Extended Reality (XR)-which includes Virtual Reality and Augmented Reality-promises to bring the virtual and telepresence experience to another level. Unfortunately, solutions leveraging these technologies require special high-performance computing platforms that degrade the cost-benefit balance. Moving processing to the cloud solves this problem but imposes strict requirements on data transmission reliability, bandwidth, and delays. The satisfaction of these requirements becomes an extremely challenging problem in the presence of other types of delay-sensitive traffic, such as remote control, industrial automation, or the control commands of the Cloud XR application itself. This article studies the joint service of the adaptive Cloud XR traffic with other high-priority delay-sensitive traffics. The paper develops an analytical model of the considered communication system. The model represents the system as a discrete state Markov chain and estimates the quality of experience for Cloud XR users in various scenarios. Using the model, the paper estimates the network capacity for the Cloud XR traffic and optimizes the bitrate adaptation function of the Cloud XR video streaming application. The goal of the optimization is to improve the visual quality of the virtual environment observed by the users, subject to the constrained probability of image impairments due to excessive delivery delays. Numerical results demonstrate the high accuracy of the developed model and the benefits provided by the optimization. INDEX TERMS Cloud XR, heterogeneous traffic, high-priority traffic, real-time adaptive video, virtual reality, quality of experience, queueing systems, analytical models, Markov chain.