Modelling bursty flows with fluid queues

Many modern systems must deal with bursty traffic, from computer sys-tems subject to jobs arriving in clusters to devices with an intermittent energy supply such as those powered by renewable sources. As computer systems become ever more commonplace, and renewable energy targets make unreliable power ubiquitous, an important part of system design will be ensuring system performance under bursty demand. We seek to understand the impact of bursty arrivals and show how system parameters can be chosen to meet service requirements in these situations. In this thesis, we will be concerned with the fluid queue, a modelling paradigm for systems subject to bursty arrivals. Fluid queues describe the evolution of a stochastic buffer fed by a source which changes rate according to a background process, typically a continuous-time Markov chain. We choose this model as it captures the key behaviour we wish to model and the characteristics we seek to compute are amenable to efficient solution. In this thesis we make three contributions to the theory of fluid queues, significantly increasing the class of systems which can be modelled without resorting to experiments or simulations. Firstly, we derive hitting times in models with multi-regime (level-dependent) behaviour, then busy periods in models where the environment process has an infinite (but countable) state space such as the M/M/c queue, and finally performance metrics in networks of fluid queues. We apply such models to give insights into mobile phone battery life, the temperature of a computer system and reserve levels in energy storage reservoirs, all systems subject to bursty arrivals. 3