Modelling complex stochastic systems: Approaches to management and stability

This thesis is about coping with variability in outcomes for complex stochastic systems. We focus on systems where jobs arrive randomly throughout time to utilise resources for a random amount of time before departure. The systems we investigate are primarily concerned with the communication and storage of data. The thesis is partitioned into two parts. The first part studies systems where congestion leads to jobs waiting for service (queueing systems) and the second part considers systems where congestion leads to losses due to departures before provision of service (loss systems). For queueing systems, we are mainly interested in the management objective of ensuring that the expected time a job must wait before entering is finite --- a property known as stability. Finite waiting times occur naturally for loss systems due to the balking behaviour of jobs in response to congestion and so our attention in this case turns to the more ambitious goal of managing systems in such a way that the number of lost jobs is minimised. Each part consists of an introductory chapter providing background knowledge, which is followed by three chapters containing original research. In both parts we progress through these chapters by first applying traditional analytical approaches to novel models and then developing novel simulation-based approaches for models which are out of reach of traditional approaches