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  • About
  • The Global ETD Search service is a free service for researchers to find electronic theses and dissertations. This service is provided by the Networked Digital Library of Theses and Dissertations.
    Our metadata is collected from universities around the world. If you manage a university/consortium/country archive and want to be added, details can be found on the NDLTD website.
21

MODELING EMERGING APP-BASED TAXI SERVICES: INTERACTIONS OF DEMAND AND SUPPLY

Wenbo Zhang (5930480) 17 January 2019 (has links)
<div>The app-based taxi services (ATS) has disrupted the traditional (street-hailing) taxi services (TTS) leading to transformative changes in the urban taxi markets and its impacts on mobility, design and environment. However, the current modeling of these new mobility markets is limited in its understanding of: (1) the underlying factors that influence the growth of the ATS market; (2) the competition of ATS and TTS markets; (3) pricing in the ATS market; (4) system wide tools to understand the impacts of the market. The overarching goal of this dissertation is to address four fundamental processes of taxi system, ranging from demand generation, supply generation and exiting, dynamic pricing generation, and vehicle-passenger matching over road network. This dissertation achieves these goals by using original large scale datasets to characterize disruptive changes in mobility, understand strategic behaviors of stakeholders, and formulate system dynamics.</div><div> </div><div>This dissertation develops various modeling structures and estimation methods, motivated from statistical, econometric, machine learning, and stochastic approaches. First, we adapt multiple econometric models for demand, supply, and platform-exiting (offline) behaviors, including mixture model of spatial lag and Poisson regression and mixture model of spatial lag and panel regression. It is apparent that all proposed econometric models should be corrected with spatial lag due to significant spatial autocorrelations. The results indicate effectiveness of dynamic pricing in controlling demand, however, it also shows no impacts on driver's online and offline behaviors. Then a dynamic pricing generation problem is formulated with multi-class classification. This model is empirically validated for the impacts of demand and supply in dynamic price generation and the significant spatial and temporal heterogeneity. Last, we propose a queueing network consisting of taxi service queues for vehicle-passenger matching and road service queue for vehicle movements at homogeneous spatial units. The method captures stochasticity in vehicle-passenger matching process, and more importantly, formulates the interactions with urban road traffic.</div><div> </div><div>In summary, this dissertation provides a holistic understanding of fundamental processes that govern the rapid rise in ATS markets and in developing quantitative tools for the system wide impacts of this evolving taxi markets. Taken together, these tools are transformative and useful for city agencies to make various decisions in the smart mobility landscape. </div>
22

Modelling And Analysis Of Event Message Flows In Distributed Discrete Event Simulators Of Queueing Networks

Shorey, Rajeev 12 1900 (has links)
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.
23

Performance Modelling of GPRS with Bursty Multi-class Traffic.

Kouvatsos, Demetres D., Awan, Irfan U., Al-Begain, Khalid January 2003 (has links)
No / An analytic framework is devised, based on the principle of maximum entropy (ME), for the performance modelling and evaluation of a wireless GSM/GPRS cell supporting bursty multiple class traffic of voice calls and data packets under complete partitioning (CPS), partial sharing (PSS) and aggregate sharing (ASS) traffic handling schemes. Three distinct open queueing network models (QNMS) under CPS, PSS and ASS, respectively, are described, subject to external compound Poisson traffic processes and generalised exponential (GE) transmission times under a repetitive service blocking mechanism and a complete buffer sharing management rule. Each QNM generally consists of three building block stations, namely a loss system with GSM/GPRS traffic and a system of access and transfer finite capacity queues in tandem dealing with GPRS traffic under head-of-line and discriminatory processor sharing scheduling disciplines, respectively. The analytic methodology is illustrated by focusing on the performance study of the GE-type tandem queueing system for GPRS under a CPS. An ME product-form approximation is characterised leading into a decomposition of the tandem system into individual queues and closed-form ME expressions for state and blocking probabilities are presented. Typical numerical examples are included to validate the ME solutions against simulation and study the effect of external GPRS bursty traffic upon the performance of the cell. Moreover, an overview of recent extensions of the work towards the analysis of a GE-type multiple server finite capacity queue with preemptive resume priorities and its implications towards the performance modelling and evaluation of GSM/GPRS cells with PSS and ASS are included. / ,
24

Maintaining QoS through preferential treatment to UMTS services

Awan, Irfan U., Al-Begain, Khalid January 2003 (has links)
One of the main features of the third generation (3G) mobile networks is their capability to provide different classes of services; especially multimedia and real-time services in addition to the traditional telephony and data services. These new services, however, will require higher Quality of Service (QoS) constraints on the network mainly regarding delay, delay variation and packet loss. Additionally, the overall traffic profile in both the air interface and inside the network will be rather different than used to be in today's mobile networks. Therefore, providing QoS for the new services will require more than what a call admission control algorithm can achieve at the border of the network, but also continuous buffer control in both the wireless and the fixed part of the network to ensure that higher priority traffic is treated in the proper way. This paper proposes and analytically evaluates a buffer management scheme that is based on multi-level priority and Complete Buffer Sharing (CBS) policy for all buffers at the border and inside the wireless network. The analytical model is based on the G/G/1/N censored queue with single server and R (R¿2) priority classes under the Head of Line (HoL) service rule for the CBS scheme. The traffic is modelled using the Generalised Exponential distribution. The paper presents an analytical solution based on the approximation using the Maximum Entropy (ME) principle. The numerical results show the capability of the buffer management scheme to provide higher QoS for the higher priority service classes.
25

Aplicação de modelos de redes de filas abertas no projeto e planejamento de sistemas discretos de manufatura. / Application of open queueing network models for the design and planning of discrete manufacturing systems.

Silva, Claudio Rogerio Negri da 29 April 2005 (has links)
Made available in DSpace on 2016-06-02T19:50:27Z (GMT). No. of bitstreams: 1 TeseCRNS.pdf: 1772351 bytes, checksum: 17b2dc82dae0e985204bfa2fd68f873b (MD5) Previous issue date: 2005-04-29 / Universidade Federal de Minas Gerais / The management of manufacturing systems have become more complex, once that new products are arising, product demands are uncertain, life cycles get shorter, and a wide variety of products compete for common resources. This thesis deals with the design and planning of discrete manufacturing systems, based on open queueing network models to support the decision making of capacity allocation. As manufacturing systems may be represented by generalized queueing networks, and there are no exact solution methods, here is employed the decomposition approximate method to evaluate the performance of systems under different configurations. It is shown in the thesis how these approximations are suitable and effective to estimate the work-in-process (WIP) and the production leadtime of an actual metallurgical industry queueing network. It is also shown that discrete capacity allocation models, based on the approximations, are effective to evaluate and optimize the performance of the case study under different configurations. Trade-off curves between capacity investment and WIP are generated and are useful not only to support a manager to estimate how much capacity he/she should allocate, but also to decide where it should be allocated in the queueing network. These curves also support the decision making in terms of capacity, if the variability of the external arrivals, the product mix and/or the throughput for the network change. Besides adding capacity, partitioning the facility is another alternative to reduce the system complexity. This thesis also approaches the focused factory design problem, involving the partition of the facility into smaller shops and the capacity allocation in each shop. Again, the decomposition approximations were employed to evaluate the system performance. Despite its importance, this problem has rarely been reported in the literature. In this thesis, the goal is to reduce the system complexity either from the product management point of view or from the workstation management point of view. From the product management point of view, a model whose complexity constraint is na upper limit on the production leadtime variance of the products passing through the network was studied. From the workstation management point of view, the complexity constraint of the model keeps constant the expected waiting time of a product at a workstation, once it waits for being served. It is shown through these models for some instances that the partition of the facility into smaller shops decreases the complexity system without necessary capacity additional investments. Futhermore, sometimes it is possible to keep the network performance (or even to improve it), partitioning the network into smaller shops which need less capacity than the original configuration with a single shop. / A gestão de sistemas de manufatura tem se tornado mais complexa na medida em que novos produtos estão surgindo, a demanda de produtos é incerta, os ciclos de vida são mais curtos e uma grande variedade de produtos competem pelos mesmos recursos. Esta tese trata o projeto e planejamento de sistemas discretos de manufatura, baseados em modelos de redes de filas abertas, para auxiliar no processo de tomada de decisões. Porque sistemas de manufatura podem ser representados por redes de filas genéricas, e não existem métodos exatos de solução, aqui é empregado o método aproximado de decomposição para avaliar o desempenho dos sistemas em diferentes configurações. Mostra-se nesta tese que estas aproximações são adequadas e efetivas para estimar os estoques em processo (WIP) e o leadtime de produção de uma rede de manufatura real de uma indústria metal-mecânica. Mostra-se ainda que os modelos de alocação de capacidade discreta, baseados nestas aproximações, também são efetivos para avaliar e otimizar o desempenho da rede do estudo de caso em diferentes configurações. Curvas de trade-off entre investimento em capacidade e WIP são geradas e são úteis não somente para auxiliar um gerente a estimar quanto alocar de capacidade, mas também para decidir onde alocá-la na rede de filas. As curvas também auxiliam a tomada de decisões em termos de capacidade, se a variabilidade das chegadas externas, o mix de produtos e/ou a taxa de produção da rede mudam. Além de adicionar capacidade, a partição da instalação é outra alternativa para reduzir a complexidade do sistema. Esta tese também aborda o problema de projeto de fábrica focalizada, envolvendo a partição da instalação em subplantas e a alocação de capacidade em cada estação das subplantas. Novamente, as aproximações por decomposição foram utilizadas para avaliar e otimizar o desempenho do sistema. Apesar de sua importância, este problema tem sido muito pouco reportado em literatura. Nesta tese, o objetivo é reduzir a complexidade do sistema do ponto de vista da gestão do produto, ou do ponto de vista da gestão da estação. Do ponto de vista da gestão do produto, é apresentado um modelo cuja restrição de complexidade é um limitante superior para a variância do leadtime dos produtos na rede. Do ponto de vista da gestão da estação, a restrição de complexidade do modelo fixa o tempo médio de espera de um produto na estação, quando há espera. Mostra-se, por meio destes modelos para alguns casos que, a partição da instalação em subplantas reduz a complexidade do sistema, sem necessidade de investimentos adicionais em capacidade. Além disso, algumas vezes, é possível manter (ou até melhorar) o desempenho da rede, particionando-a em subplantas que necessitam de menos capacidade do que a configuração original com uma planta única.
26

Estudo comparativo das aproximações baseadas no método de decomposição paramétrico para avaliar redes de filas de manufatura utilizando planejamento de experimentos / A comparative study of approximations based on the parametric decomposition method to evaluate manufacturing queueing networks using designing of experiments

Camorim, José Eduardo Vieira 29 February 2008 (has links)
Made available in DSpace on 2016-06-02T19:51:35Z (GMT). No. of bitstreams: 1 1770.pdf: 2888839 bytes, checksum: 18c57ba21e9192d597b74f8d1d0fc997 (MD5) Previous issue date: 2008-02-29 / Universidade Federal de Minas Gerais / This is a study of approximations based on parametric decomposition methods used in open queueing networks for modeling discrete job-shop manufacturing systems. These approximations play an important role in evaluating the performance of productive systems and have proved effective in many situations. Besides, these approximations are relatively easy to apply requiring fewer data compared to other methods because they use the average rate and SCV (square coefficient of variation) as the only parameters to characterize the network arrival and service processes. This work is aimed at analyzing and comparing several approximations since they are not yet available in the literature. Hence, several network situations were tested in order to identify the most adequate approximation for each situation. Firstly, a two-station network was analyzed followed by the analysis of a five-station network and lastly, a real example of a semiconductor plant, analyzed by Bitran e Tirupati (1988), was used. In order to reach these goals, the state of the art of approximation methods to evaluate the performance of open queueing networks was studied, and the approximations were compared using the experiment planning technique, important factors for building network configuration and data analysis The findings of this work demonstrate that approximations can be highly efficient to evaluate the performance of discrete job-shop manufacturing systems. Regardless of the configurations studied, it is worth mentioning that approximations 3 and 2, in general, showed the best results if compared to the other values obtained from simulations to evaluate the performance of open queueing networks, OQN,. The other approximations tended to overestimate E(Lj) when the number of stations is higher. This study intends to contribute to the development of computing systems in order to support project decisions and the planning and control of discrete manufacturing systems using approximations based on the parametric decomposition method / Esta dissertação estuda as aproximações baseadas nos métodos analíticos paramétricos de decomposição usados em redes de filas abertas que modelam sistemas discretos de manufatura do tipo job-shop. Estas aproximações possuem um importante papel na avaliação do desempenho de sistemas produtivos e vem se mostrando eficiente para uma grande diversidade de situações. Além disso, são aproximações relativamente fáceis de serem aplicadas, necessitando poucos dados em relação a outros métodos, pois utilizam apenas a média e o scv (coeficiente quadrático de variação) como parâmetros para caracterizar os processos de chegadas e os processos de serviço da rede. O foco deste trabalho está em realizar análises e comparações entre diversas aproximações, pois ainda não existe nenhuma comparação mais efetiva entre elas na literatura. Para isso, diversas situações de redes foram exploradas para identificar quais aproximações são mais adequadas para quais situações. Primeiramente é analisado uma rede com 2 estações, posteriormente uma outra com 5 estações e por fim usou um exemplo real de uma fábrica de semi-condutores, analisada por Bitran e Tirupati (1988). Para que seja possível atingir esses objetivos, estudou-se o estado da arte das aproximações dos métodos de avaliação de desempenho para redes de filas abertas, e comparouse as aproximações por meio de técnicas de planejamento de experimentos, parte importante na construção das configurações das redes e análise dos resultados. Os resultados apresentados nesta dissertação mostram que essas aproximações podem ser bem eficientes ao avaliar o desempenho de sistemas discretos de manufatura do tipo job-shop. Independente das configurações analisadas, vale destacar a Aproximação 3 e a Aproximação 2, em geral, obtendo os melhores resultados, entre as aproximações, em comparação aos valores obtidos pela simulação para avaliar o desempenho de redes de filas OQN. As outras aproximações demonstraram certo comportamento em sobreestimar E(Lj), quando o número de estações aumentam. Este estudo pretende contribuir para o desenvolvimento de sistemas computacionais 13 para apoiar decisões de projeto, planejamento e controle dos sistemas discretos de manufatura, usando aproximações baseadas em métodos de decomposição paramétrico
27

Performance Analysis of Virtualisation in a Cloud Computing Platform. An application driven investigation into modelling and analysis of performance vs security trade-offs for virtualisation in OpenStack infrastructure as a service (IaaS) cloud computing platform architectures.

Maiyama, Kabiru M. January 2019 (has links)
Virtualisation is one of the underlying technologies that led to the success of cloud computing platforms (CCPs). The technology, along with other features such as multitenancy allows delivering of computing resources in the form of service through efficient sharing of physical resources. As these resources are provided through virtualisation, a robust agreement is outlined for both the quantity and quality-of-service (QoS) in a service level agreement (SLA) documents. QoS is one of the essential components of SLA, where performance is one of its primary aspects. As the technology is progressively maturing and receiving massive acceptance, researchers from industry and academia continue to carry out novel theoretical and practical studies of various essential aspects of CCPs with significant levels of success. This thesis starts with the assessment of the current level of knowledge in the literature of cloud computing in general and CCPs in particular. In this context, a substantive literature review was carried out focusing on performance modelling, testing, analysis and evaluation of Infrastructure as a Service (IaaS), methodologies. To this end, a systematic mapping study (SMSs) of the literature was conducted. SMS guided the choice and direction of this research. The SMS was followed by the development of a novel open queueing network model (QNM) at equilibrium for the performance modelling and analysis of an OpenStack IaaS CCP. Moreover, it was assumed that an external arrival pattern is Poisson while the queueing stations provided exponentially distributed service times. Based on Jackson’s theorem, the model was exactly decomposed into individual M/M/c (c ≥ 1) stations. Each of these queueing stations was analysed in isolation, and closed-form expressions for key performance metrics, such as mean response time, throughput, server (resource) utilisation as well as bottleneck device were determined. Moreover, the research was extended with a proposed open QNM with a bursty external arrival pattern represented by a Compound Poisson Process (CPP) with geometrically distributed batches, or equivalently, variable Generalised Exponential (GE) interarrival and service times. Each queueing station had c (c ≥ 1) GE-type servers. Based on a generic maximum entropy (ME) product form approximation, the proposed open GE-type QNM was decomposed into individual GE/GE/c queueing stations with GE-type interarrival and service times. The evaluation of the performance metrics and bottleneck analysis of the QNM were determined, which provided vital insights for the capacity planning of existing CCP architectures as well as the design and development of new ones. The results also revealed, due to a significant impact on the burstiness of interarrival and service time processes, resulted in worst-case performance bounds scenarios, as appropriate. Finally, an investigation was carried out into modelling and analysis of performance and security trade-offs for a CCP architecture, based on a proposed generalised stochastic Petri net (GSPN) model with security-detection control model (SDCM). In this context, ‘optimal’ combined performance and security metrics were defined with both M-type or GE-type arrival and service times and the impact of security incidents on performance was assessed. Typical numerical experiments on the GSPN model were conducted and implemented using the Möbius package, and an ‘optimal’ trade-offs were determined between performance and security, which are crucial in the SLA of the cloud computing services. / Petroleum technology development fund (PTDF) of the government of Nigeria Usmanu Danfodiyo University, Sokoto
28

An Exposition of Performance-Security Trade-offs in RANETs Based on Quantitative Network Models

Miskeen, Guzlan M.A., Kouvatsos, Demetres D., Habib Zadeh, Esmaeil January 2013 (has links)
No / Security mechanisms, such as encryption and authentication protocols, require extra computing resources and therefore, have an adverse effect upon the performance of robotic mobile wireless ad hoc networks (RANETs). Thus, an optimal performance and security trade-off should be one of the main aspects that should be taken into consideration during the design, development, tuning and upgrading of such networks. In this context, an exposition is initially undertaken on the applicability of Petri nets (PNs) and queueing networks (QNs) in conjunction with their generalisations and hybrid integrations as robust quantitative modelling tools for the performance analysis of discrete flow systems, such as computer systems, communication networks and manufacturing systems. To overcome some of the inherent limitations of these models, a novel hybrid modelling framework is explored for the quantitative evaluation of RANETs, where each robotic node is represented by an abstract open hybrid G-GSPN_QN model with head-of-line priorities, subject to combined performance and security metrics (CPSMs). The proposed model focuses on security processing and state-based control and it is based on an open generalised stochastic PN (GSPN) with a gated multi-class 'On-Off' traffic and mobility model. Moreover, it employs a power consumption model and is linked in tandem with an arbitrary QN consisting of finite capacity channel queues with blocking for 'intra' robot component-to-component communication and 'inter' robot-to-robot transmission. Conclusions and future research directions are included.
29

Passeios aleatórios em redes finitas e infinitas de filas / Random walks in finite and infinite queueing networks

Gannon, Mark Andrew 27 April 2017 (has links)
Um conjunto de modelos compostos de redes de filas em grades finitas servindo como ambientes aleatorios para um ou mais passeios aleatorios, que por sua vez podem afetar o comportamento das filas, e desenvolvido. Duas formas de interacao entre os passeios aleatorios sao consideradas. Para cada modelo, e provado que o processo Markoviano correspondente e recorrente positivo e reversivel. As equacoes de balanceamento detalhado sao analisadas para obter a forma funcional da medida invariante de cada modelo. Em todos os modelos analisados neste trabalho, a medida invariante em uma grade finita tem forma produto. Modelos de redes de filas como ambientes para multiplos passeios aleatorios sao estendidos a grades infinitas. Para cada modelo estendido, sao especificadas as condicoes para a existencia do processo estocastico na grade infinita. Alem disso, e provado que existe uma unica medida invariante na rede infinita cuja projecao em uma subgrade finita e dada pela medida correspondente de uma rede finita. Finalmente, e provado que essa medida invariante na rede infinita e reversivel. / A set of models composed of queueing networks serving as random environments for one or more random walks, which themselves can affect the behavior of the queues, is developed. Two forms of interaction between the random walkers are considered. For each model, it is proved that the corresponding Markov process is positive recurrent and reversible. The detailed balance equa- tions are analyzed to obtain the functional form of the invariant measure of each model. In all the models analyzed in the present work, the invariant measure on a finite lattice has product form. Models of queueing networks as environments for multiple random walks are extended to infinite lattices. For each model extended, the conditions for the existence of the stochastic process on the infinite lattice are specified. In addition, it is proved that there exists a unique invariant measure on the infinite network whose projection on a finite sublattice is given by the corresponding finite- network measure. Finally, it is proved that that invariant measure on the infinite lattice is reversible.
30

Passeios aleatórios em redes finitas e infinitas de filas / Random walks in finite and infinite queueing networks

Mark Andrew Gannon 27 April 2017 (has links)
Um conjunto de modelos compostos de redes de filas em grades finitas servindo como ambientes aleatorios para um ou mais passeios aleatorios, que por sua vez podem afetar o comportamento das filas, e desenvolvido. Duas formas de interacao entre os passeios aleatorios sao consideradas. Para cada modelo, e provado que o processo Markoviano correspondente e recorrente positivo e reversivel. As equacoes de balanceamento detalhado sao analisadas para obter a forma funcional da medida invariante de cada modelo. Em todos os modelos analisados neste trabalho, a medida invariante em uma grade finita tem forma produto. Modelos de redes de filas como ambientes para multiplos passeios aleatorios sao estendidos a grades infinitas. Para cada modelo estendido, sao especificadas as condicoes para a existencia do processo estocastico na grade infinita. Alem disso, e provado que existe uma unica medida invariante na rede infinita cuja projecao em uma subgrade finita e dada pela medida correspondente de uma rede finita. Finalmente, e provado que essa medida invariante na rede infinita e reversivel. / A set of models composed of queueing networks serving as random environments for one or more random walks, which themselves can affect the behavior of the queues, is developed. Two forms of interaction between the random walkers are considered. For each model, it is proved that the corresponding Markov process is positive recurrent and reversible. The detailed balance equa- tions are analyzed to obtain the functional form of the invariant measure of each model. In all the models analyzed in the present work, the invariant measure on a finite lattice has product form. Models of queueing networks as environments for multiple random walks are extended to infinite lattices. For each model extended, the conditions for the existence of the stochastic process on the infinite lattice are specified. In addition, it is proved that there exists a unique invariant measure on the infinite network whose projection on a finite sublattice is given by the corresponding finite- network measure. Finally, it is proved that that invariant measure on the infinite lattice is reversible.

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