Stochastic Graph Processes for Performance Evaluation of Content Delivery Applications in Overlay Networks
This paper addresses the study of fundamental properties of stream-based content distributions services. We assume the presence of an overlay network (such as those built by P2P systems) with limited connectivity degree, and we develop a mathematical model that captures the essential properties of overlay-based streaming protocols and systems. The methodology is based on graph theory and models the steaming system as a stochastic process, whose characteristics are related to the streaming protocol. The models captures the fundamental properties of the streaming system, such as the number of active connections, the different play-out delays of nodes and the probability of not receiving the stream due to nodes failures/misbehavior. Besides the static properties, the model is able to capture the transient behavior of the distribution graphs, i.e., the evolution of the structure over time, for instance in the initial phase of the distribution process. Contributions of this paper include the detailed definition of the methodology, its comparison with other analytical approaches, and a discussion of the additional insights enabled by this methodology. Results show that mesh based architectures are able to provide bounds on the receiving delay and maintain rate fluctuations due to system dynamics very low. Additionally, given the tight relationship between the stochastic process and the properties of the distribution protocol, this methodology gives basic guidelines for the design of such protocols and systems.