Recent advances in networking and computing technologies have led to an increased interest in considering computation and communication in a joint and distributed mode according to the computing in the network paradigm. Furthermore, the emergence of the sixth generation (6G) networks is profiling the ever more challenging applications' requirements imposed by the new era service classes. In order to guarantee efficient implementation and availability to the upcoming applications, characterized by stringent quality of experience requirements, an accurate network design and delay analysis is becoming mandatory to pursue efficient 6G network dimensioning and enable computing in the network-based applications. Toward this goal, this article proposes a suitable end-to-end delay performance analysis and reliability evaluation in the case of a 6G network offering virtual reality services, which is considered one of the most challenging technologies for the coming new era service classes. More in depth, the aim of the article is the formulation of the stochastic end-to-end delay bound by applying supermartingale envelopes in order to allow accurate VR reliability prediction in relation to the number of users linked to the same computing node with a specified service profile. The goodness and effectiveness of the proposed approach is validated by providing comparison with simulation results and analytical predictions derived by resorting to the use of the classical Markov queueing theory.