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

Modeling and analysis to improve the quality of healthcare services

For many healthcare services or medical procedures, patients have extensive risk of complication or face death when treatment is delayed. When a queue is formed in such a situation, it is very important to assess the suffering and risk faced by patients in queue and plan sufficient medical capabilities in advance to address the concerns. As the diversity of care settings increases, congestion in facilities causes many patients to unnecessarily spend extra days in intensive care facilities. Performance evaluation of current healthcare service systems using queueing theory gains more and more importance because of patient flows and systems complexity. Queueing models have been used in handsome number of healthcare studies, but the incorporation of blocking is still limited. In this research work, we study an efficient two-stage multi-class queueing network system with blocking and phase-type service time distribution to analyze such congestion processes. We also consider parallel servers at each station and first-come-first-serve non-preemptive service discipline are used to improve the performance of healthcare service systems

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

Fluid flow models in performance analysis

We review several developments in fluid flow models: feedback fluid models, linear stochastic fluid networks and bandwidth sharing networks. We also mention some promising new research directions

Performance analysis of load based M/M/3 transient queueing system with finite capacity

This paper deals with the investigation of M/M/3 queueing model under the provision of service rates of jobs depend upon the load of the jobs arrived in the system. The customers (jobs) arrive in the system in Poisson fashion and they are served in the chronological order of their arrival. Differential equations of transient probability distribution functions by using a transition diagram have been set up. Laplace Transform, probability generating function, and Rouchey’s Theorem have been applied to get the probability of n customer in time t. Various performance indices such as the mean number of customers in the system, expected number of customers in a queue, probability that one has not to wait, expected mean time spent in a system, expected mean time spent in a queue, probability that the queue size being greater than or equal to N have been obtained analytically. Finally, the analytical results are validated graphically with the help of computing software.Publisher's Versio

An analytic finite capacity queueing network model capturing blocking, congestion and spillbacks

Analytic queueing network models often assume infinite capacity for all queues. For real systems this infinite capacity assumption does not hold, but is often maintained due to the difficulty of grasping the between-queue correlation structure present in finite capacity networks. This correlation structure helps explain bottleneck effects and spillbacks, the latter being of special interest in networks containing loops because they are a source of potential deadlock. We present an analytic queueing network model which acknowledges the finite capacity of the different queues. By explicitly modeling the blocking phase the model yields a description of the congestion effects. The model is adapted for multiple server finite capacity queueing networks with an arbitrary topology and blocking-after-service. A decomposition method allowing the evaluation of the model is described. The method is validated, by comparison to both pre-existing methods and simulation results. A real application to the study of patient flow in a network of operative and post-operative units of the Geneva University Hospital is also presented

Queues with Congestion-dependent Feedback

This dissertation expands the theory of feedback queueing systems and applies a number of these models to a performance analysis of the Transmission Control Protocol, a flow control protocol commonly used in the Internet