No / Given only the traffic correlations of counts and intervals, a Batch Renewal Arrival Process (BRAP) is completely determined, as the least biased choice and thus, it provides the analytic means to construct suitable traffic models for the study of queueing systems independently of any other traffic characteristics. In this context, the BRAP and the Batch Markovian Arrival Process (BMAP) are employed in the continuous time domain towards the analysis of the stable BRAP/GE/1 and BMAP/GE/1 queues with infinite capacity, single servers and generalized exponential (GE) service times. Novel closed form expressions for the steady state probabilities of these queues are obtained, based on the embedded Markov chains (EMCs) technique and the matrix-geometric (M-G) method, respectively. Moreover, the stable GEsGGeo/GE/1 queue with GE-type service times and a GEsGGeo BRAP consisting of bursty GE-type batch interarrival times and a shifted generalized geometric (sGGeo) batch size distribution is adopted to assess analytically the combined adverse effects of varying degrees of correlation of intervals between individual arrivals and the burstiness of service times upon the typical quality of service (QoS) measure of the mean queue length (MQL). Moreover, a comprehensive experimental study is carried out to investigate numerically the relative impact of count and interval traffic correlations as well as other traffic characteristics upon the performance of stable BRAP/GE/1 and BMAP/GE/1 queues. It is suggested via a conjecture that the BRAP/GE/1 queue is likely to yield pessimistic performance metrics in comparison to those of the stable BMAP/GE/1 queues under the worst case scenario (i.e., a worst case scenario) of the same positive count and interval traffic correlations arising from long sojourn in each phase.

整合電腦及通訊網路技術之分散式系統(Digtributed System)，係將分散各地的電腦 系統及相關的資訊設備透過通訊網路連接在一起，以形成能夠相互效換資訊，分享資 源，並具備分散式處理能力的系統。由於電腦及通訊網路技術突破性的進展，在許多 情況下，已使分散式系統較傳統的集中式系統具有低成本、高可靠度、容易擴充、效 能較佳等優勢。 本研究根據分散式系統的基本架構，使用排隊網路(Queueing Network)分析技術，建 立一套一般性的分散式系統模式，此模式可用以評估分散式系統運作之效能(Perfor- mance)，探討影響分散式系統效能的因素。同時，本研究進一步利用系統模擬(Syst- em Simulation)技術分析分散式系統模式，並進行分析結果的比較與驗證，以做為規 劃與設計分散式系統的參考依據。為說明其應用，我們並以校園線上即時選課資訊網 路系統為例，找出影響其效能的主要因素及可接受的設計方案，以做為校園資訊網路 整體系統架構設計決策的參考依據。 本研究之預期貢獻主要在於提供一套簡單經濟且具有相當程度準確性的方法，藉以模 擬、預測或評估分散式系統之行為與效能，這套方法可以廣泛應用在各種不同組態下 的分散式系統。

The performance modelling of large-scale systems using discrete-state approaches is fundamentally hampered by the well-known problem of state-space explosion, which causes exponential growth of the reachable state space as a function of the number of the components which constitute the model. Because they are mapped onto continuous-time Markov chains (CTMCs), models described in the stochastic process algebra PEPA are no exception. This thesis presents a deterministic continuous-state semantics of PEPA which employs ordinary differential equations (ODEs) as the underlying mathematics for the performance evaluation. This is suitable for models consisting of large numbers of replicated components, as the ODE problem size is insensitive to the actual population levels of the system under study. Furthermore, the ODE is given an interpretation as the fluid limit of a properly defined CTMC model when the initial population levels go to infinity. This framework allows the use of existing results which give error bounds to assess the quality of the differential approximation. The computation of performance indices such as throughput, utilisation, and average response time are interpreted deterministically as functions of the ODE solution and are related to corresponding reward structures in the Markovian setting. The differential interpretation of PEPA provides a framework that is conceptually analogous to established approximation methods in queueing networks based on meanvalue analysis, as both approaches aim at reducing the computational cost of the analysis by providing estimates for the expected values of the performance metrics of interest. The relationship between these two techniques is examined in more detail in a comparison between PEPA and the Layered Queueing Network (LQN) model. General patterns of translation of LQN elements into corresponding PEPA components are applied to a substantial case study of a distributed computer system. This model is analysed using stochastic simulation to gauge the soundness of the translation. Furthermore, it is subjected to a series of numerical tests to compare execution runtimes and accuracy of the PEPA differential analysis against the LQN mean-value approximation method. Finally, this thesis discusses the major elements concerning the development of a software toolkit, the PEPA Eclipse Plug-in, which offers a comprehensive modelling environment for PEPA, including modules for static analysis, explicit state-space exploration, numerical solution of the steady-state equilibrium of the Markov chain, stochastic simulation, the differential analysis approach herein presented, and a graphical framework for model editing and visualisation of performance evaluation results.

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.

<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>

Uma série de problemas de filas em sistemas de transportes com picos de tráfego, ou um número finito de elementos no sistema, são usualmente representados pelo modelo de fonte infinita, dadas as dificuldades de utilização do modelo exato de fonte finita. Este trabalho apresenta uma solução alternativa baseada no cálculo de um limitante superior para as probabilidades de equilíbrio do modelo exato de fonte finita, e compara as medidas de desempenho dos sistemas calculadas pelos dois modelos. Mostra-se que para índices de congestionamento menores que um, as diferenças entre estas medidas são tanto menores quanto menor for este índice. A partir destes resultados, compara-se as medidas de desempenho do modelo aproximado proposto com as do modelo de população infinita, para diferentes tamanhos de população e números de servidores. Conclui-se que os modelos conduzem a resultados numéricos muito próximos para uma ampla variação do índice de congestionamento, e que estes resultados são tão melhores quanto maior for o número de servidores no sistema e o número de elementos na população. São também apresentados três estudos de casos comparando os resultados induzidos pelos modelos exato, proposto e usual de fonte infinita, que ilustram a aplicabilidade prática dos resultados deste trabalho em sistemas de transportes. / A set of stochastic queueing problems in transportation systems with traffic peaks, or a finite number of elements in the system, are usually represented by the infinite source model, due to the difficulties of applying the exact finite source model. This study presents an alternative solution based on the upper bound values of the equilibrium probabilities of the exact finite source model, and compares the performance measurements of the two models. It is shown that for congestion factors below one, the smaller the value of the congestion factor, the smaller is the difference between the models. Based on this results the measures of performance of the proposed aproximate model are compared with the results of the usual infinite source model for different population sizes and number of servers. It is concluded that the models lead to very close numerical results for a wide range of congestion factors of the system and that these results are the better the larger is the number of servers and the number of elements in the system. Three case studies ilustrating the pratical applicability of the results of this study to transportation systems are also presented.

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.

Uma série de problemas de filas em sistemas de transportes com picos de tráfego, ou um número finito de elementos no sistema, são usualmente representados pelo modelo de fonte infinita, dadas as dificuldades de utilização do modelo exato de fonte finita. Este trabalho apresenta uma solução alternativa baseada no cálculo de um limitante superior para as probabilidades de equilíbrio do modelo exato de fonte finita, e compara as medidas de desempenho dos sistemas calculadas pelos dois modelos. Mostra-se que para índices de congestionamento menores que um, as diferenças entre estas medidas são tanto menores quanto menor for este índice. A partir destes resultados, compara-se as medidas de desempenho do modelo aproximado proposto com as do modelo de população infinita, para diferentes tamanhos de população e números de servidores. Conclui-se que os modelos conduzem a resultados numéricos muito próximos para uma ampla variação do índice de congestionamento, e que estes resultados são tão melhores quanto maior for o número de servidores no sistema e o número de elementos na população. São também apresentados três estudos de casos comparando os resultados induzidos pelos modelos exato, proposto e usual de fonte infinita, que ilustram a aplicabilidade prática dos resultados deste trabalho em sistemas de transportes. / A set of stochastic queueing problems in transportation systems with traffic peaks, or a finite number of elements in the system, are usually represented by the infinite source model, due to the difficulties of applying the exact finite source model. This study presents an alternative solution based on the upper bound values of the equilibrium probabilities of the exact finite source model, and compares the performance measurements of the two models. It is shown that for congestion factors below one, the smaller the value of the congestion factor, the smaller is the difference between the models. Based on this results the measures of performance of the proposed aproximate model are compared with the results of the usual infinite source model for different population sizes and number of servers. It is concluded that the models lead to very close numerical results for a wide range of congestion factors of the system and that these results are the better the larger is the number of servers and the number of elements in the system. Three case studies ilustrating the pratical applicability of the results of this study to transportation systems are also presented.

We propose a situation in which a single employee is responsible for processing incoming claims to an insurance company that can be classified as being one of two possible types. More specifically, we consider a priority-based system having separate buffers to store high priority and low priority incoming claims. We construct a mathematical model and perform queueing analysis to evaluate the performance of this priority-based system, which incorporates the possibility of claims being redistributed, lost, or prematurely processed.

We consider a single-part, two-echelon supply chain problem for spare parts. The network consists of a single manufacturing plant, a set of service centers (SCs) and a set of customers. Both echelons keep spare parts using the base-stock replenishment policy. The plant behaves as an M/M/1 queueing system and has limited production and storage capacity. Demand faced by each SC follows an independent Poisson process. The problem is to determine optimal location-allocation and optimal base-stock levels at both echelons while satisfying the target service levels and customer preferences of SCs. We develop a mixed integer non-linear programming model and use cutting-plane method to optimize the inventory-location decisions. We present an exact solution procedure for the inventory stocking problem and demonstrate the limitations of using traditional inventory models like METRIC-like and Approximate in case of high utilization rates. We show the effectiveness of our proposed cutting-plane algorithm and provide important managerial insights for spare parts management.