On Probability Characteristics for a Class of Queueing Models with Impatient Customers

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Performance modelling with adaptive hidden Markov models and discriminatory processor sharing queues

In modern computer systems, workload varies at different times and locations. It is important to model the performance of such systems via workload models that are both representative and efficient. For example, model-generated workloads represent realistic system behaviour, especially during peak times, when it is crucial to predict and address performance bottlenecks. In this thesis, we model performance, namely throughput and delay, using adaptive models and discrete queues. Hidden Markov models (HMMs) parsimoniously capture the correlation and burstiness of workloads with spatiotemporal characteristics. By adapting the batch training of standard HMMs to incremental learning, online HMMs act as benchmarks on workloads obtained from live systems (i.e. storage systems and financial markets) and reduce time complexity of the Baum-Welch algorithm. Similarly, by extending HMM capabilities to train on multiple traces simultaneously it follows that workloads of different types are modelled in parallel by a multi-input HMM. Typically, the HMM-generated traces verify the throughput and burstiness of the real data. Applications of adaptive HMMs include predicting user behaviour in social networks and performance-energy measurements in smartphone applications. Equally important is measuring system delay through response times. For example, workloads such as Internet traffic arriving at routers are affected by queueing delays. To meet quality of service needs, queueing delays must be minimised and, hence, it is important to model and predict such queueing delays in an efficient and cost-effective manner. Therefore, we propose a class of discrete, processor-sharing queues for approximating queueing delay as response time distributions, which represent service level agreements at specific spatiotemporal levels. We adapt discrete queues to model job arrivals with distributions given by a Markov-modulated Poisson process (MMPP) and served under discriminatory processor-sharing scheduling. Further, we propose a dynamic strategy of service allocation to minimise delays in UDP traffic flows whilst maximising a utility function.Open Acces

Scheduling for today’s computer systems: bridging theory and practice

Scheduling is a fundamental technique for improving performance in computer systems. From web servers to routers to operating systems, how the bottleneck device is scheduled has an enormous impact on the performance of the system as a whole. Given the immense literature studying scheduling, it is easy to think that we already understand enough about scheduling. But, modern computer system designs have highlighted a number of disconnects between traditional analytic results and the needs of system designers. In particular, the idealized policies, metrics, and models used by analytic researchers do not match the policies, metrics, and scenarios that appear in real systems. The goal of this thesis is to take a step towards modernizing the theory of scheduling in order to provide results that apply to today’s computer systems, and thus ease the burden on system designers. To accomplish this goal, we provide new results that help to bridge each of the disconnects mentioned above. We will move beyond the study of idealized policies by introducing a new analytic framework where the focus is on scheduling heuristics and techniques rather than individual policies. By moving beyond the study of individual policies, our results apply to the complex hybrid policies that are often used in practice. For example, our results enable designers to understand how the policies that favor small job sizes are affected by the fact that real systems only have estimates of job sizes. In addition, we move beyond the study of mean response time and provide results characterizing the distribution of response time and the fairness of scheduling policies. These results allow us to understand how scheduling affects QoS guarantees and whether favoring small job sizes results in large job sizes being treated unfairly. Finally, we move beyond the simplified models traditionally used in scheduling research and provide results characterizing the effectiveness of scheduling in multiserver systems and when users are interactive. These results allow us to answer questions about the how to design multiserver systems and how to choose a workload generator when evaluating new scheduling designs

Optimal control of queueing systems with multiple heterogeneous facilities

This thesis discusses queueing systems in which decisions are made when customers arrive, either by individual customers themselves or by a central controller. Decisions are made concerning whether or not customers should be admitted to the system (admission control) and, if they are to be admitted, where they should go to receive service (routing control). An important objective is to compare the effects of "selfish" decision-making, in which customers make decisions aimed solely at optimising their own outcomes, with those of "socially optimal" control policies, which optimise the economic performance of the system as a whole. The problems considered are intended to be quite general in nature, and the resulting findings are therefore broad in scope. Initially, M/M/1 queueing systems are considered, and the results presented establish novel connections between two distinct areas of the literature. Subsequently, a more complicated problem is considered, involving routing control in a system which consists of heterogeneous, multiple-server facilities arranged in parallel. It is shown that the multiple-facility system can be formulated mathematically as a Markov Decision Process (MDP), and this enables a fundamental relationship to be proved between individually optimal and socially optimal policies which is of great theoretical and practical importance. Structural properties of socially optimal policies are analysed rigorously, and it is found that 'simple' characterisations of socially optimal policies are usually unattainable in systems with heterogeneous facilities. Finally, the feasibility of finding 'near-optimal' policies for large scale systems by using heuristics and simulation-based methods is considered