230 research outputs found

    Optimal control and performance analysis of an M-X/M/1 queue with batches of negative customers

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    We consider a Markov decision process for an MX/M/1 queue that is controlled by batches of negative customers. More specifically, we derive conditions that imply threshold-type optimal policies, under either the total discounted cost criterion or the average cost criterion. The performance analysis of the model when it operates under a given threshold-type policy is also studied. We prove a stability condition and a complete stochastic comparison characterization for models operating under different thresholds. Exact and asymptotic results concerning the computation of the stationary distribution of the model are also derived

    Analysis of a batch-service queue with variable service capacity, correlated customer types and generally distributed class-dependent service times

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    Queueing models with batch service have been studied frequently, for instance in the domain of telecommunications or manufacturing. Although the batch server's capacity may be variable in practice, only a few authors have included variable capacity in their models. We analyse a batch server with multiple customer classes and a variable service capacity that depends on both the number of waiting customers and their classes. The service times are generally distributed and class-dependent. These features complicate the analysis in a non-trivial way. We tackle it by examining the system state at embedded points, and studying the resulting Markov Chain. We first establish the joint probability generating function (pgf) of the service capacity and the number of customers left behind in the queue immediately after service initiation epochs. From this joint pgf, we extract the pgf for the number of customers in the queue and in the system respectively at service initiation epochs and departure epochs, and the pgf of the actual server capacity. Combined with additional techniques, we also obtain the pgf of the queue and system content at customer arrival epochs and random slot boundaries, and the pgf of the delay of a random customer. In the numerical experiments, we focus on the impact of correlation between the classes of consecutive customers, and on the influence of different service time distributions on the system performance. (C) 2019 Elsevier B.V. All rights reserved

    Size-based scheduling vs fairness for datacenter flows: a queuing perspective

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    Contrary to the conclusions of a recent body of work where approximate shortest remaining processing time first (SRPT) flow scheduling is advocated for datacenter networks, this paper aims to demonstrate that per-flow fairness remains a preferable objective. We evaluate abstract queuing models by analysis and simulation to illustrate the non-optimality of SRPT under the reasonable assumptions that datacenter flows occur in batches and bursts and not, as usually assumed, individually at the instants of a Poisson process. Results for these models have significant implications for the design of bandwidth sharing strategies for datacenter networks. In particular, we propose a novel "virtual fair scheduling" algorithm that enforces fairness between batches and is arguably simple enough to be implemented in high speed devices.Comment: 16 pages, 5 figure

    Controlling the order pool in make-to-order production systems

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    Voor ‘Make-To-Order’ (MTO, oftewel klantordergestuurde) productiesystemen is de tijd die orders moeten wachten op beschikbare productiecapaciteit cruciaal. Het beheersen van die wachttijd is van groot belang om zowel korte als betrouwbare doorlooptijden te realiseren. Daarom analyseerde en ontwierp Remco Germs regels voor orderacceptatie en ordervrijgave, om daarmee de wachttijden te beheersen. Orderacceptatie en -vrijgave zijn de twee belangrijkste mechanismen om de lengte van wachttijden te beïnvloeden en zodoende de productie te sturen. De logistieke prestatie hangt in grote mate af van specifieke kenmerken van MTO-systemen, zoals routing variabiliteit, beperkte productiecapaciteit, omsteltijden, strikte leveringsvoorwaarden en onzekerheid in het aankomstpatroon van orders. Om een beter begrip te krijgen van de afwegingen die MTO-bedrijven in dit opzicht moeten maken richt het proefschrift zich op de modellering van de belangrijkste kenmerken van MTO-systemen. De inzichten die dat oplevert worden vervolgens gebruikt om orderacceptatie- en ordervrijgaveregels te ontwikkelen die eenvoudig te begrijpen en daarom makkelijk in praktijksituaties te implementeren zijn. Deze relatief eenvoudige beslissingsregels kunnen al leiden tot significante verbeteringen in de logistieke prestaties van MTO-bedrijven. The thesis of Remco Germs analyses and develops order acceptance and order release policies to control queues in make-to-order (MTO) production systems. Controlling the time orders spend waiting in queues is crucial for realizing short and reliable delivery times, two performance measures which are of strategic importance for many MTO com-panies. Order acceptance and order release are the two most important production con-trol mechanisms to influence the length of these queues. Their performance depends on typical characteristics of MTO systems, such as random (batch) order arrival, routing variability, fixed capacities, setup times and (strict) due-dates. To better understand the underlying mechanisms of good order acceptance and order release policies the models in this thesis focus on the main characteristics of MTO systems. The insights obtained from these models are then used to develop order acceptance and order release policies that are easy to understand and thereby easy to implement in practice. The results show that these relatively simple policies may already lead to significant performance improvements for MTO companies.

    Controlling the order pool in make-to-order production systems

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    Controlling the order pool in make-to-order production systems

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