Utilizing Continuous Time Markov Chain for analyzing video-on-demand streaming in multimedia systems

Abstract

In multimedia systems, Tree and Mesh-based topologies are the popular ways to organize the peers in an overlay and provide video streaming services. Unlike Content Delivery Networks (CDN), providing streaming services through a Peer-to-Peer (P2P) overlay poses the challenge of unpredictable churn for both provider and consumer peers. The dynamically arriving and departing peers, with Video Cassette Recorder (VCR) actions like jump, pause, forward, rewind, etc., controlled by end users, makes it challenging to reason about such systems. Though techniques like prototype test beds, simulation, etc., are successful to some extent in analyzing the behavior of such complex systems before the actual deployment, they either require lots of effort to set up or fail to capture the finer anomalies. Therefore, there is a need to have a formal framework that can specify the system at the desired abstraction level and capture the stochastic behavior exhibited by the actors of such systems. This paper addresses this issue and provides a platform for analyzing the behavior of real-time Video-on-Demand (VoD) streaming behavior with VCR actions over P2P overlays. To capture the stochastic behavior of actors, the Continuous Time Markov Chain (CTMC) is used to design a model of both the tree and mesh-based systems. This CTMC model is written in the Probabilistic Symbolic Model Checker (PRISM) language, which assists in containing the state space explosion and specifies the QoUX properties using Continuous Stochastic Logic (CSL). The proposed methodology uses the scenarios described in various simulation-based studies and industry standards of VoD systems available in the proposed formal model and finds a striking resemblance in the results. Eventually, given a joining-delay threshold of 170 ms, a P2P-Tree-based architecture resulted in an optimal tree height of 4-5 levels; after that, the startup delay of playback gets affected. Similarly, for a given startup delay threshold of 700 ms after departure and seek-jump actions, the maximum P2P-Tree height should be 5. We have also compared the performance properties of P2P tree and mesh-based VoD streaming systems with industry standards of centralized VoD systems. It is observed that the performance of P2P-tree and P2P-mesh-based VoD streaming systems also meet the industry standards. The results we got from the proposed formal framework are conclusive and establish the applicability of the approach.