We consider a class of queueing systems that consist of server pools in parallel and multiple customer classes. Customer service times are assumed to be exponentially distributed. We study the asymptotic behavior of these queueing systems in a heavy traffic regime that is known as the Halfin and Whitt many-server asymptotic regime. Our main contribution is a general framework for establishing state space collapse results in the Halfin and Whitt many-server asymptotic regime for parallel server systems having multiple customer classes. In our work, state space collapse refers to a decrease in the dimension of the processes tracking the number of customers in each class waiting for service and the number of customers in each class being served by various server pools. We define and introduce a state space collapse function, which governs the exact details of the state space collapse. Our methodology is similar in spirit to that in Bramson (1998); however, Bramson studies an asymptotic regime in which the number of servers is fixed and Bramson does not require a state space collapse function. We illustrate the applications of our results in three different parallel server systems. The first system is a distributed parallel server system under the minimum-expected-delay faster-server-first (MED-FSF) or minimumexpected- delay load-balancing (MED-LB) policies. We prove that the MED-FSF policy minimizes the stationary distribution of total number of customers in the system. However, under the MED-FSF policy all the servers in our distributed system except those with the lowest service rate experience 100% utilization but under the MED-LB policy, on the other hand, the utilizations of all the server pools are equal. The second system we consider is known as the N-model. We show that when the service times only depend on the server pool providing service a static priority rule is asymptotically optimal. Finally, we study two results conjectured in the literature for V-systems. We show for all of these systems that the conditions on the hydrodynamic limits can easily be checked using the standard tools that have been developed in the literature to analyze fluid models.

Composition of web services is one of the flexible and easiest approaches for creating composite services that fulfill complex tasks. Together with providing convenience in creation of new software applications, service composition has various challenges. One of them is the satisfaction of user-defined Quality of Service (QoS) requirements while selecting services for a composition. Load balancing issue is another challenge as uncontrolled workload may lead to violation of service providers&rsquo / QoS declarations. This thesis work proposes a QoS aware method for optimum service composition while taking into account load balancing. M/M/C queuing model is utilized for the individual services to determine sojourn time distribution for possible compositions. Percentile of the execution time, price and availability are considered as QoS parameters. Proposed algorithm selects the optimum composition according to QoS constraints and utility provided by the services. The performance of the method is evaluated by custom simulation software and is compared to two other methods, random selection and average execution timebased optimal service selection.

We study two classes of stochastic systems, the limited processor sharing system and the multi-server system. They share the common feature that multiple jobs/customers are being processed simultaneously, which makes the study of them intrinsically difficult. In the limited processor sharing system, a limited number of jobs can equally share a single server, and the excess ones wait in a first-in-first-out buffer. The model is mainly motivated by computer related applications, such as database servers and packet transmission over the Internet. This model is studied in the first part of the thesis. The multi-server queue is mainly motivated by call centers, where each customer is handled by an agent. The number of customers being served at any time is limited by number of agents employed. Customers who can not be served upon arrival wait in a first-in-first-out buffer. This model is studied in the second part of the thesis.

Thesis (M.S.)--Worcester Polytechnic Institute. / Keywords: PI; PISA; PIMC; cwnd; TCP. Includes bibliographical references (p. 49-50).

This thesis focuses on increasing the efficiency of systems with cross-trained workforce and finite storage spaces. Our objective is to maximize the throughput and minimize the setup costs (if they exist). More specifically, we are interested in determining effective cross-training strategies and dynamic server assignment policies for flexible servers in production lines with finite buffers. In the first part of this thesis, we study non-Markovian systems and support the conjecture that effective server assignment policies are robust to service time distributions. Next, we consider understaffed tandem lines with partially or fully flexible servers, determine optimal and heuristic server assignment policies, and show that most of the benefits of full flexibility can be achieved with limited flexibility. Finally, we incorporate the setups to our model, determine the optimal server assignment policy for some systems and show how the effective assignment of servers depends on the magnitude of the setup costs.

Thesis (M.S.)--State University of New York at Binghamton, Thomas J. Watson School of Engineering and Applied Science, Department of Computer Science, 2009. / Includes bibliographical references.

Este trabalho tem como objetivo contribuir com o processo de decisões em estratégias de produção no que se refere a decisões de curto prazo e otimização de recursos produtivos. Algumas dessas decisões, foco deste trabalho, relacionam-se com questões clássicas: o que deve ser produzido, quanto deve ser produzido, quais produtos devem ser produzidos e qual deverá ser o prazo para a entrega de seu produto ao cliente. Estas questões poderiam de certa maneira ser respondidas facilmente quando os mercados possuíam menores exigências quanto à qualidade, prazos e quantidades. Para determinados mercados cuja competição é baseada na diversidade de produtos e no tempo de resposta, isto é, clientes que desejam velocidade no atendimento, alta variedade e confiabilidade, estas questões tornaram-se complexas. Este trabalho demonstra que se pode conseguir bons resultados por meio de análises estatísticas e otimização de recursos produtivos mesmo considerando um sistema de entradas aleatórias, com um único recurso produtivo e limitado por restrições e tendo que decidir por dois tipos de atendimento conflitantes: produzir para estoque ou produzir sob encomenda. Propõe por meio de uma abordagem quantitativa analisar a questão sob a perspectiva da teoria das filas e análises estatísticas melhorar a eficiência de um recurso produtivo por meio de uma estratégia diferenciada de programação e planejamento. Também se demonstrou que as decisões tomadas pelos gestores de produção podem influenciar e impactar no processo competitivo da empresa. / This work aims to contribute to the process of decisions on production strategies with regard to short-term decisions and optimization of productive resources. Some of these decisions, the focus of this work relates to the classic questions: what should be produced, how much should be produced, which products should be produced and what should be the deadline for delivery of your product to the customer. These questions could be answered in a way easily when markets had lower requirements for quality, quantity and deadlines. For certain markets where competition is based on product diversity and response time, ie customers who want speed in service, high reliability and variety, these issues have become complex. This article demonstrates that good results can be achieved through statistical analysis and optimization of productive resources even considering a system of random inputs with a single productive resource and limited by constraints and having to decide for two types of care conflicting produce to stock or produce custom. It proposes using a quantitative approach to analyze the issue from the perspective of queuing theory and statistical analysis to improve the efficiency of a productive resource through a differentiated strategy planning and programming. It was also demonstrated that the decisions taken by the managers of production can influence and impact the companys competitive process.

This work is focused on solving problems in Industry 4.0. Main part of this work describes development of a discreet simulation model based on queuing theory. This model will be used for a heuristic optimization of a production line. Model will be validated with data from real production line. Improvement of effectivity using discrete model and heuristic optimization will be shown on virtual production line.

L'analyse de la performance à l'état stationnaire dans de nombreux systèmes de files d'attente est complexe et les résultats sous forme explicite ne sont disponibles que dans des cas particuliers. Nous avons donc développé des approximations pour des critères de performance importants à l'état stationnaire tels que la longueur de la file d'attente, le temps d'attente et le temps de traitement total. Nous analysons d'abord la performance dans des cas à faible et fort trafic. Nous montrons ensuite comment développer une approximation basée sur une interpolation qui est valable pour n'importe quelle condition de trafic. Un avantage de l'approche proposée est qu'elle n'est pas dépendante d’un modèle particulier et donc elle peut être appliquée à d'autres modèles de files d'attente complexes. Nous appliquons cette technique pour trois modèles largement utilisés dans l'évaluation des performances des réseaux stochastiques : le modèle du supermarché, la file d'attente Discriminatory-Processor-Sharing (DPS) et la file d'attente Relative Priority (RP). Le modèle du supermarché est une file d'attente à plusieurs serveurs où lorsqu’un client arrive, deux serveurs sont choisis au hasard dans un ensemble de serveurs. La politique Join-the-Shortest-Queue (JSQ) est ensuite utilisée parmi les deux serveurs sélectionnés. DPS et RP sont deux files d'attente à plusieurs classes et à serveur unique mettant en œuvre des priorités relatives entre les clients des différentes classes. La discipline DPS sert tous les clients simultanément, tandis que RP sert un seul client à la fois de manière non-préemptive. Nous montrons que dans certains cas, l'interpolation est exacte. Nous utilisons ensuite cette approximation pour déduire comment la performance dépend des paramètres des modèles, et nous effectuons des expériences numériques illustrant la précision de l'interpolation dans un grand nombre de cas de figure / The analysis of the steady-state performance in many queuing systems is complex and closed-form results are available only in particular cases. We therefore set out to develop approximations for important performance measures in steady-state such as the queue length vector, waiting time and sojourn time. We first analyse the performance in a light-traffic and heavy-traffic regime. We then show how to develop an interpolation-based approximation that is valid for any load in the system. An advantage of the approach taken is that it is not model dependent and hence could potentially be applied to other complex queuing models. We apply this technique to three widely used models in the performance evaluation of stochastic networks: The supermarket model, the Discriminatory-Processor-Sharing (DPS) queue and the Relative Priority (RP) queue. The supermarket model is a multi-server queue where upon arrival of a customer two servers are selected at random from the available pool of servers. The Join-the-Shortest-Queue policy is then used in isolation with these two servers. DPS and RP are both single-server multi-class queues that implement relative priorities among customers of the various classes. The DPS discipline serves all customers simultaneously while RP serves one customer at a time in a non-preemptive way. We show that in some instances the interpolation approximation is exact. We then use the approximation to draw structural insights onto the performance of the system, and we carry out numerical experiments that illustrate that the interpolation approximation is accurate over a wide range of parameters

Queueing theory has often been applied to study communication and service queueing systems such as call centers, hospital emergency departments and ride-sharing platforms. Unfortunately, it is complicated to analyze queueing systems. That is largely because the arrival and service processes that mainly determine a queueing system are uncertain and must be represented as stochastic processes that are difficult to analyze. In response, service providers might be able to partially capture the main characteristics of systems given partial data information and limited domain knowledge. An effective engineering response is to develop tractable approximations to approximate queueing characteristics of interest that depend on critical partial information. In this thesis, we contribute to developing high-quality approximations by studying tight bounds for the transient and the steady-state mean waiting time given partial information. We focus on single-server queues and multi-server queues with the unlimited waiting room, the first-come-first-served service discipline, and independent sequences of independent and identically distributed sequences of interarrival times and service times. We assume some partial information is known, e.g., the first two moments of inter-arrival and service time distributions. For the single-server GI/GI/1 model, we first study the tight upper bounds for the mean and higher moments of the steady-state waiting time given the first two moments of the inter-arrival time and service-time distributions. We apply the theory of Tchebycheff systems to obtain sufficient conditions for classical two-point distributions to yield the extreme values. For the tight upper bound of the transient mean waiting time, we formulate the problem as a non-convex non-linear program, derive the gradient of the transient mean waiting time over distributions with finite support, and apply classical non-linear programming theory to characterize stationary points. We then develop and apply a stochastic variant of the conditional gradient algorithm to find a stationary point for any given service-time distribution. We also establish necessary conditions and sufficient conditions for stationary points to be three-point distributions or special two-point distributions. Our studies indicate that the tight upper bound for the steady-state mean waiting time is attained asymptotically by two-point distributions as the upper mass point of the service-time distribution increases and the probability decreases, while one mass of the inter-arrival time distribution is fixed at 0. We then develop effective numerical and simulation algorithms to compute the tight upper bound. The algorithms are aided by reductions of the special queues with extremal inter-arrival time and extremal service-time distributions to D/GI/1 and GI/D/1 models. Combining these reductions yields an overall representation in terms of a D/RS(D)/1 discrete-time model involving a geometric random sum of deterministic random variables, where the two deterministic random variables have different values, so that the extremal waiting times need not have a lattice distribution. We finally evaluate the tight upper bound to show that it offers a significant improvement over established bounds. In order to understand queueing performance given only partial information, we propose determining intervals of likely performance measures given that limited information. We illustrate this approach for the steady-state waiting time distribution in the GI/GI/K queue given the first two moments of the inter-arrival time and service time distributions plus additional information about these underlying distributions, including support bounds, higher moments, and Laplace transform values. As a theoretical basis, we apply the theory of Tchebycheff systems to determine extremal models (yielding tight upper and lower bounds) on the asymptotic decay rate of the steady-state waiting-time tail probability, as in the Kingman-Lundberg bound and large deviations asymptotics. We then can use these extremal models to indicate likely intervals of other performance measures. We illustrate by constructing such intervals of likely mean waiting times. Without extra information, the extremal models involve two-point distributions, which yield a wide range for the mean. Adding constraints on the third moment and a transform value produces three-point extremal distributions, which significantly reduce the range, yielding practical levels of accuracy.