Loss systems in a random environment

We consider a single server system with infinite waiting room in a random environment. The service system and the environment interact in both directions. Whenever the environment enters a prespecified subset of its state space the service process is completely blocked: Service is interrupted and newly arriving customers are lost. We prove an if-and-only-if-condition for a product form steady state distribution of the joint queueing-environment process. A consequence is a strong insensitivity property for such systems. We discuss several applications, e.g. from inventory theory and reliability theory, and show that our result extends and generalizes several theorems found in the literature, e.g. of queueing-inventory processes. We investigate further classical loss systems, where due to finite waiting room loss of customers occurs. In connection with loss of customers due to blocking by the environment and service interruptions new phenomena arise. We further investigate the embedded Markov chains at departure epochs and show that the behaviour of the embedded Markov chain is often considerably different from that of the continuous time Markov process. This is different from the behaviour of the standard M/G/1, where the steady state of the embedded Markov chain and the continuous time process coincide. For exponential queueing systems we show that there is a product form equilibrium of the embedded Markov chain under rather general conditions. For systems with non-exponential service times more restrictive constraints are needed, which we prove by a counter example where the environment represents an inventory attached to an M/D/1 queue. Such integrated queueing-inventory systems are dealt with in the literature previously, and are revisited here in detail

Construction and Verification of Performance and Reliability Models

Over the last two decades formal methods have been extended towards performance and reliability evaluation. This paper tries to provide a rather intuitive explanation of the basic concepts and features in this area. Instead of striving for mathematical rigour, the intention is to give an illustrative introduction to the basics of stochastic models, to stochastic modelling using process algebra, and to model checking as a technique to analyse stochastic models

Reliability engineering of large jit production systems

This paper introduces the rationale and the fundamental elements and algorithms of a reliability engineering methodology, and discusses its application to the design of a large, multi-cell and heterogeneous production system with just-in-time (JIT) deliveries. The failure analysis and the non-reliability costs assessment of such systems is a complex task. In order to cope with such complexity, a two level hierarchical modelling and evaluation framework was developed. According to this framework, the internal behaviour of each manufacturing cell and the overall flow of materials are described, respectively, by local and global models. Local models are firstly obtained from the failure and repair processes of the manufacturing equipment. Then, these models are combined with the failure propagation delays introduced by the work-in-process buffers in order to obtain the system level model. The second part of the paper addresses several design issues of the production system that directly impact the reliability of the deliveries, such as the layout of the plant, the redundancy of the manufacturing equipment and the capacity of the work-in-process buffers. A distinctive feature of the reliability evaluation algorithm resides on the ability to deal with reliability models containing stochastic processes with generalized distributions. This fundamental requirement comes from the fact that repair and failure propagation processes typically present hyper-exponential distributions, e.g., lognormal distributions, that can’t be assessed using the conventional reliability techniques. The paper will also explain how the behavioural and structural characteristics of JIT production systems were explored in order to implement effective evaluation algorithms that fit the requirements of this class of systems.DST -Department of Science and Technology, Government of Kerala(600/09

Transient analysis of manufacturing system performance

Includes bibliographical references (p. 28-34).Supported by the INDO-US Science and Technology Fellowship Program.Y. Narahari, N. Viswanadham

Manufacturing flow line systems: a review of models and analytical results

The most important models and results of the manufacturing flow line literature are described. These include the major classes of models (asynchronous, synchronous, and continuous); the major features (blocking, processing times, failures and repairs); the major properties (conservation of flow, flow rate-idle time, reversibility, and others); and the relationships among different models. Exact and approximate methods for obtaining quantitative measures of performance are also reviewed. The exact methods are appropriate for small systems. The approximate methods, which are the only means available for large systems, are generally based on decomposition, and make use of the exact methods for small systems. Extensions are briefly discussed. Directions for future research are suggested.National Science Foundation (U.S.) (Grant DDM-8914277

Functional properties of throughput in tandem lines with unreliable servers and finite buffers

optimization;queueing theory;production

Data-driven Prediction of Internal Turbulences in Production Using Synthetic Data

Production planning and control are characterized by unplanned events or so-called turbulences. Turbulences can be external, originating outside the company (e.g., delayed delivery by a supplier), or internal, originating within the company (e.g., failures of production and intralogistics resources). Turbulences can have far-reaching consequences for companies and their customers, such as delivery delays due to process delays. For target-optimized handling of turbulences in production, forecasting methods incorporating process data in combination with the use of existing flexibility corridors of flexible production systems offer great potential. Probabilistic, data-driven forecasting methods allow determining the corresponding probabilities of potential turbulences. However, a parallel application of different forecasting methods is required to identify an appropriate one for the specific application. This requires a large database, which often is unavailable and, therefore, must be created first. A simulation-based approach to generate synthetic data is used and validated to create the necessary database of input parameters for the prediction of internal turbulences. To this end, a minimal system for conducting simulation experiments on turbulence scenarios was developed and implemented. A multi-method simulation of the minimal system synthetically generates the required process data, using agent-based modeling for the autonomously controlled system elements and event-based modeling for the stochastic turbulence events. Based on this generated synthetic data and the variation of the input parameters in the forecast, a comparative study of data-driven probabilistic forecasting methods was conducted using a data analytics tool. Forecasting methods of different types (including regression, Bayesian models, nonlinear models, decision trees, ensemble, deep learning) were analyzed in terms of prediction quality, standard deviation, and computation time. This resulted in the identification of appropriate forecasting methods, and required input parameters for the considered turbulences

Petri Nets Modelling and Analysis of the Veneer Layup System of Plywood Manufacturing Plant

In this paper performance behaviour is analysed in respect of the availability of the Veneer layup system of a plywood manufacturing plant. Generalized Stochastic Petri Nets (GSPN) technique is applied for modelling interactions among various components as well as the subsystems. The effects of the failure and repair rates, as well as availability of repair facilities on the behaviour of the system is investigated using a licensed software package. The outcomes will provide guidelines for the effective maintenance priorities to the practitioners and help in selecting appropriate maintenance strategies