Performance Evaluation of Transition-based Systems with Applications to Communication Networks

Since the beginning of the twenty-first century, communication systems have witnessed a revolution in terms of their hardware capabilities. This transformation has enabled modern networks to stand up to the diversity and the scale of the requirements of the applications that they support. Compared to their predecessors that primarily consisted of a handful of homogeneous devices communicating via a single communication technology, today's networks connect myriads of systems that are intrinsically different in their functioning and purpose. In addition, many of these devices communicate via different technologies or a combination of them at a time. All these developments, coupled with the geographical disparity of the physical infrastructure, give rise to network environments that are inherently dynamic and unpredictable. To cope with heterogeneous environments and the growing demands, network units have taken a leap from the paradigm of static functioning to that of adaptivity. In this thesis, we refer to adaptive network units as transition-based systems (TBSs) and the act of adapting is termed as transition. We note that TBSs not only reside in diverse environment conditions, their need to adapt also arises following different phenomena. Such phenomena are referred to as triggers and they can occur at different time scales. We additionally observe that the nature of a transition is dictated by the specified performance objective of the relevant TBS and we seek to build an analytical framework that helps us derive a policy for performance optimization. As the state of the art lacks a unified approach to modelling the diverse functioning of the TBSs and their varied performance objectives, we first propose a general framework based on the theory of Markov Decision Processes. This framework facilitates optimal policy derivation in TBSs in a principled manner. In addition, we note the importance of bespoke analyses in specific classes of TBSs where the general formulation leads to a high-dimensional optimization problem. Specifically, we consider performance optimization in open systems employing parallelism and closed systems exploiting the benefits of service batching. In these examples, we resort to approximation techniques such as a mean-field limit for the state evolution whenever the underlying TBS deals with a large number of entities. Our formulation enables calculation of optimal policies and provides tangible alternatives to existing frameworks for Quality of Service evaluation. Compared to the state of the art, the derived policies facilitate transitions in Communication Systems that yield superior performance as shown through extensive evaluations in this thesis