Taxonomy of batch queueing models in manufacturing systems

Batching plays an important role in performance evaluation of manufacturing systems. Three types of batching are commonly seen: transfer batches, parallel batches and serial batches. To model the batching behavior correctly, a comprehensive classification of batching is proposed. Eight types of batching behavior are classified and corresponding queueing models are given. The newly proposed models are validated by simulation.     

A review of open queueing network models of manufacturing systems

In this paper we review open queueing network models of manufacturing systems. The paper consists of two parts. In the first part we discuss design and planning problems arising in manufacturing. In doing so we focus on those problems that are best addressed by queueing network models. In the second part of the paper we describe developments in queueing network methodology. We are primarily concerned with features such as general service times, deterministic product routings, and machine failures — features that are prevalent in manufacturing settings. Since these features have eluded exact analysis, approximation procedures have been proposed. In the second part of this paper we review the developments in approximation procedures and highlight the assumptions that underlie these approaches.     

On the validity and utility of queueing models of human service systems

Based on observations made during an extensive study of police patrol operations in New York City, we examine the issues of the validity and utility of queueing models of service systems in which adaptive behavior by the (human) customers or servers is likely. We find that in addition to depending on the technical accuracy of its assumptions, the accuracy of such a model will also depend upon the level of managerial control of the system and adequacy of resources. We recommend that queueing models of human service systems be used in a normative fashion and incorporated in the management feedback loop.     

Structural results for the control of queueing systems using event-based dynamic programming

In this paper we study monotonicity results for optimal policies of various queueing and resource sharing models. The standard approach is to propagate, for each specific model, certain properties of the dynamic programming value function. We propose a unified treatment of these models by concentrating on the events and the form of the value function instead of on the value function itself. This is illustrated with the systematic treatment of one and two-dimensional models. This revised version was published online in June 2006 with corrections to the Cover Date.     

Robustness of perturbation analysis estimators for queueing systems with unknown distributions

Sample-path-based stochastic gradient estimators for performance measures of queueing systems rely on the assumption that a probability distribution of the random vector of interest (e.g., a service or interarrival time sequence) is given. In this paper, we address the issue of dealing with unknown probability distributions and investigate the robustness of such estimators with respect to possibly erroneous distribution choices. We show that infinitesimal perturbation analysis (IPA) can be robust in this sense and, in some cases, provides distribution-independent estimates. Comparisons with other gradient estimators are provided, including experimental results. We also show that finite perturbation analysis (FPA), though only providing gradient approximations, possesses some attractive robustness properties with respect to unknown distribution parameters. An application of FPA estimation is included for a queueing system performance optimization problem involving customers with real-time constraints.This work was supported in part by the National Science Foundation Grant ECS-88-01912 and by the Office of Naval Research Contract N00014-87-K-0304.The authors wish to thank Dr. Jack Holtzman for several useful comments and suggestions.     

On the control of queueing systems with failures and repairs

Several classes of problems can be modelled as queueing systems with failures where preventative maintenance has to be optimized: relevant examples are computer systems, databases and production lines. This paper studies a simple case of such a situation based on the M/M/1 queue where the state of the server can take two values (on, off); the transition on–off happens either when there is a failure or when one decides to maintain. The characterization and an approximation of an optimal policy are given. Extensions to more general models, including general Markov processes, are examined.     

The achievable region method in the optimal control of queueing systems; formulations,bounds and policies

We survey a new approach that the author and his co-workers have developed to formulate stochastic control problems (predominantly queueing systems) asmathematical programming problems. The central idea is to characterize the region of achievable performance in a stochastic control problem, i.e., find linear or nonlinear constraints on the performance vectors that all policies satisfy. We present linear and nonlinear relaxations of the performance space for the following problems: Indexable systems (multiclass single station queues and multiarmed bandit problems), restless bandit problems, polling systems, multiclass queueing and loss networks. These relaxations lead to bounds on the performance of an optimal policy. Using information from the relaxations we construct heuristic nearly optimal policies. The theme in the paper is the thesis that better formulations lead to deeper understanding and better solution methods. Overall the proposed approach for stochastic control problems parallels efforts of the mathematical programming community in the last twenty years to develop sharper formulations (polyhedral combinatorics and more recently nonlinear relaxations) and leads to new insights ranging from a complete characterization and new algorithms for indexable systems to tight lower bounds and nearly optimal algorithms for restless bandit problems, polling systems, multiclass queueing and loss networks.     

Convergence to equilibria for fluid models of head-of-the-line proportional processor sharing queueing networks

Fluid models have recently become an important tool for the study of open multiclass queueing networks. We are interested in a family of such models, which we refer to as head-of-the-line proportional processor sharing (HLPPS) fluid models. Here, the fraction of time spent serving a class present at a station is proportional to the quantity of the class there, with all of the service going into the first customer of each class. To study such models, we employ an entropy function associated with the state of the system. The corresponding estimates show that if the traffic intensity function is at most 1, then such fluid models converge exponentially fast to equilibria. When the traffic intensity function is strictly less than 1, the limit is always the empty state and occurs after a finite time. A consequence is that generalized HLPPS networks with traffic intensity strictly less than 1 are positive Harris recurrent. Related results for FIFO fluid models of Kelly type were obtained in Bramson [4].Partially supported by NSF Grants DMS-93-00612 and DMS-93-04580. The paper was written while the author was in residence at the Institute for Advanced Study.     

Convergence to equilibria for fluid models of FIFO queueing networks

The qualitative behavior of open multiclass queueing networks is currently a topic of considerable activity. An important goal is to formulate general criteria for when such networks possess equilibria, and to characterize these equilibria when possible. Fluid models have recently become an important tool for such purposes. We are interested here in a family of such models, FIFO fluid models of Kelly type. That is, the discipline is first-in, first-out, and the service rate depends only on the station. To study such models, we introduce an entropy function associated with the state of the system. The corresponding estimates show that if the traffic intensity function is at most 1, then such fluid models converge exponentially fast to equilibria with fixed concentrations of customer types throughout each queue. When the traffic intensity function is strictly less than 1, the limit is always the empty state and occurs after a finite time. A consequence is that generalized Kelly networks with traffic intensity strictly less than 1 are positive Harris recurrent, and hence possess unique equilibria.1991Mathematics Subject Classification, 60K25, 68M20, 90B10. Partially supported by NSF Grant DMS-93-00612.     

Modeling circulation systems in buildings using state dependent queueing models

Circulation systems within buildings are analyzed using M/G/C/C queueing models. Congestion aspects of the traffic flow are represented by introducing state dependent service rates as a function of the number of occupants in each region of the circulation system. Analytical models for unidirectional and multi-source/single sink flows are presented. Finally, use of the queueing models to analytically determine the optimal size and capacity of the links of the circulation systems is incorporated into a series of software programs available from the authors.This material is based upon work supported by the National Science Foundation under grant #MSM-8417942 and #MSM-8715152.     

Design of cellular manufacturing systems using Latent Semantic Indexing and Self Organizing Maps

A new, efficient clustering method for solving the cellular manufacturing problem is presented in this paper. The method uses the part-machine incidence matrix of the manufacturing system to form machine cells, each of which processes a family of parts. By doing so, the system is decomposed into smaller semi-independent subsystems that are managed more effectively improving overall performance. The proposed method uses Self Organizing Maps (SOMs), a class of unsupervised learning neural networks, to perform direct clustering of machines into cells, without first resorting to grouping parts into families as done by previous approaches. In addition, Latent Semantic Indexing (LSI) is employed to significantly reduce the complexity of the problem resulting in more effective training of the network, significantly improved computational efficiency, and, in many cases, improved solution quality. The robustness of the method and its computational efficiency has been investigated with respect to the dimension of the problem and the degree of dimensionality reduction. The effectiveness of grouping has been evaluated by comparing the results obtained with those of the k-means classical clustering algorithm.AMS classification: 62H30     

Capacity planning in networks of queues with manufacturing applications

This paper addresses capacity planning in systems that can be modeled as a network of queues. More specifically, we present an optimization model and solution methods for the minimum cost selection of capacity at each node in the network such that a set of system performance constraints is satisfied. Capacity is controlled through the mean service rate at each node. To illustrate the approach and how queueing theory can be used to measure system performance, we discuss a manufacturing model that includes upper limits on product throughput times and work-in-process in the system. Methods for solving capacity planning problems with continuous and discrete capacity options are discussed. We focus primarily on the discrete case with a concave cost function, allowing fixed charges and costs exhibiting economies of scale with respect to capacity to be handled.     

Queueing network modelling of flexible manufacturing system using mean value analysis

In the present investigation, we develop queueing model for the performance prediction of flexible manufacturing systems (FMSs) with a multiple discrete material-handling devices (MHD). An iterative method has been suggested using mean value analysis (MVA) for the state-dependent routing. Two queueing network models are considered to determine the material-handling device interference. In the first one, we model the interference from the MHD by inflating the station service times but neglect queueing at the MHD. In another network, the queueing for the MHD is taken into consideration. The performance of FMS configuration is obtained by iterating between two networks. The suggested algorithms demonstrate better results than the algorithm used by earlier workers for single MHD. Some performance indices viz. throughput, mean service time, mean waiting time, etc. are obtained. Numerical results are provided to highlight the effect of the system parameters on performance indices, which are further evaluated by using neuro-fuzzy controller system to validate the tactability of soft computing approach.     

Performance optimization of queueing systems with perturbation realization

After the intensive studies of queueing theory in the past decades, many excellent results in performance analysis have been obtained, and successful examples abound. However, exploring special features of queueing systems directly in performance optimization still seems to be a territory not very well cultivated. Recent progresses of perturbation analysis (PA) and sensitivity-based optimization provide a new perspective of performance optimization of queueing systems. PA utilizes the structural information of queueing systems to efficiently extract the performance sensitivity information from a sample path of system. This paper gives a brief review of PA and performance optimization of queueing systems, focusing on a fundamental concept called perturbation realization factors, which captures the special dynamic feature of a queueing system. With the perturbation realization factors as building blocks, the performance derivative formula and performance difference formula can be obtained. With performance derivatives, gradient-based optimization can be derived, while with performance difference, policy iteration and optimality equations can be derived. These two fundamental formulas provide a foundation for performance optimization of queueing systems from a sensitivity-based point of view. We hope this survey may provide some inspirations on this promising research topic.     

Integrated cellular manufacturing systems design with production planning and dynamic system reconfiguration

This paper presents and analyzes a comprehensive model for the design of cellular manufacturing systems (CMS). A recurring theme in research is a piecemeal approach when formulating CMS models. In this paper, the proposed model, to the best of the authors’ knowledge, is the most comprehensive one to date with a more integrated approach to CMS design, where production planning and system reconfiguration decisions are incorporated. Such a CMS model has not been proposed before and it features the presence of alternate process routings, operation sequence, duplicate machines, machine capacity and lot splitting. The developed model is a mixed integer non-linear program. Linearization procedures are proposed to convert it into a linearized mixed integer programming formulation. Computational results are presented by solving some numerical examples, extracted from the existing literature, with the linearized formulation.     

Experimental investigation of real-time scheduling in flexible manufacturing systems

This paper presents a new two-phase (TP) approximate method for real-time scheduling in a flexible manufacturing system (FMS). This method combines a reduced enumeration schedule generation algorithm with a 0–1 optimization algorithm. In order to make the combined algorithm practicable, heuristic rules are introduced for the selection of jobs to be scheduled. The relative performance of the TP method vis-a-vis conventional heuristic dispatching rules such as SPT, LPT, FCFS, MWKR, and LWKR is investigated using combined process-interaction/discrete-event simulation models. An efficient experimental procedure is designed and implemented using these models, and the statistical analysis of the results is presented. For the particular case investigated, the conclusions are very encouraging. In terms of mean flow time, the TP method performs significantly better than any other tested heuristic dispatching rules. Also, the experimental results show that using global information significantly improves the FMS performance.     

On modeling failure and repair times in stochastic models of manufacturing systems using generalized exponential distributions

Failures of machines have a significant effect on the behavior of manufacturing systems. As a result it is important to model this phenomenon. Many queueing models of manufacturing systems do incorporate the unreliability of the machines. Most models assume that the times to failure and the times to repair of each machine are exponentially distributed (or geometrically distributed in the case of discrete-time models). However, exponential distributions do not always accurately represent actual distributions encountered in real manufacturing systems. In this paper, we propose to model failure and repair time distributions bygeneralized exponential (GE) distributions (orgeneralized geometric distributions in the case of a discretetime model). The GE distribution can be used to approximate distributions with any coefficient of variation greater than one. The main contribution of the paper is to show that queueing models in which failure and repair times are represented by GE distributions can be analyzed with the same complexity as if these distributions were exponential. Indeed, we show that failures and repair times represented by GE distributions can (under certain assumptions) be equivalently represented by exponential distributions.This work was performed while the author was visiting the Laboratory for Manufacturing and Productivity, Massachusetts Institute of Technology, Cambridge, MA 02139, USA.     

Impact of flexible machines on automated manufacturing systems

Although the problem of scheduling dynamic job shops is well studied, setup and changeover times are often assumed to be negligibly small and therefore ignored. In cases where the product mix changes occur frequently, setup and changeover times are of critical importance. This paper applies some known results from the study of multi-class single-server queues with setup and changeover times to develop an approximation for evaluating the performance of job shops. It is found that the product mix, setup and changeover times, and scheduling rules affect the performance significantly, in particular at high levels of machine utilisation. This approach could be used to determine the required level of flexibility of machines and to choose an appropriate scheduling policy such that production rates remain within acceptable limits for foreseeable changes in the product mix.