态平衡方程,并推导出库存水平稳态概率分布以及作为库存控制的系统稳态性能指标。以库存成本最小化为目标,构建服务水平约束的库存控制模型。针对模型的非线性约束与整数型变量的特征,采用一种改进的遗传算法(IGA)用于决策变量的寻优。数值实验表明,当目标服务水平大于库存系统内生的服务水平时,实施服务水平约束能够降低库存控制成本。     

Realization probability in multi-class closed queuing networks

Perturbation analysis results of single-class queuing networks are extended to the multi-class case. The realization probability is defined and used to calculate the limiting value of the sample derivative of the system throughout with respect to mean service times a multi-class closed queuing network with exponentially distributed service times. A necessary condition for this value to be an asymptotically unbiased estimate of the derivative of the steady-state throughout is given.     

Investigation of almost deterministic queueing systems

Two almost deterministic queuing models are investigated. The influence of small stochastic disturbances on deterministic queuing systems under high loading is estimated. The queuing system G|G|1|∞ with group service is investigated in the case where the group size n tends to infinity. A theorem about the tendency of a stationary probability of a group queue to go to zero if n→∞ is formulated and proved. An application of the group-service model to the construction of an insurance system with a small insurance percent, a small initial capital, and a small ruin probability is considered. This construction is based on the cooperative effect of unification of independent and identically distributed insurance systems. Proceedings of the Seminar on Stability Problems for Stochastic Models, Vologda, Russia, 1998, Part I.     

离散时间服务台可修的排队系统MAP／PH（PH／PH）／1

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。     

多服务台并联排队系统的随机模拟

针对多服务台并联排队系统,提出了计算机随机模拟的方法.分别研究了基本和非基本排队系统中,诸如排队人数、排队时间、平稳分布、忙期及其忙期服务人数等各项排队指标的模拟求解方法.通过模拟例子和实际数据分析,显示了本文所提模拟方法的有效性、灵活性和实用性.     

Analysis of a Fork/Join Synchronization Station with Inputs from Coxian Servers in a Closed Queuing Network

Fork/join stations are commonly used to model the synchronization constraints in queuing models of computer networks, fabrication/assembly systems and material control strategies for manufacturing systems. This paper presents an exact analysis of a fork/join station in a closed queuing network with inputs from servers with two-phase Coxian service distributions, which models a wide range of variability in the input processes. The underlying queue length and departure processes are analyzed to determine performance measures such as throughput, distributions of the queue length and inter-departure times from the fork/join station. The results show that, for certain parameter settings, variability in the arrival processes has a significant impact on system performance. The model is also used to study the sensitivity of performance measures such as throughput, mean queue lengths, and variability of inter-departure times for a wide range of input parameters and network populations.     

Optimal control of an M/G/1 queuing system with removable server via diffusion approximation

In this paper, applying the technique of diffusion approximation to an M/G/1 queuing system with removable server, we provide a robust approximation model for determining an optimal operating policy of the system. The following costs are incurred to the system: costs per hour for keeping the server on or off, fixed costs for turning the server on or off, and a holding cost per customer per hour. The expected discounted cost is used as a criterion for optimality. Using a couple of independent diffusion processes approximating the number of customers in the system, we derive approximation formulae of the expected discounted cost that do not depend on the service time distribution but its first two moments. Some new results on the characterization of the optimal operating policy are provided from these results. Moreover, in order to examine the accuracy of the approximation, they are numerically compared with the exact results.     

Capacity and price setting for dispersed,time-sensitive customer segments

We consider joint pricing and capacity decisions for a facility serving heterogeneous consumers that span a continuous range of locations, and are sensitive to time delays. Within this context, we analyze two contrasting service strategies: segmentation and pooling. Consumer segments differ with respect to their reservation prices and time sensitivities, and are dispersed over a single distance dimension. The firm serves these consumers using a process that we initially model as an M/M/1 queuing system. We analyze profit-maximizing price and capacity levels for a monopolist, and contrast the optimal segmentation and pooling policies. We find that when consumers are time sensitive, and can expect queuing delays at the firm’s facility (due to random arrival and service times), then scale economies from pooling can outweigh segmentation benefits. Yet, segmentation outperforms pooling when consumer segments differ substantively, in which case the firm can use capacity as a lever to price discriminate between the segments. Moreover, by contrasting a dedicated-services strategy, which directly targets specific segments and serves them separately, with the alternative of allowing consumers to self-select, we find that self-selection has a moderate negative influence on profits. We also examine the profit impact of employing alternative queuing systems, and find that a hybrid strategy based on a prioritized queuing discipline, that combines elements of segmentation (by offering different waiting times) and pooling (by sharing capacity across consumer segments), can outperform both the pure segmentation and pooling strategies.