Diffusion approximation in overloaded switching queueing models

The asymptotic behavior of a queueing process in overloaded state-dependent queueing models (systems and networks) of a switching structure is investigated. A new approach to study fluid and diffusion approximation type theorems (without reflection) in transient and quasi-stationary regimes is suggested. The approach is based on functional limit theorems of averaging principle and diffusion approximation types for so-called Switching processes. Some classes of state-dependent Markov and non-Markov overloaded queueing systems and networks with different types of calls, batch arrival and service, unreliable servers, networks (MSM, Q/MSM, Q/1/∞ )r switched by a semi-Markov environment and state-dependent polling systems are considered

Performance and reliability in distributed systems

PhD ThesisThis thesis is devoted to the construction and analysis of models which can be used to evaluate the performance and reliability of distributed systems. The general object of the research therefore is to extend the types of queueing models with breakdowns which have been solved, with a particular interest in networking structures. The systems that are studied involve various collections of servers and their associated queues. These range from isolated nodes, though parallel nodes coupled by the effect of breakdowns on arrivals, to pipelines of such parallel stages and more general networks. The issues that are explored include the influence of breakdowns and repairs on delays, job losses and optimal routeing. Obtaining performance measures for interacting queues is difficult, however a degree of abstraction has been used here which allows long run averages to be calculated (exactly in many cases) for quite complex systems. A variety of different techniques are used in order to obtain solutions to these models, including exact equations, exact numerical and approximate numerical techniques

Performance of Computer Systems; Proceedings of the 4th International Symposium on Modelling and Performance Evaluation of Computer Systems, Vienna, Austria, February 6-8, 1979

These proceedings are a collection of contributions to computer system performance, selected by the usual refereeing process from papers submitted to the symposium, as well as a few invited papers representing significant novel contributions made during the last year. They represent the thrust and vitality of the subject as well as its capacity to identify important basic problems and major application areas. The main methodological problems appear in the underlying queueing theoretic aspects, in the deterministic analysis of waiting time phenomena, in workload characterization and representation, in the algorithmic aspects of model processing, and in the analysis of measurement data. Major areas for applications are computer architectures, data bases, computer networks, and capacity planning. The international importance of the area of computer system performance was well reflected at the symposium by participants from 19 countries. The mixture of participants was also evident in the institutions which they represented: 35% from universities, 25% from governmental research organizations, but also 30% from industry and 10% from non-research government bodies. This proves that the area is reaching a stage of maturity where it can contribute directly to progress in practical problems

Modelling activities in a Critical Care Unit

The Critical Care Unit (CCU) is the sector of the hospital where, as the name suggests, critically ill patients receive treatment. The main aim of this research is to identify and apply suitable Operational Research techniques to model patient flow in the CCU at the University Hospital of Wales, Cardiff. The Operational Research techniques employed in this thesis include queueing theory and simulation. These methods have been utilised previously in the field of healthcare with much success. The thesis begins by considering two aspects of queueing theory, namely batch service queueing theory and batch arrival queueing theory. The latter of these is utilised to model patient flow within the CCU. Although queueing theory may be used as a good approximation to activities in the Unit, it does not incorporate all aspects of real-life. Thus discrete-event simulation is suggested as an alternative approach. Two types of statistical analysis, CART and Regression, are applied to both length of stay and mortality variables. The results from these statistical tests are compiled and investigated in more depth. Finally, a discrete event simulation model is built in Visual Basic for Applications, for Microsoft Excel. This simulation model incorporates many of the complexities of a CCU, such as patient priority and cancellation of scheduled patients if all beds on the Unit are occupied. The model is then used to test various "what-if type" scenarios, including the possibility of funding additional beds, the concept of ring-fencing of beds for different levels of care, and the likely effect of reducing the impact of bed-blocking

Application of Mathematical and Computational Models to Mitigate the Overutilization of Healthcare Systems

The overutilization of the healthcare system has been a significant issue financially and politically, placing burdens on the government, patients, providers and individual payers. In this dissertation, we study how mathematical models and computational models can be utilized to support healthcare decision-making and generate effective interventions for healthcare overcrowding. We focus on applying operations research and data mining methods to mitigate the overutilization of emergency department and inpatient services in four scenarios. Firstly, we systematically review research articles that apply analytical queueing models to the study of the emergency department, with an additional focus on comparing simulation models with queueing models when applied to similar research questions. Secondly, we present an agent-based simulation model of epidemic and bioterrorism transmission, and develop a prediction scheme to differentiate the simulated transmission patterns during the initial stage of the event. Thirdly, we develop a machine learning framework for effectively selecting enrollees for case management based on Medicaid claims data, and demonstrate the importance of enrolling current infrequent users whose utilization of emergency visits might increase significantly in the future. Lastly, we study the role of temporal features in predicting future health outcomes for diabetes patients, and identify the levels to which the aggregation can be most informative

Queueing Systems with Heavy Tails

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Power Control and Resource Allocation for QoS-Constrained Wireless Networks

Developments such as machine-to-machine communications and multimedia services are placing growing demands on high-speed reliable transmissions and limited wireless spectrum resources. Although multiple-input multiple-output (MIMO) systems have shown the ability to provide reliable transmissions in fading channels, it is not practical for single-antenna devices to support MIMO system due to cost and hardware limitations. Cooperative communication allows single-antenna devices to share their spectrum resources and form a virtual MIMO system where their quality of service (QoS) may be improved via cooperation. Most cooperative communication solutions are based on fixed spectrum access schemes and thus cannot further improve spectrum efficiency. In order to support more users in the existing spectrum, we consider dynamic spectrum access schemes and cognitive radio techniques in this dissertation. Our work includes the modelling, characterization and optimization of QoS-constrained cooperative networks and cognitive radio networks. QoS constraints such as delay and data rate are modelled. To solve power control and channel resource allocation problems, dynamic power control, matching theory and multi-armed bandit algorithms are employed in our investigations. In this dissertation, we first consider a cluster-based cooperative wireless network utilizing a centralized cooperation model. The dynamic power control and optimization problem is analyzed in this scenario. We then consider a cooperative cognitive radio network utilizing an opportunistic spectrum access model. Distributed spectrum access algorithms are proposed to help secondary users utilize vacant channels of primary users in order to optimize the total utility of the network. Finally, a noncooperative cognitive radio network utilizing the opportunistic spectrum access model is analyzed. In this model, primary users do not communicate with secondary users. Therefore, secondary users are required to find vacant channels on which to transmit. Multi-armed bandit algorithms are proposed to help secondary users predict the availability of licensed channels. In summary, in this dissertation we consider both cooperative communication networks and cognitive radio networks with QoS constraints. Efficient power control and channel resource allocation schemes have been proposed for optimization problems in different scenarios.Cambridge Overseas Trust; China Scholarship Counci