双排队系统下大型超市运营效率的优化研究

对实际中存在“快速通道”的大型超市排队系统的运营效率进行优化,基于M/M/1排队模型,以顾客排队等待时间为目标函数,证明了存在“快速通道”的大型超市的双排队系统要优于单排队系统,并得到了双排队系统下各自服务台的最优配置数量。在此基础上,进一步给出了求得双排队系统下的最优商品数量分界点的方法。最后,通过调研数据的结果分析说明了研究的结论。研究结果对银行、收费站、医院等有着极大的启示意义。     

超市收银台最优数量的设置

本文运用排队论理论对超市多个M/M/1/∞/∞的排队系统进行研究,将M/M/s/∞/∞与多个M/M/1/∞/∞进行对比,然后通过对结果进行对比分析、参赛的灵敏度分析,确定出收银台的最佳数量.     

服务员多重休假的易逝品排队库存系统的稳态分析

考虑(s,S)库存策略的易逝品M/M/1排队库存系统,其中库存为空时服务员多重休假,休假时间服从指数分布.顾客的到达过程服从泊松过程,服务员的服务时间,易逝品的寿命和补货时间均服从指数分布.首先,利用拟生灭过程给出系统的稳态条件.其次,研究忽略服务时间的M/M/1休假库存系统模型,并求出了系统的稳态分布.在此基础上,进一步研究具有正服务时间的M/M/1休假排队库存系统模型,并得到了系统队长,库存水平和服务员状态的乘积形式的稳态联合分布.此外,还计算了系统的性能指标,并给出了系统单位时间的平均费用函数.最后,利用数值算例分析系统参数对一些主要性能指标的影响,并利用遗传算法计算系统最优库存策略和最优平均费用.     

基于排队论的内场维修设备数量确定方法

在内场车间维修设备配置研究中,为了科学合理地确定维修设备数量需求,运用排队论的基本方法,结合飞机内场维修工作特点,提出了基于排队论的内场维修设备数量确定方法,构建了相应的数量确定模型,结合实例验证了该方法可行有效.结果表明方法可以提高飞机基层级内场车间维修设备数量确定的准确性.     

带有负顾客的M/M/c多重工作休假排队

考虑服务台在休假期间不是完全停止工作,而是以相对于正常服务期低些的服务率服务顾客的M/M/c工作休假排队模型.在此模型基础上,针对现实的M/M/c排队模型中可能出现的外来干扰因素,提出了带有负顾客的M/M/c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异步多重工作休假.抵消原则为负顾客一对一抵消处于正常服务期的正顾客,若系统中无处于正常服务期的正顾客时,到达的负顾客自动消失,负顾客不接受服务.首先,由该多重休假模型得到其拟生灭过程及生成元矩阵,然后运用矩阵几何方法给出系统队长的稳态分布表达式和若干系统指标.     

具有不耐烦顾客和多重工作休假的排队库存系统

研究具有不耐烦顾客和多重工作休假的M/M/1/N排队库存系统模型,分别考虑了系统中库存为零时服务员休假和系统中顾客数为零时服务员休假两种休假方式,基于(s,S)库存策略,运用矩阵迭代方法得到了系统稳态概率分布,并给出系统相关性能指标,进而建立系统平均库存费用函数.通过数值算例对比分析了两种休假方式下的系统主要参数变化对系统重要性能指标的影响,并在最优费用的层面对两个模型的优劣进行了对比分析.     

基于Q-过程和随机模拟的病床安排方案

本文设计的一个新的住院病床安排方案,可用来取代传统的FCFS(先到先得)规则.患者在等候队列中的优先级将基于病情和手术的紧急程度.本文把患者的入住情况转化为经典的M/M/N排队论问题,利用可逆Q-过程的性质以及经典排队论的结果,得到各类疾病患者的平均逗留时间以及所需床位数的先验估计.根据独立Poisson过程的性质确定排队过程的Q-矩阵,从而作出相应的先验估计和具体表达式.在若干约束条件的基础上,利用C++编程求得最优病床分配方案.本文建立的评价指标体系,通过计算机随机模拟,证明了在多种情形下,该模型较FCFS(先到先得)规则更具优势.     

具有N-策略休假的M/G/1排队的随机分解与最优策略

本文利用向量Markov过程方法,研究了具有N-策略休假且休假时间为一般分布的M/G/1排队,它的两种特殊情况分别是具有多重休假的M/G/1排队和具有N-策略控制的M/G/1排队。我们得到了这个排队系统稳态时的队长分布,证明了它的稳态队长存在随机分解。然后讨论了当休假时间服从指数分布时的最优策略问题。     

成批排队系统GI/M/I的忙时(busy cycle)

§1.引言 尽管成批排队系统M/G/1的忙期(busy period)与忙时(busy cycle)已有若干作者作了成功的研究,但多年来成批到来成批服务的排队系统GI/M/1的相应研究却几乎没有进展。正如文献[1]中指出,此问题是困难的。 本文由研究嵌入马氏链与半马氏序列入手,考虑了成批排队系统GI/M/1。运用文中定理可以得到上述系统的忙时分布,忙时内服务的到来顾客的批数的分布,以及与此相关     

基于有限服务排队系统的未决赔款准备金分布

若保险赔付工作中赔付人员有限,根据服务人员有限的排队系统的性质,可以研究保险公司所需计提的未决赔款准备金的分布函数.当假设赔付服务工作人员为c个,使用M/M/c/∞和G/M/c/∞排队系统的性质可以得到未决赔款准备金分布函数和年末所需增加计提的未决赔款准备金的分布及其界值.当假设赔付服务工作人员仅一个,使用M/G/1/∞排队系统的性质可以得到此时未决赔款准备金的分布函数.并且在假设损失赔付额取正整数的条件下,得到年末保险公司所需增加计提的未决赔款准备金分布的递推公式.而且通过计算实例表明结论的实用性,及所得到的递推公式在以往难以准确求解未决赔款准备金分布时是十分有效的.     

汽车修理排队系统数据分析及配置优化

利用排队理论研究汽车修理系统,通过实例对输入过程和服务时间数据的整理进而验证了它们的分布规律,由此指出了应用排队模型类型,得到排队系统的各种基本运行参数,然后从顾客消费心理考虑,以区间估计的方法,在进入修理店时告知需要等待时间,最后给出汽车修理服务台的优化配置数.     

A closed queuing maintenance network for automated manufacturing systems

This paper models an unreliable automated manufacturing system (AMS) by a closed queuing network. The AMS consists of a multi-stage network of automated work stations linked by a computer. A closed queuing algorithm is applied to determine the system availability under steady state for the AMS. This algorithm is then integrated into a cost optimization model. By applying the revised genetic algorithm, the optimal (or near-optimal) number of standby units and repair rates for the repair stations are derived by minimizing the total cost. The model is verified by the intuitive results from the sensitivity analysis. A numerical example is used to compare the revised genetic algorithm and the conventional genetic algorithm. The results show that the proposed revised algorithm leads to significant improvement in execution time and lower average total cost.     

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。     

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.     

Admission control strategies for tandem Markovian loss systems

Motivated by communication networks, we study an admission control problem for a Markovian loss system comprised of two finite capacity service stations in tandem. Customers arrive to station 1 according to a Poisson process, and a gatekeeper, who has complete knowledge of the number of customers at both stations, decides whether to accept or reject each arriving customer. If a customer is rejected, a rejection cost is incurred. If an admitted customer finds that station 2 is full at the time of his service completion at station 1, he leaves the system and a loss cost is incurred. The goal is to find easy-to-implement policies that minimize long-run average cost per unit time. We formulate two intuitive, extremal policies and provide analytical results on their performances. We also present necessary and/or sufficient conditions under which each of these policies is optimal. Next, we show that for some states of the system it is always optimal to admit new arrivals. We also fully characterize the optimal policy when the capacity of each station is two and discuss some characteristics of optimal policies in general. Finally, we design heuristic admission control policies using these insights. Numerical experiments indicate that these heuristic policies yield near-optimal long-run average cost performance.     

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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.     

Optimal warranty policies for systems with imperfect repair

We investigate a system whose basic warranty coverage is minimal repair up to a specified warranty length. An additional service is offered whereby first failure is restored up to the consumers’ chosen level of repair. The problem is studied under two system replacement strategies: periodic maintenance before and after warranty. It turns out that our model generalizes the model of Rinsaka and Sandoh [K. Rinsaka, H. Sandoh, A stochastic model with an additional warranty contract, Computers and Mathematics with Applications 51 (2006) 179–188] and the model of Yeh et al. [R.H. Yeh, M.Y. Chen, C.Y. Lin, Optimal periodic replacement policy for repairable products under free-repair warranty, European Journal of Operational Research 176 (2007) 1678–1686]. We derive the optimal maintenance period and optimal level of repair based on the structures of the cost function and failure rate function. We show that under certain assumptions, the optimal repair level for additional service is an increasing function of the replacement time. We provide numerical studies to verify some of our results.     

Using mixture of Gamma distributions for Bayesian analysis in an M/G/1 queue with optional second service

The paper proposes Bayesian framework in an M/G/1 queuing system with optional second service. The semi-parametric model based on a finite mixture of Gamma distributions is considered to approximate both the general service and re-service times densities in this queuing system. A Bayesian procedure based on birth-death MCMC methodology is proposed to estimate system parameters, predictive densities and some performance measures related to this queuing system such as stationary system size and waiting time. The approach is illustrated with several numerical examples based on various simulation studies.     

A multi-objective lead time control problem in multi-stage assembly systems using genetic algorithms

In this paper, we develop a multi-objective model to optimally control the lead time of a multi-stage assembly system, using genetic algorithms. The multi-stage assembly system is modelled as an open queueing network. It is assumed that the product order arrives according to a Poisson process. In each service station, there is either one or infinite number of servers (machines) with exponentially distributed processing time, in which the service rate (capacity) is controllable. The optimal service control is decided at the beginning of the time horizon. The transport times between the service stations are independent random variables with generalized Erlang distributions. The problem is formulated as a multi-objective optimal control problem that involves four conflicting objective functions. The objective functions are the total operating costs of the system per period (to be minimized), the average lead time (min), the variance of the lead time (min) and the probability that the manufacturing lead time does not exceed a certain threshold (max). Finally, we apply a genetic algorithm with double strings using continuous relaxation based on reference solution updating (GADSCRRSU) to solve this multi-objective problem, using goal attainment formulation. The results are also compared against the results of a discrete-time approximation technique to show the efficiency of the proposed genetic algorithm approach.