Optimal periodic maintenance strategy under an intermittently used environment

In this paper, the optimal periodic replacement-like strategy with minimal repairs is considered under an intermittently used environment. Suppose that transactions or jobs with exponential service times arrive at a system according to a homogeneous Poisson process and the system is alternatively in either a busy or an idle period subject to demand for use. We derive approximately the optimal preventive maintenance schedule which minimizes the relevant expected cost criterion for the system which behaves intermittently on an M/M/1 queueing process, and compare it with the usual maintenance schedule for the continuously used system.     

Analysis of a single stage production system with heterogeneous machines

The performance of a single stage production system with two heterogeneous machines and two classes of jobs is investigated. The machines have a common buffer with jobs of both classes waiting for service. The arrivals are assumed to follow a Poisson process and the service times to be distributed exponentially. The evaluated production system differs from a classical homogeneous multiple server queueing system with regard to inhomogeneities of the two machines. Time inhomogeneity – the service times of the two machines being unequal – and functional inhomogeneity – one of the machines can handle only one class (A) of jobs – are to be distinguished. In the case of time inhomogeneity the calculation of system performance parameters may be carried out using an explicit formula, whereas for the analysis of functional inhomogeneity a numerical solution has to be derived. The impact of time inhomogeneity is very small and decreases with the system workload. On the contrary, functional inhomogeneity leads to elevated cycle times of up to 40% depending on the degree of inhomogeneity (measured by the fraction of A jobs) and the workload. Therefore, in contrast to the time-inhomogeneous case, single stage production systems with functional inhomogeneity can only be approximated tolerably by a homogeneous multiple server queueing system if the fraction of one-machine jobs is less than 30%. The increased throughput times above 30% are supplied by the diagram developed from the numerical solutions. RID="*" ID="*" While this research was constructed the author was affiliated to Institute of Conveying Technology and Logistics. Correspondence to: C. R. Lippolt     

State-dependent models of material handling systems in closed queueing networks

A comprehensive algorithmic analysis of finite state-dependent queueing models and exponentially distributed workstations is formulated and presented. The material handling system is modeled with finite state-dependent queueing network M/G/c/c models and the individual workstations are modeled with exponentially distributed single and multi-server M/M/c queueing models. The coupling of these queueing models is unique via the material handling structure. The performance modeling of the systems for series, merge, and split and other complex network topologies are included so as to demonstrate the type of topological network design that is possible with these incorporated material handling systems. Of some importance, it is shown that these integrated M/M/c and M/G/c/c networks have a product form when the population arriving at the M/G/c/c queues is controlled. Numerous experimental results demonstrate the efficacy of our approach for a variety of contexts and situations.     

Control charts for traffic intensity monitoring of Markovian multiserver queues

A number of recent research studies have applied queueing theory as an approximate modeling tool to mathematically describe industrial systems, which include manufacturing, distribution, and service, for instance. Among the main observable characteristics in queues, the number of users in the system can be controlled to keep waiting times as minimal as possible. The design of efficient control charts is an attempt to monitor and control such systems. Control charts are proposed to monitor infinite queues with Markovian arrivals, exponential service times, and s identical parallel servers. The proposed charts monitor traffic intensities, which are the ratio between the arrival rate and the service rate, estimated through the number of users in the queueing system at random epochs. The effectiveness and efficiency of the proposed approaches in terms of the average run lengths are established by a comprehensive set of Monte Carlo simulations.     

两类排队网络的逼近研究

本文给出了两类排队网络。一类是容量有限的队列网络,我们证明了在高负荷下,标准化的队长过程弱收敛于半鞅反射的布朗运动：另一类是带有反馈的多类顾客多服务台队列网络,我们获得了队列网络中负荷过程的扩散逼近。     

On the optimality of exhaustive service policies in multiclass queueing systems with modulated arrivals and switchovers

Consider a single-server multiclass queueing system withK classes where the individual queues are fed byK-correlated interrupted Poisson streams generated in the states of aK-state stationary modulating Markov chain. The service times for all the classes are drawn independently from the same distribution. There is a setup time (and/or a setup cost) incurred whenever the server switches from one queue to another. It is required to minimize the sum of discounted inventory and setup costs over an infinite horizon. We provide sufficient conditions under which exhaustive service policies are optimal. We then present some simulation results for a two-class queueing system to show that exhaustive, threshold policies outperform non-exhaustive policies. This research was supported in part by the Office of Naval Research and the Department of Science and Technology grant N00014-93-1017.     

CAD and Video Somatograpby: A liaison for creating ergonomic work systems†

CAD systems and other planning instruments are used more and more in designing manual and partly automated work systems. Ergonomic aspects are often not taken into consideration because of a lack of usable ergonomic design instruments. On the other side, a planning system for the dimensional designing of movement facilities was developed and used with success in West Germany—the Video Somatography. In connecting the two different systems, a new integrated ergonomic system was created. Thereby workplaces can be planned and designed using ergonomic and technical criteria in an optimal way. Further advantages are expected by integrating ergonomic knowledge into the system. With this, it will be possible for the workplanner to get information about ergonomic and economic conditions (workload, strength, assembly duration, etc.)     

维修服务契约的最优设计和分析

本文研究了一个带服务契约的机器维修模型.为了合理优化设计机器维修服务契约,本文利用多服务器排队系统理论对具有多台机器和多个修理工的机器维修模型进行分析,得到了每台机器产生的纯收益和代理商的纯收益期望值;利用非合作博弈论对维修服务契约进行分析,得到了最优保修期、保修费和修理工数目.我们发现最优保修期和修理工数目均与保修价格函数无关.而且,对于固定寿命的机器,机器总数几乎不影响最优保修期的设定.     

Lot size optimisation under pooled and unpooled scenarios in batch production system

The lot-sizing problem in batch manufacturing systems with capacity constraints is studied using queueing relationships and optimisation techniques. In this research, the effect of lot sizes when there are parallel machines and multiple part types is considered. Furthermore, the issue of whether or not to use pooled queues, based on part types, to feed the machines is examined. Different scenarios are evaluated using GI/G/n queueing approximations to predict performance and optimise lot sizes. Optimisation is based on minimising the mean flowtimes, which include queue and lot service times. The results show that if part types are very different, there are situations in which pooling is not advantageous.     

Performance analysis of an inbound call center with skills-based routing

Many call centers provide service for customers of different classes with differently qualified groups of agents. Since call arrivals and call handling times are random in inbound call centers, we investigate queueing models for their performance analysis. This paper describes a Markov queueing model with two customer classes and three groups of specialized or flexible agents. The mean call handling time may depend on the respective customer class as well as on the agent group serving this call. The customers are assumed to be impatient. We consider skills-based routing with priority-based rules and derive both steady-state probabilities and performance measures. We present some numerical experiments and show the impact of different mean processing times. The influence of the allocation of the agents into the three groups is analyzed for different levels of patience.Correspondence to: Raik Stolletz . R. Stolletz, S. Helber: The authors thank the anonymous referees for their helpful comments and suggestions.     

Optimization problems in k-out-of-n systems with minimal repair

The k-out-of-n system is a system with n independent components such that the system operates if and only if at least k of these n components operate succesfully. Such a system is an important complex system and is used for mass transit, safety systems and computer systems. This paper considers what is the most economical k-out-of-n system with minimal repair. We solve two problems to minimise the long term expected cost rate per unit time; (i) the optimal number of elements, and (ii) the optimal replacement time before system failure. Finally, a numerical example is given.     

多服务速率多重休假M/G(M/G)/1可修排队

本文通过对系统中顾客数设置门限N,考虑研究了服务台的服务速度依门限发生变化且当服务台未服务顾客(休假或故障)时到达顾客仅以概牢p进入系统的多重休假可修M／G(M／G)／1排队系统。通过L-变换、母函数以及补充变量方法得到了队长分布的瞬态解、稳态解及一些可靠性结果,并指出当两个服务速度相等时该模型与前人研究的M／G／1(E,MV）排队一致。     

CUSUM Statistical Monitoring of M/M/1 Queues and Extensions

Many production and service systems can be modeled as queueing systems. Their operational efficiency and performance are often measured using queueing performance metrics (QPMs), such as average cycle time, average waiting length, and throughput rate. These metrics need to be quantitatively evaluated and monitored in real time to continuously improve the system performance. However, QPMs are often highly stochastic, and hence are difficult to monitor using existing methods. In this article, we propose the cumulative sum (CUSUM) schemes to efficiently monitor the performance of typical queueing systems based on different sampling schemes. We use M/M/1 queues to illustrate how to design the CUSUM chart and compare their performance with several alternative methods. We demonstrate that the performance of CUSUM is superior, responding faster to many shift patterns through extensive numerical studies. We also briefly discuss the extensions of CUSUM charts to more general queues, such as M/G/1, G/G/1, or M/M/c queues. We use case studies to demonstrate the applications of our approach. Supplementary materials for this article are available online.     

GERTS QR: A Model for Multi-Resource Constrained Queueing Systems Part I: Concepts, Notation, and Examples

This paper presents a new GERTS model and simulator, GERTS QR, directed to the modeling and analysis of Multi-Resource Constrained (MRC) queueing systems. That is, systems where resource requirements, in addition to the availability of a service center or channel, may constrain the system. The development and notation of the GERTS QR model are briefly summarized, and three examples of MRC queueing systems are given to illustrate the application of the model. The three examples are: (1) a labor-limited job shop queueing system, (2) a retail sales outlet, and (3) the planning of a jet engine overhaul facility.     

Queueing network model for a class of material-handling systems

A queueing network-based approximation model was developed to evaluate the performance of a fixed-route material-handling system supporting a multiple-workcentre manufacturing facility. The closest transporter allocation scheme was used to assign empty transporters to jobs needing to be moved between various workcentres. This control methodology creates two interesting difficulties that require solving for an accurate approximation model. A model of the distributions of the location of an assigned transporter as a function of the number of available transporters is developed. In addition, it is shown that owing to the strong dependent service time aspect of this situation, the standard queueing network decomposition approach of treating the material-handling systems as a GI/G/c queue can be highly inaccurate. Thus, it is necessary to develop a dependent service-time model for approximating the queueing delay encountered while waiting for an empty transporter assignment.     

A Sequential Bounding Approach for Optimal Appointment Scheduling

This study is concerned with the determination of optimal appointment times for a sequence of jobs with uncertain durations. Such appointment systems are used in many customer service applications to increase the utilization of resources, match workload to available capacity, and smooth the flow of customers. We show that the problem can be expressed as a two-stage stochastic linear program that includes the expected cost of customer waiting, server idling, and a cost of tardiness with respect to a chosen session length. We exploit the problem structure to derive upper bounds that are independent of job duration distribution type. These upper bounds are used in a variation of the standard L-shaped algorithm to obtain optimal solutions via successively finer partitions of the support of job durations. We present new analytical insights into the problem as well as a series of numerical experiments that illustrate properties of the optimal solution with respect to distribution type, cost structure, and number of jobs.     

受需求扰动的供应链系统最优跟踪控制

针对动态供应链系统中市场需求扰动引起的牛鞭效应问题,提出一种基于前馈补偿的最优跟踪控制设计方法.首先,针对需求扰动可模型化为线性外系统的情形,引入了一个渐近稳定的期望系统;然后,基于线性二次型性能指标,给出了受需求扰动的供应链系统的前馈反馈最优跟踪控制器设计方法.控制器的反馈增益和前馈增益可分别通过求解Riccati方程和Stein方程得到.仿真结果表明,提出的前馈反馈最优跟踪控制方法能有效抑制需求扰动对供应链系统的影响,改善供应链系统的动态性能,且该方法明显优于经典的最优跟踪控制.     

Modelling and optimisation of a two-server queue with multiple vacations and working breakdowns

This paper presents a steady-state analysis of an M/M/2 queue with heterogeneous servers (Server 1 and Server 2). Server 1 is reliable and may leave for a vacation when the system becomes empty. Sever 2 is unreliable and may break down while serving customers. When a breakdown occurs, Server 2 reduces the service rate rather than halting service. We formulate this queueing model as a quasi birth-and-death (QBD) process, using the matrix geometric method to compute the stationary distribution of system size. We also develop several measures to evaluate the performance of the system. A cost model based on system performance measures is formulated as a heuristic cost optimisation problem subject to stability conditions. A canonical particle swarm optimisation algorithm is used to obtain numerical solutions for the approximate optimal service rates of Server 1 and Server 2. Moreover, we present numerical results showing the effects of various parameters on the approximate optimal service rates as well as a practical example illustrating the application of the proposed model.     

Heuristic analysis of closed queueing networks

In this paper we consider closed queueing networks having M single server queueing stations with arbitrary interconnections and general service time distributions. Here we propose an iterative approximation procedure, based on a decomposition approximation. Numerical results are reported to demonstrate the accuracy of the method. We also discuss the sensitivity of the results to the initial guess for the server utilizations.     

Global exponential stabilization for a class of nonlinear singularly perturbed systems

Abstract

A globally exponentially (asymptotically) stabilizing composite feedback control is proposed in this paper for a general class of nonlinear multiple time‐delay singularly perturbed systems in which the slow subsystem is exponentially stable in the absence of the fast states. The chosen design manifold under this composite feedback control becomes an exact integral manifold and the trajectories of the closed‐loop systems are steered globally along the integral manifold to the origin exponentially, with some guaranteed convergence rate, for all sufficiently small singular perturbation parameter ?.