17 research outputs found

    On transient queue-size distribution in the batch arrival system with the N-policy and setup times

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    In the paper the MX/G/1M^{X}/G/1 queueing system with the NN-policy and setup times is considered. An explicit formula for the Laplace transform of the transient queue-size distribution is derived using the approach consisting of few steps. Firstly, a "special\u27\u27 modification of the original system is investigated and, using the formula of total probability, the analysis is reduced to the case of the corresponding system without limitation in the service. Next, a renewal process generated by successive busy cycles is used to obtain the general result. Sample numerical computations illustrating theoretical results are attached as well

    Analysis of operating characteristics for the heterogeneous batch arrival queue with server startup and breakdowns

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    In this paper we consider a like-queue production system in which server startup and breakdowns are possible. The server is turned on (i.e. begins startup) when N units are accumulated in the system and off when the system is empty. We model this system by an M[x]/M/1 queue with server breakdowns and startup time under the N policy. The arrival rate varies according to the server's status: off, startup, busy, or breakdown. While the server is working, he is subject to breakdowns according to a Poisson process. When the server breaks down, he requires repair at a repair facility, where the repair time follows the negative exponential distribution. We study the steady-state behaviour of the system size distribution at stationary point of time as well as the queue size distribution at departure point of time and obtain some useful results. The total expected cost function per unit time is developed to determine the optimal operating policy at a minimum cost. This paper provides the minimum expected cost and the optimal operating policy based on assumed numerical values of the system parameters. Sensitivity analysis is also provided

    Non-stationary departure process in a batch-arrival queue with finite buffer capacity and threshold-type control mechanism

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    summary:Non-stationary behavior of departure process in a finite-buffer MX/G/1/KM^{X}/G/1/K-type queueing model with batch arrivals, in which a threshold-type waking up NN-policy is implemented, is studied. According to this policy, after each idle time a new busy period is being started with the NNth message occurrence, where the threshold value NN is fixed. Using the analytical approach based on the idea of an embedded Markov chain, integral equations, continuous total probability law, renewal theory and linear algebra, a compact-form representation for the mixed double transform (probability generating function of the Laplace transform) of the probability distribution of the number of messages completely served up to fixed time tt is obtained. The considered queueing system has potential applications in modeling nodes of wireless sensor networks (WSNs) with battery saving mechanism based on threshold-type waking up of the radio. An illustrating simulational and numerical study is attached

    Inventory control in multi-item production systems

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    This thesis focusses on the analysis and construction of control policies in multiitem production systems. In such systems, multiple items can be made to stock, but they have to share the finite capacity of a single machine. This machine can only produce one unit at a time and if it is set-up for one item, a switch-over or set-up time is needed to start the production of another item. Customers arrive to the system according to (compound) Poisson processes and if they see no stock upon arrival, they are either considered as a lost sale or backlogged. In this thesis, we look at production systems with backlog and production systems with lost sales. In production systems with lost sales, all arriving customers are considered lost if no stock is available and penalty costs are paid per lost customer. In production systems with backlog, arriving customers form a queue if they see no stock and backlogging costs are paid for every backlogged customer per time unit. These production systems find many applications in industry, for instance glass and paper production or bulk production of beers, see Anupindi and Tayur [2]. The objective for the production manager is to minimize the sum of the holding and penalty or backlogging costs. At each decision moment, the manager has to decide whether to switch to another product type, to produce another unit of the type that is set-up or to idle the machine. In order to minimize the total costs, a balance must be found between a fast switching scheme that is able to react to sudden changes in demand and a production plan with a little loss of capacity. Unfortunately, a fast switching scheme results in a loss of capacity, because switching from one product type to another requires a switch-over or set-up time. In the optimal production strategy, decisions depend on the complete state of the system. Because the processes at the different product flows depend on these decisions, the processes also depend on the complete state of the system. This means that the processes at the different product flows are not independent, which makes the analysis and construction of the optimal production strategy very complex. In fact, the complexity of the determination of this policy grows exponentially in the number of product types and if this number is too large, the optimal policy becomes intractable. Production strategies in which decisions depend on the complete system are defined as global lot sizing policies and are often difficult to construct or analyse, because of the dependence between the different product flows. However, in this thesis the construction of a global lot sizing policy is presented which also works for production systems with a large number of product types. The key factor that makes the construction possible is the fact that it is based on a fixed cycle policy. In Chapter 2, the fixed cycle policy is analysed for production systems with lost sales and in Chapter 6, the fixed cycle policy is analysed for production systems with backlog. The fixed cycle policy can be analysed per product flow and this decomposition property allows for the determination of the so called relative values. If it is assumed that one continues with a fixed cycle control, the relative values per product type represent the relative expected future costs for each decision. Based on these relative values, an improvement step (see Norman [65]) is performed which results in a ‘one step improvement’ policy. This policy is constructed and analysed in Chapters 2 and 7 for production systems with lost sales and production systems with backlog, respectively. This global lot sizing policy turns out to perform well compared to other, heuristic production strategies, especially in systems with a high load and demand processes with a high variability. A similar approach as for the production system with a single machine is performed in a system with two machines and lost sales in Chapter 3. Results show that in some cases the constructed strategy works well, although in some systems two separate one step improvement policies perform better. Examples of more heuristic production strategies are gated and exhaustive basestock policies. In these ’local lot sizing‘ policies, decisions depend only on the stock level of the product type that is set-up. But even in these policies, the processes at the different product flows are dependent. This makes the analysis difficult, but for production systems with backlog a translation can be made to a queueing system by looking at the number of products short to the base-stock level. So the machine becomes a server and each product flow becomes a queue. In these queueing systems, also known as polling systems, gated and exhaustive base-stock policies become gated and exhaustive visit disciplines. For polling systems, an exact analysis of the queue length or waiting time distribution is often possible via generating functions or Laplace-Stieltjes transforms. In Chapter 5, the determination of the sojourn time distribution of customers in a polling system with a (globally) gated visit discipline is presented, which comes down to the determination of the lead time distribution in the corresponding production system

    Modelling deadlock in queueing systems

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    Motivated by the needs of Aneurin Bevan University Health Board, this thesis ex- plores three themes: the phenomenon of deadlock in queueing systems, the develop- ment of discrete event simulation software, and applying modelling to the evaluation of the effects of a new healthcare intervention, Stay Well Plans, for older people in Gwent. When customers in a restricted queueing network become mutually blocked, and all possible movement ceases, that system becomes deadlocked. This thesis novelly investigates deadlock. A graph theoretical method of detecting deadlock in discrete event simulations is given, analytical models of deadlocking systems are built, and these are used to investigate the effect of system parameters on the expected time until reaching deadlock. Furthermore a deadlock resolution procedure is proposed. An open source discrete event simulation software, Ciw, is developed. This software is designed and developed using best practice principles. Furthermore it permits the use of best practice, such as reproducibility, in simulation modelling. Ciw is used for the modelling of a healthcare system, in order to evaluate the effect of Stay Well Plans. During the development of these models, a number of techniques are employed to overcome the difficulties of lack of data. Insightful results from these models are obtained, indicating a shift in demand from residential care services to community care services

    Performance study of asynchronous/ synchronous optical burst/ packet switching with partial wavelength conversion

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    Cataloged from PDF version of article.Wavelength conversion is known to be one of the most effective methods for contention resolution in optical packet/burst switching networks. In this thesis, we study various optical switch architectures that employ partial wavelength conversion, as opposed to full wavelength conversion, in which a number of converters are statistically shared per input or output link. Blocking is inevitable in case contention cannot be resolved and the probability of packet blocking is key to performance studies surrounding optical packet switching systems. For asynchronous switching systems with per output link converter sharing, a robust and scalable Markovian queueing model has recently been proposed by Akar and Karasan for calculating blocking probabilities in case of Poisson traffic. One of the main contributions of this thesis is that this existing model has been extended to cover the more general case of a Markovian arrival process through which one can study the impact of traffic parameters on system performance. We further study the same problem but with the converters being of limited range type. Although an analytical model is hard to build for this problem, we show through simulations that the so-called far conversion policy in which the optical packet is switched onto the farthest available wavelength in the tuning range, outperforms the other policies we studied. We point out the clustering effect in the use of wavelengths to explain this phenomenon. Finally, we study a synchronous optical packet switching architecture employing partial wavelength conversion at the input using the per input line converter sharing. For this architecture, we first obtain the optimal wavelength scheduler using integer linear programming and then we propose a number of heuristical scheduling algorithms. These algorithms are tested using simulations under symmetric and asymmetric traffic scenarios. Our results demonstrate that one can substantially reduce the costs of converters used in optical switching systems by using share per input link converter sharing without having to sacrifice much from the low blocking probabilities provided by full input wavelength conversion. Moreover, we show that the heuristic algorithm that we propose in this paper provides packet loss probabilities very close to those achievable using integer linear programming and is also easy to implement.DoÄŸan, KaanM.S

    On the dynamic allocation of assets subject to failure and replenishment

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    Problems of the dynamic allocation of assets subject to both failure and replenishment are common. We consider a problem inspired by naval search, where unmanned aerial vehicles are required to search an area of ocean for targets. The vehicles will require refuelling or rearming; this is represented by the aspects of failure and replenishment. Similar models can arise from considering problems of search and rescue, environmental monitoring, or project management. We formulate several versions of the problem, initially using the framework of a Markov decision process, bearing in mind trade-offs between real-world fidelity and mathematical tractability. We first consider models where rewards are gained independently from different tasks, before moving on to consider a specific kind of dependence in the rewards. We use a variety of mathematical techniques, including restless bandits, to formulate near-optimal policies for a slew of models. We consider and investigate the various policies through comprehensive computational modelling. For the independent case, we find that a Whittle index policy is extremely close to optimal while being computationally efficient. For the dependent formulation, we create a class of policies guaranteed to contain the optimal, parameterise the space, then choose the best from a limited set of parameters, augmenting with a single step of policy improvement. We close with some thoughts about what we have learned, considerations about applying the results presented in this thesis, and a discussion of intensifications and extensions we did not have time to consider
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