Stochastic Network Calculus Based Peak Age of Information Analysis in XR Interactive Systems

Extended Reality (XR) is defined as an example use case for 6 G networks by the International Telecommunication Union (ITU), where the quality of interactive experience is a crucial factor influencing the XR service performance. In this paper, we focuse on the timeliness and reliability of XR interactive systems. We investigate the peak Age of Information (PAoI) violation probability and backlog violation probability within these systems using Stochastic Network Calculus (SNC). Specifically, we establish a Discrete-Time Markov Modulated Process (MMP) for the frame generation process of XR services and conduct an SNC analysis to characterize the traffic and channel models within XR interactive systems. Additionally, we derive upper bounds for the PAoI violation probability and transmission backlog violation probability in scenarios with finite buffers. Furthermore, we formulate a low-complexity algorithm for solving the involved parameters. Subsequently, we analyze the numerical results to verify the accuracy of our derivations and further discuss why the PAoI violation probability is more suitable than the delay violation probability for characterizing XR interactive performance. Finally, we analyze the impact of system parameters on the PAoI bounds. The proposed violation probability upper bound metrics can be utilized to guide deployment decisions for the XR services.