Este trabalho estuda medidas de desempenho aproximadas em centrais de atendimento, apresentadas pelo modelo M/G/s/r+G. As aproximações são calculadas a partir do modelo M/M/s/r+M(n). Os resultados foram extendidos para o caso de mais de um tipo de cliente, apresentado pelo modelo M/Mi/s/r+Mi(n). Para dois casos particulares com 2 tipos de clientes, as aproximações citadas foram avaliadas numericamente e comparadas com os resultados de referência obtidos através de simulação. Os resultados aproximados comprovam que a aproximação é bastante satisfatória. / We study approximations for performance measures of call centers, represented by M/G/s/r+G queueing model. We use the measures computed in the M/M/s/r+M(n) queueing model. The results were extended for more then one type of customer, represented by M/Mi/s/r+Mi(n) queueing model. For two particular cases with two types of customers, the mentioned approaches were numerically evaluated and compared with the results of reference obtained by simulation. The approximate results show that the approach is quite satisfactory.

<p>Many types of services are provided using some equipment or machines, e.g. transportation systems using vehicles. Designs of these systems require capacity decisions, e.g., the number of vehicles. In my dissertation, I use many-server and conventional heavy-traffic limit theory to derive asymptotically optimal capacity decisions, giving the desired level of delay and availability performance with minimum investment. The results provide near-optimal solutions and insights to otherwise analytically intractable problems.</p> <p>The dissertation will comprise two essays. In the first essay, &ldquoAsymptotic Analysis of Delay-based Performance Metrics and Optimal Capacity Decisions for the Machine Repair Problem with Spares,&rdquo I study the M/M/R machine repair problem with spares. This system can be represented by a closed queuing network. Applications include fleet vehicles' repair and backup capacity, warranty services' staffing and spare items investment decisions. For these types of systems, customer satisfaction is essential; thus, the delays until replacements of broken units are even more important than delays until the repair initiations of the units. Moreover, the service contract may include conditions on not only the fill rate but also the probability of acceptable delay (delay being less than a specified threshold value).</p> <p>I address these concerns by expressing delays in terms of the broken-machines process; scaling this process by the number of required operating machines (or the number of customers in the system); and using many-server limit theorems (limits taken as the number of customers goes to infinity) to obtain the limiting expected delay and probability of acceptable delay for both delay until replacement and repair initiation. These results lead to an approximate optimization problem to decide on the repair and backup-capacity investment giving the minimum expected cost rate, subject to a constraint on the acceptable delay probability. Using the characteristics of the scaled broken-machines process, we obtain insights about the relationship between quality of service and capacity decisions. Inspired by the call-center literature, we categorize capacity level choice as efficiency-driven, quality-driven, or quality- and efficiency-driven. Hence, our study extends the conventional call center staffing problem to joint staffing and backup provisioning. Moreover, to our knowledge, the machine-repair problem literature has focused mainly on mean and fill rate measures of performance for steady-state cost analysis. This approach provides complex, nonlinear expressions not possible to solve analytically. The contribution of this essay to the machine-repair literature is the construction of delay-distribution approximations and a near-optimal analytical solution. Among the interesting results, we find that for capacity levels leading to very high utilization of both spares and repair capacity, the limiting distribution of delay until replacement depends on one type of resource only, the repair capacity investment.</p> <p>In the second essay, &ldquoDiffusion Approximations and Near-Optimal Design of a Make-to-Stock Queue with Perishable Goods and Impatient Customers,&rdquo I study a make-to-stock system with perishable inventory and impatient customers as a two-sided queue with abandonment from both sides. This model describes many consumer goods, where not only spoilage but also theft and damage can occur. We will refer to positive jobs as individual products on the shelf and negative jobs as backlogged customers. In this sense, an arriving negative job provides the service to a waiting positive job, and vice versa. Jobs that must wait in queue before potential matching are subject to abandonment. Under certain assumptions on the magnitude of the abandonment rates and the scaled difference between the two arrival rates (products and customers), we suggest approximations to the system dynamics such as average inventory, backorders, and fill rate via conventional heavy traffic limit theory.</p> <p>We find that the approximate limiting queue length distribution is a normalized weighted average of two truncated normal distributions and then extend our results to analyze make-to-stock queues with/without perishability and limiting inventory space by inducing thresholds on the production (positive) side of the queue. Finally, we develop conjectures for the queue-length distribution for a non-Markovian system with general arrival streams. We take production rate as the decision variable and suggest near-optimal solutions.</p> / Dissertation

Distributed Discrete Event Simulation (DDES) has received much attention in recent years, owing to the fact that uniprocessor based serial simulations may require excessive amount of simulation time and computational resources. It is therefore natural to attempt to use multiple processors to exploit the inherent parallelism in discrete event simulations in order to speed up the simulation process. In this dissertation we study the performance of distributed simulation of queueing networks, by analysing queueing models of message flows in distributed discrete event simulators. Most of the prior work in distributed discrete event simulation can be catego­rized as either empirical studies or analytic (or formal) models. In the empirical studies, specific experiments are run on both conservative and optimistic simulators to see which strategy results in a faster simulation. There has also been increasing activity in analytic models either to better understand a single strategy or to compare two strategies. Little attention seems to have been paid to the behaviour of the interprocessor message queues in distributed discrete event simulators. To begin with, we study how to model distributed simulators of queueing networks. We view each logical process in a distributed simulation as comprising a message sequencer with associated message queues, followed by an event processor. A major contribution in this dissertation is the introduction of the maximum lookahead sequencing protocol. In maximum lookahead sequencing, the sequencer knows the time-stamp of the next message to arrive in the empty queue. Maximum lookahead is an unachievable algorithm, but is expected to yield the best throughput compared to any realisable sequencing technique. The analysis of maximum lookahead, therefore, should lead to fundamental limits on the performance of any sequencing algorithm We show that, for feed forward type simulators, with standard stochastic assump-tions for message arrival and time-stamp processes, the message queues are unstable for conservative sequencing, and for conservative sequencing with maximum lookahead and hence for optimistic resequencing, and for any resequencing algorithm that does not employ interprocessor "flow control". It follows that the resequencing problem is fundamentally unstable and some form of interprocessor flow control is necessary in order to make the message queues stable (without message loss). We obtain some generalizations of the insta­bility results to time-stamped message arrival processes with certain ergodicity properties. For feedforward type distributed simulators, we study the throughput of the event sequencer without any interprocessor flow control. We then incorporate flow control and study the throughput of the event sequencer. We analyse various flow control mechanisms. For example, we can bound the buffers of the message queues, or various logical processes can be prevented from getting too far apart in virtual time by means of a mechanism like Moving Time Windows or Bounded Lag. While such mechanisms will serve to stabilize buffers, our approach, of modelling and analysing the message flow processes in the simulator, points towards certain fundamental limits of efficiency of distributed simulation, imposed by the synchronization mechanism. Next we turn to the distributed simulation of more general queueing networks. We find an upper bound to the throughput of distributed simulators of open and closed queueing networks. The upper bound is derived by using flow balance relations in the queueing network and in the simulator, processing speed constraints, and synchronization constraints in the simulator. The upper bound is in terms of parameters of the queueing network, the simulator processor speeds, and the way the queueing network is partitioned or mapped over the simulator processors. We consider the problem of choosing a mapping that maximizes the upper bound. We then study good solutions o! this problem as possible heuristics for the problem of partitioning the queueing network over the simulator processors. We also derive a lower bound to the throughput of the distributed simulator for a simple queueing network with feedback. We then study various properties of the maximum lookahead algorithm. We show that the maximum lookahead algorithm does not deadlock. Further, since there are no syn­chronization overheads, maximum lookahead is a simple algorithm to study. We prove that maximum lookahead sequencing (though unrealisable) yields the best throughput compared to any realisable sequencing technique. These properties make maximum lookahead a very useful algorithm in the study of distributed simulators of queueing networks. To investigate the efficacy of the partitioning heuristic, we perform a study of queue­ing network simulators. Since it is important to study the benefits of distributed simula­tion, we characterise the speedup in distributed simulation, and find an upper bound to the speedup for a given mapping of the queues to the simulator processors. We simulate distributed simulation with maximum lookahead sequencing, with various mappings of the queues to the processors. We also present throughput results foT the same mappings but using a distributed simulation with the optimistic sequencing algorithm. We present a num­ber of sufficiently complex examples of queueing networks, and compare the throughputs obtained from simulations with the upper bounds obtained analytically. Finally, we study message flow processes in distributed simulators of open queueing networks with feedback. We develop and study queueing models for distributed simulators with maximum lookahead sequencing. We characterize the "external" arrival process, and the message feedback process in the simulator of a simple queueing network with feedback. We show that a certain "natural" modelling construct for the arrival process is exactly correct, whereas an "obvious" model for the feedback process is wrong; we then show how to develop the correct model. Our analysis throws light on the stability of distributed simulators of queueing networks with feedback. We show how the stability of such simulators depends on the parameters of the queueing network.

Different applications of communication networks have different requirements that depend on the type of application. We consider the problem of differentiating between delay-sensitive applications based on their average delay requirements, as may be of interest in signalling networks. We consider packets of different classes that are to be transmitted on the same link with different average delay requirements, to reside in separate queues with the arrival statistics for the queues being specified. This statistical multiplexer has to schedule packets from different queues in so that the average delays of the queues approach the specified target delays as quickly as possible. For simplicity, we initially consider a discrete-time model with two queues and a single work-conserving server, with independent Bernoulli packet arrivals and unit packet service times. With arrival rates specified, achieving mean queue lengths in a ratio which corresponds to the ratio of target mean delays is a means of achieving individual target mean delays. We formulate the problem in the framework of Markov decision theory. We study two scheduling policies called Queue Length Balancing and Delay Balancing respectively, and show through numerical computation that the expectation of magnitude of relative error in θ (1/m) and θ (1/√m) respectively, and that the expectation of the magnitude of relative error in weighted average delays decays as θ (1/√m) and θ (1/m) respectively, where m is the averaging interval length. We then consider the model for an arbitrary number of queues each with i.i.d. batch arrivals, and analyse the errors in the average delays of individual queues. We assume that the fifth moment of busy period is finite for this model. We show that the expectation of the absolute value of error in average queue length for at least one of the queues decays at least as slowly as θ (1/√m), and that the mean squared error in queue length for at least one of the queues decays at least as slowly as θ (1/m). We show that the expectation of the absolute value of error in approximating Little’s law for finite horizon is 0 (1/m). Hence, we show that the mean squared error in delay for at least one of the queues decays at least slowly as θ (1/m). We also show that if the variance of error in delay decays for each queue, then the expectation of the absolute value of error in delay for at least one of the queues decays at least as slowly as θ (1/√m).

Šiuolaikinio verslo sektorius yra labai sudėtingas, kadangi daugybė programinės ir kompiuterinės įrangos yra naudojama skirtingose platformose: internetinių sistemų bendravimui, verslo sistemų integravimui ir t. t. Dauguma šiuolaikinės programinės įrangos priklauso paskirstytų sistemų tipui. Ją sudaro kliento-serverio architektūra. Nagrinėjant konkrečią paskirstytą sistemą, joje klientų ir serverių kiekis gali būti gausus. Tokio tipo sistemos turi labai daug privalumų, tačiau turi ir trūkumų. Paprastai paskirstytas sistemas sudaro ne viena duomenų bazė, veikia daug servisų, kurie ne visada gali būti pasiekiami, visa tai yra galimų klaidų šaltinis. Kliento programinė įranga bendrauja tarp įvairių programinės įrangos komponentų (pavyzdžiui servisų), kaip ir jie tarpusavyje, naudodama nuotolinių procedūrų kvietimo technologijas ir žinutes. Naudojant žinučių technologiją, bendravimas tarp servisų gali būti daug patikimesnis, kadangi ši technologija užtikrina žinutės pristatymą, net ir tada, kai gavėjas yra už ryšio ribų. Šiuolaikinėse servisais paremtose sistemose, bendravimas tarp komponentų yra paremtas žinučių, naudojančių eiles, metodu. Šiame darbe bus nagrinėjama bendravimo tarp komponentų technologija, kuri paremta žinutėmis. Taip pat bus apžvelgiamos ir nagrinėjamos trečių šalių sukurtos, nemokamos technologijos, kurios skirtos bendravimui tarp paskirstytų sistemų komponentų žinučių metodu. Kadangi magistrinio darbo sistema buvo sukurta naudojant Microsoft technologijas... [toliau žr. visą tekstą] / Nowadays a lot of systems are residing in distributed environments. These systems are composed of the client side software and server side software. That is called distributed systems architecture. Those types of systems can contain many services and many clients and may be substituted of many databases and many services. Distributed software components do not always run at the same time, networks, especially wide-area networks, are not always available and reliable. These parts communicate using remote procedure calls, or request/response messages and message queues. In this work we research third party components which are used to communicate between parts of distributed systems using messages and Microsoft message queues. The research is performed on two chosen components, which best fits in the developed system’s context. The choice of components and research based on usability problems using developed system called Business layer framework. The obtained results evaluated using user recommendation form.

L'analyse des risques est devenu un enjeu majeur dans notre société. Quels que soient les champs d'application dans lesquels une situation à risque peut survenir, les mathématiques et plus particulièrement les statistiques et les probabilités se révèlent être des outils essentiels. L'objet principal de cette thèse est de développer des indicateurs de risque pertinents et d'étudier les propriétés extrémales de processus intervenant dans deux domaines d'applications : en risque alimentaire et en assurance. La théorie du risque se situe entre l'analyse des valeurs extrêmes et la théorie des variables aléatoires à variations régulières ou à queues lourdes. Dans le premier chapitre, on définit les éléments clefs de la théorie du risque ainsi que la notion de variation régulière et on introduit différents modèles liés au risque alimentaire qui seront étudiés dans les chapitres 2 et 3. Le chapitre 2 présente les travaux effectués avec Olivier Wintenberger. Pour des classes de processus stochastiques, sous des hypothèses de variations régulières, on développe une méthode qui permet d'obtenir des équivalents asymptotiques en horizon fini d'indicateurs de risque en assurance et en risque alimentaire tels que la probabilité de ruine, le "temps passé au dessus d'un seuil" ou encore la "sévérité de la ruine". Le chapitre 3 se concentre sur des modèles en risque alimentaire. Précisément, on étudie les propriétés extrémales de différentes généralisations d'un processus d'exposition à un contaminant nommé KDEM pour Kinetic Dietary Exposure Model proposé par Patrice Bertail et ses co-auteurs en 2008. Sous des hypothèses de variations régulières, on propose des équivalents asymptotiques du comportement de queue et de l'indice extrémal du processus d'exposition. Enfin, le chapitre 4 passe en revue différentes techniques statistiques particulièrement adaptées à l'étude du comportement extrémal de certains processus de Markov. Grâce à des propriétés de régénérations, il est possible de découper le chemin des observations en blocs indépendants et identiquement distribués et de n'étudier ainsi que le processus sur un bloc. Ces techniques s'appliquent même si la chaîne de Markov n'est pas atomique. On se concentre ici sur l'estimation de l'indice de queue et de l'indice extrémal. On illustre la performance de ces techniques en les appliquant sur deux modèles - en assurance et en finance - dont on connaît les résultats théoriques / Risk analyses play a leading role within fields such as dietary risk, hydrology, nuclear security, finance and insurance and is more and more present in theapplications of various probability tools and statistical methods. We see a significant impact on the scientific literature and on public institutions in the past years. Risk theory, which is really close to extreme value analysis, typically deals with the occurrences of rare events which are functions of heavy-tailed random variables, for example, sums or products of regularly varying random variables. The purpose of this thesis is the following : to develop revelant risk indicators and to study the extremal properties of stochastic processes used in dietary risk assessment and in insurance. In Chapter 1, we present the main tools used in risk theory and the notion of regular variation and introduce different models involved in dietary risk assessment, which will be specifically studied in Chapters 2 and 3. Chapter 2 presents a joint work with Olivier Wintenberger. For a particular class of stochastic processes, under the assumption of regular variation, we propose a method that gives way to asymptotic equivalents on a finite-time horizon of risk indicators such as the ruin probability, the Expected Time over a Threshold or the Expected Severity of the ruin. Chapter 3 focuses on dietary risk models. To be precise, we study the extremal properties of an extension of a model called KDEM for Kinetic Dietary Exposure Model introduced by Patrice Bertail and his co-authors in 2008. Under the assumption of regular variation, we provide asymptotic equivalents for the tail behavior and the extremal index of the exposure process. In Chapter 4, we review different statistical tools specifically tailored for the study of the extremal behavior of Markov processes. Thanks to regeneration properties, we can split the path of observations into blocks which are independent and identically distributed. This technic still works even if the Markov chain is not atomic. We focus here on the estimation of the tail index and the extremal index. We illustrate the performance of these technics applying them on two models in insurance and finance for which we know the theoritical results.

No presente trabalho, estudamos alguns sistemas de partículas interagentes que podem ser vistos como modelos simples de fluxo de tráfego, a saber: O Processo de Hammersley-Aldous-Diaconis e o Processo de Exclusão. Exploramos suas representações como modelos de crescimento no plano. Ênfase é dada aos casos em que há mais de um tipo de partícula, aos processos multiclasses e às suas relações com modelos de filas. Analogia entre os modelos é usada para provar os resultados. Por fim, damos uma nova prova para o cálculo da variância assintótica reescalonada do fluxo de partículas de segunda classe no processo de Hammersley multiclasse em equilíbrio. / In the present work we study the following interacting particle systems which can be seen as simple models of traffic flow: The Hammersley-Aldous-Diaconis Process and the Exclusion Process. We explore the related growth models in the plane. Focus is given to cases where there are more than one kind of particles, to the multitype processes and to their relations with queue models. Analogy between the models is used to prove the results. At last, we give a new proof for the calculation of the asimptotic flux of second class particles in the Multiclass Hammersley process in equilibrium.

Made available in DSpace on 2016-06-02T19:52:09Z (GMT). No. of bitstreams: 1 6571.pdf: 4032074 bytes, checksum: e0d2561f673f9fff989f2b9d7c179d5e (MD5) Previous issue date: 2015-02-20 / Financiadora de Estudos e Projetos / This paper aims to diagnose the passenger boarding and landing processes of the Uberlândia airport using the mapping process and computer simulation. The paper presents a review of literature about the airport sector, techniques of mapping process, data collection, queue management and computer simulation. The objective is to analyze each subsystem used by the passenger during their boarding and landing, from the vehicle access areas and check- in counters until the departure lounge and the receipt of baggage. In conclusion, alternatives are proposals to reduce the total time of the passengers in queues, contributing to a possible improvement project for the airport. / O presente trabalho tem como proposta diagnosticar os processos de embarque e desembarque de passageiros no aeroporto de Uberlândia por meio do uso do mapeamento de processo e da simulação computacional. O trabalho apresenta uma revisão da literatura acerca do setor aeroportuário, técnicas de mapeamento de processos, coleta de dados, gestão de filas e simulação computacional. O objetivo é analisar cada subsistema utilizado pelo passageiro durante seu embarque e desembarque, desde as áreas de acesso de veículos e de balcões de check-in até as áreas de embarque e de recebimento de bagagens. Como conclusão são propostas alternativas capazes de reduzir o tempo total dos passageiros em filas, contribuindo para um possível projeto de melhoria para o aeroporto.

Submitted by Fabio Sobreira Campos da Costa (fabio.sobreira@ufpe.br) on 2016-08-05T13:25:31Z No. of bitstreams: 2 license_rdf: 1232 bytes, checksum: 66e71c371cc565284e70f40736c94386 (MD5) Dissertação Bruno Nunes_FINAL.pdf: 1523588 bytes, checksum: feea1e49f7dc0fcebbcf54602098e8e1 (MD5) / Made available in DSpace on 2016-08-05T13:25:31Z (GMT). No. of bitstreams: 2 license_rdf: 1232 bytes, checksum: 66e71c371cc565284e70f40736c94386 (MD5) Dissertação Bruno Nunes_FINAL.pdf: 1523588 bytes, checksum: feea1e49f7dc0fcebbcf54602098e8e1 (MD5) Previous issue date: 2016-02-19 / CNPq / A growing trend in hiring maintenance services has been observed in companies in general in order to enhance competition and reduce costs. This practice becomes even more evident in the context of health institutions, as they strongly employ technology-intensive equipment that must follow tight quality standards that intend to ensure the continuity of the service and the safety of patients. These characteristics contribute in allowing the maintenance to be executed by the Original Equipment Manufacturer (OEM), since several pre-established procedures must be attended during maintenance. Thus, it becomes relevant to analyze the interaction among customers (hospitals) and the equipment manufacturer in this particular maintenance services market. In the developed model the customers are divided into 2 classes, great size hospitals belong to class 1 and small hospitals belong to class 2 and class 1 customers have priority over class 2 customers. Class 1 customers have the option of hiring an Extended Warranty (EW) with priority or of paying for each maintenance intervention on demand, while class 2 customers have the option of hiring an standard EW (with no priority) or of paying for each maintenance intervention on demand. To model such dynamics a 2-class priority queuing system is implemented. The customers select the option that maximize their expected utilities, as they are risk averse, while the manufacturer needs to set the EW and maintenance intervention prices and select the optimal number of customers of each class to service in order to maximize their expected profit. A Stackelberg Game is used to model the interaction among players, in which the OEM is the leader and the customer is the follower. In the numerical example it has been found that the customers of class 1 decide to hire EW with priority, while class 2 customers decide to pay for maintenance services on demand. Also the OEM decides to service 3 customers of class 1 and 100 customers of class 2, which yields an expected profit of $ 3,204,450. A sensitivity analysis is also performed to analyze how the optimal solution changes due to parameters variations. / Uma tendência crescente para a contratação de serviços de manutenção tem sido observada em empresas em geral com o objetivo de aumentar sua competitividade e reduzir custos. Tal prática se torna ainda mais evidente no contexto de instituições de saúde, já que elas utilizam diversos equipamentos intensivos em tecnologia que precisam se adequar a rígidos padrões de qualidade de forma a garantir a continuidade do serviço e a segurança dos pacientes. Essas características contribuem para que os serviços de manutenção sejam executados pelo fabricante do equipamento, já que diversos procedimentos específicos precisam ser seguidos durante a manutenção. Assim, torna-se relevante analisar a interação entre clientes (hospitais) e o fabricante do equipamento neste mercado particular. No modelo desenvolvido, os clientes foram divididos em 2 classes, hospitais de grande porte pertencem à classe 1 e hospitais pequenos pertencem à classe 2 e os clientes da classe 1 têm prioridade em relação aos clientes da classe 2. Os clientes da classe 1 têm a opção de contratar uma garantia estendida com prioridade ou de pagar por cada intervenção de manutenção sob demanda, já os clientes da classe 2 têm a opção de contratar uma garantia estendida padrão (sem prioridade) ou de pagar por cada intervenção de manutenção sob demanda. Para modelar esta dinâmica um sistema de filas com 2 classes de prioridade foi implementado. Os clientes escolhem a opção que maximiza suas utilidades esperadas, já que são avessos ao risco, enquanto o fabricante deve determinar os preços das garantias estendidas e das intervenções avulsas além do número ótimo de clientes que ele deve atender de forma a maximizar o seu lucro esperado. Para modelar a interação entre os jogadores foi utilizado um Jogo de Stackelberg em que o fabricante é o líder e o cliente, o seguidor. O exemplo numérico apresentado mostra que a decisão ótima para os clientes da classe 1 é adquirir a garantia estendida com prioridade, enquanto para os clientes da classe 2 a decisão-ótima é pagar pelos serviços de manutenção sob demanda. O fabricante decide atender 3 clientes da classe 1 e 100 clientes da classe 2, o que lhe gera um lucro de $ 3,204,450. Uma análise de sensibilidade é apresentada em seguida para investigar como a solução ótima muda em decorrência de variações nos parâmetros.

In the last few years, the number of real-time applications has increased. These applications are sensitive and require the methods to utilize existing network capacity efficiently to meet performance requirements and achieve the maximum throughput to overcome delay, jitter and packet loss. In such cases, when the network needs to support highly interactive traffic like packet-switched voice, the network congestion is an issue that can lead to various problems. If the level of congestion is high enough, the users may not be able to complete their calls and have existing calls dropped or may experience a variety of delays that make it difficult to participate smooth conversation. In this paper, we investigate the effect of priority levels on soft real-time performance. We use the priority queues to help us manage the congestion, handle the interactive traffic and improve the over all performance of the system. We consider switched multi-hop network with priority queues. All the switches and end-nodes control the real-time traffic with “Earlier Deadline First” scheduling. The performance of the network is characterized in terms of the average delay, the deadline missing ratio and the throughput. We will analyze these parameters with both the bursty traffic and evenly distributed traffic. We will analyze different priority levels and will see how the increase in priority level increases the performance of the soft real-time system.