On dynamic resource allocation in systems with bursty sources

Abstract

There is a trend to use computing resources in a way that is more removed from the technical constraints. Users buy compute time on machines that they do not control or necessarily know the specifics of. Conversely this means the providers of such resources have more freedom in allocating them amongst different tasks. They can use this freedom to provide more, or better, service by reallocating resources as demand for them changes. However deciding when to reallocate resources is not trivial. In order to make good reallocation decisions, this thesis constructs a series of models. Each of the models concerns a resource allocation problem in the presence of bursty sources. The focus of the modelling, however, varies. In its most basic form it considers several different job types competing over the allocation of a limited number of servers. The goal there is to minimize the (weighted) mean time jobs spend in the system. The weighting can reflect the relative importance of the different job types. Reallocation of servers between job types is in general considered to be neither free nor instantaneous. We then show how to find the optimal static allocation of servers over job types. Finding the optimal dynamic allocation of servers is formulated as solving a Markov decision process. We show that this is practically unfeasible for all but the most simple systems. Instead a number of heuristics are introduced. Some are fluid-approximation based and some are parameterless, i.e. do not require the a priori knowledge of parameters of the system. The performance of these heuristic policies is then explored in a series of simulations. A slightly different model is formulated next. Its goal is not to optimize allocation of servers over several job types, but rather between powered up and powered down states. In the powered up state servers can provide service for incoming jobs. In the powered down state servers cannot service incoming jobs but incur a profit due to power savings. Balancing power and performance is again formulated as a Markov decision process. This is not explicitly solved but instead some of the heuristics considered earlier are adapted to give dynamic policies for powering servers up and v down. Their performance is again tested in a number of simulations, including some where the arrival process is not only bursty but also non-Markovian. The third and final model considers allocation of servers over different job types again. This time the servers experience breakdowns and subsequent repairs. During a repair period the servers cannot process any incoming jobs. To reduce the complexity of this model, it is assumed that switches of servers between job types are instantaneous, albeit not necessarily free. This is modeled as a Markov decision process and we show how to find the optimal static allocation of servers. For the dynamic allocation previously considered heuristics are adapted again. Simulations then show the performance of these heuristics and the optimal static allocation in a number of scenarios.