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.     

考虑患者回诊情况下的门诊科室调度优化

目前国内大型三甲医院最突出的问题就是资源稀缺,这些稀缺资源主要包括手术室、大型检查设备以及门诊科室等,造成患者严重的排队现象,从而导致患者等待时间过长,满意度下降。通过对哈尔滨市某大型医院进行调研,收集相关数据,研究在考虑患者回诊(即患者当天做完各项检查后又回到初次检查的门诊科室)情况下,对医生门诊科室的数量进行调度优化。利用排队论中的动态优先级对排队规则进行限定,同时引入前景理论中的价值函数,确立以最小化患者时间感知不满意度为主要目标,最小化医院运营成本为次要目标的多目标优化问题。并且分析了两个目标的权重参数变化对总体满意度的影响。建立相应的数学模型,利用模拟植物生长算法( plant growth simulation algorithm,简称PGSA)进行算法设计,通过MATLAB进行仿真,得出在有限度优先的排队规则下,能够更大程度的降低患者不满意度,同时保证较低的运营成本,证明了此研究的有效性和可行性。     

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.     

服务率可变的批服务排队网络

大部分排队网络的研究结果是在服务率不变的条件下给出的。本文分析了两类成批服务的排队网络。并在服务率依赖于批服务大小的条件下，利用各节点的准可逆性，给出了不带信号和带消极信号的两类排队网络的乘积形式稳态解．并利用不动点原理，证明了交通方程解的存在性．并给出求法。     

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。     

Performance analysis of CONWIP systems with batch size constraints

Multi-product manufacturing systems operating under CONWIP control are often modeled as closed queuing networks with synchronization stations. Performance analysis of these systems can be challenging, especially when batch size constraints are explicitly considered. This research develops a new approach for evaluating the performance of these systems based on parametric characterizations and traffic process approximations. The approach explicitly models the effect of batch size constraints on the departure process and waiting times at the different stations in the network to derive new characterization equations. These equations are used to derive a set of linking equations that is solved using an iterative algorithm to obtain estimates of network performance. Numerical studies indicate that the proposed method is yields fairly accurate performance estimates and can be useful in evaluating tradeoffs that guide managerial decisions.     

Modelling activities at a neurological rehabilitation unit

A queuing model of a specialist neurological rehabilitation unit is studied. The application is to the Neurological Rehabilitation Centre at Rookwood Hospital (Cardiff, UK), the national rehabilitation unit for Wales. Due to high demand this 21-bed inpatient facility is nearly always at maximum occupancy, and with a significant bed-cost per day this makes it a prime candidate for mathematical modelling. Central to this study is the concept that treatment intensity has an effect on patient length of stay. The model is constructed in four stages. First, appropriate patient groups are determined based on a number of patient-related attributes. Second, a purpose-built scheduling program is used to deduce typical levels of treatment to patients of each group. These are then used to estimate the mean length of stay for each patient group. Finally, the queuing model is constructed. This consists of a number of disconnected homogeneous server queuing systems; one for each patient group. A Coxian phase-type distribution is fitted to the length of time from admission until discharge readiness and an exponential distribution models the remainder of time until discharge. Some hypothetical scenarios suggested by senior management are then considered and compared on the grounds of a number of performance measures and cost implications.     

Equivalent single-queue–single-server model for a Pentium processor

In this paper, a Pentium processor is represented as a queuing network. The objective of this paper is to deduce an equivalent single-queue–single-server model for the original queuing network. Closed-form expressions for the equivalent service rate, equivalent queue lengths, equivalent response and waiting times of the equivalent single-queue–single-server model are derived and plotted. For large values of arrival rate, queue lengths increase faster than the response times and waiting times for both the cases. Performance measures like, queue lengths, response times and waiting times are higher for lower service rates and lower for higher service rates (which is expected) of the different servers in the original queuing network. Also, the reliability in estimating performance measures for homogeneous workloads is much better than that for heterogeneous workloads.     

The optimality of balancing workloads in certain types of flexible manufacturing systems

Symmetric mathematical programming is used to analyze the optimality of balancing workloads to maximize the expected production in a single-server closed queuing network model of a flexible manufacturing system (FMS). In particular, using generalized concavity we prove that, even though the production function is not concave, balancing workloads maximizes the expected production in certain types of m-machine FMS's with n parts in the system. Our results are compared and contrasted with previous models of production systems.     

Dynamic multi-appointment patient scheduling for radiation therapy

Seeking to reduce the potential impact of delays on radiation therapy cancer patients such as psychological distress, deterioration in quality of life and decreased cancer control and survival, and motivated by inefficiencies in the use of expensive resources, we undertook a study of scheduling practices at the British Columbia Cancer Agency (BCCA). As a result, we formulated and solved a discounted infinite-horizon Markov decision process for scheduling cancer treatments in radiation therapy units. The main purpose of this model is to identify good policies for allocating available treatment capacity to incoming demand, while reducing wait times in a cost-effective manner. We use an affine architecture to approximate the value function in our formulation and solve an equivalent linear programming model through column generation to obtain an approximate optimal policy for this problem. The benefits from the proposed method are evaluated by simulating its performance for a practical example based on data provided by the BCCA.     

Use of an orthogonal projector for accelerating a queuing problem solver

Overflow queuing models are often analyzed by explicitly solving a large sparse singular linear systems arising from Kolmogorov balance equations. The system is often converted into an eigenvalue problem the dominant eigenvector of which is the desired null vector. In this paper, we convert an overflow queuing problem into an eigen-value problem of size 1/2 of the original. Then we devise an orthogonal projector that enhances its convergence by removing unwanted eigen-components effectively. Numerical result with some suggestion is given at the end.     

Modeling the number of insureds’ cars using queuing theory

In this paper, we propose to model the number of insured cars per household. We use queuing theory to construct a new model that needs 4 different parameters: one that describes the rate of addition of new cars on the insurance contract, a second one that models the rate of removal of insured vehicles, a third parameter that models the cancellation rate of the insurance policy, and finally a parameter that describes the rate of renewal. Statistical inference techniques allow us to estimate each parameter of the model, even in the case where there is censorship of data. We also propose to generalize this new queuing process by adding some explanatory variables into each parameter of the model. This allows us to determine which policyholder’s profiles are more likely to add or remove vehicles from their insurance policy, to cancel their contract or to renew annually. The estimated parameters help us to analyze the insurance portfolio in detail because the queuing theory model allows us to compute various kinds of useful statistics for insurers, such as the expected number of cars insured or the customer lifetime value that calculates the discounted future profits of an insured. Using car insurance data, a numerical illustration based on a portfolio from a Canadian insurance company is included to support this discussion.     

Fuzzy sets and the modelling of physician decision processes,part I: The initial interview-information gathering session

Most mathematical models of physician decision processes offered to date, especially those relative to diagnosis and patient treatment, suffer from the inability to incorporate all useful data on the patient. Pertinent information so neglected or poorly modelled relate to variables that are intrinsically fuzzy but which describe the patient's health status. We present mathematical models based on fuzzy set theory for physician aided evaluation of a complete representation of information emanating from the initial interview including patient past history, present symptoms, signs observed upon physical examination, and results of clinical and diagnostic tests.     

A mathematical model of a flexible manufacturing system with limited in-process inventory

This paper describes a computationally simple, asymptotic model of a flexible job shop, especially designed for estimating the influence of limited in-process inventory level on the production rate. Its main features make it very similar to the one by Solberg. While Solberg's model consists of a closed queuing network, we propose an open queuing network with a limited amount of inprocess customers; a single customer class is assumed, the various actual processing routes being accounted for by routing probabilities. For such a queuing network, the product form of state probabilities is valid, and the normalization constant can be very simply obtained by a convolution algorithm, close to the one used by Solberg. Various performance indices are calculated, regarding the job shop behaviour over a long period of time. Comparison of analytical results of the model and simulation results are provided in order to estimate the amount of error introduced by assuming exponentially distributed processing times and Poisson inputs in the mathematical representation. Simulations were carried out in FORTRAN-based SLAM language.     

A four-input three-stage queuing network approach to model an industrial system

An industrial system is represented as a four-input, three-stage queuing network in this paper. The four-input queuing network receives orders from clients, and the orders are waiting to be served. Each order comprises (i) time of occurrence of the orders, and (ii) quantity of items to be delivered in each order. The objective of this paper is to compute the optimal path which produces the least response time for the delivery of items to the final destination along the three stages of the network. The average number of items that can be delivered with this minimum response time constitute the optimum capacity of the queuing network. After getting serviced by the last node (a queue and its server) in each stage of the queuing network, a decision is made to route the items to the appropriate node in the next stage which can produce the least response time. Performance measures such as average queue lengths, average response times, average waiting times of the jobs in the four-input network are derived and plotted. Closed-form expressions for the equivalent service rate, equivalent average queue lengths, equivalent response and waiting times of a single equivalent queue with a server representing the entire four-input queuing network are also derived and plotted.     

A closed queuing network model with single servers for multi-threaded architecture

In this paper, a closed queuing network model with single servers for each queue is proposed to model dataflow in a multi-threaded architecture. Multi-threading is useful in reducing the latency by switching among a set of threads in order to improve the processor utilization. Two sets of processors, synchronization and execution processors exist. Synchronization processors handle load/store operations and execution processors handle arithmetic/logic and control operations. A closed queuing network model is suitable for large number of job arrivals. The normalization constant is derived using a recursive algorithm for the given model. State diagrams are drawn from the closed queuing network model, and the steady-state balance equations are derived from it. Performance measures such as average response times and average system throughput are derived and plotted against the total number of processors in the closed queuing network model. Other important performance measures like processor utilizations, average queue lengths, average waiting times and relative utilizations are also derived.     

Effective cancellation policy to reduce the negative impact of patient no-show

The problem of patient no-show in outpatient delivery systems has been a long recognized issue. The negative impacts include underutilized medical resources, increased healthcare costs, decreased access to care, and reduced clinic efficiency and provider productivity. Many clinics have cancellation policies of asking their patients to cancel 24 or 48?h in advance. However, there is no logical or mathematical basis for such a policy. The objective is to develop an effective cancellation policy that accounts for current no-show rates, the clinic's flow, and its fill rates to minimize the cost of patient wait time, physician idle time, and overtime. A simulation approach is presented to determine the hours required for patients to call in advance for cancelling appointments. The findings indicate that when fill rates are low and no-show probabilities are high, the time required for patients to cancel appointments needs to increase in order to achieve the goal of being cost-effective.     

A network queuing approach for evaluation of performance measures in autonomous vehicle storage and retrieval systems

A network queuing approach is used to estimate performance measures for Autonomous Vehicle Storage and Retrieval (AVS/R) Systems using opportunistic interleaving. The model exploits the distribution of cycle types and random storage assumptions to estimate the proportion of single and dual command cycles in a system. Comparable in accuracy and computational efficiency to procedures based on standard queuing models, the proposed technique provides the additional advantage of flexibility for modeling the interfaces between a storage system and the overall material flow system in a facility. The procedure is demonstrated for a range of problem scenarios.     

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.