Massive ultra-reliable and low-latency communication (mURLLC) in the sixth generation (6G) wireless networks aims at providing a wide range of delay-sensitive real-time services and applications for massive accessing by satisfying users' stringent requirements on the delay-bound and error rate. The age of information (AoI) theory characterizes the freshness of information, which measures the time-difference between the current time and the time-stamp of the latest observation, and thus, has been recognized to be able to analyze the mURLLC information transmission latency. How to statistically upperbound the AoI is critically important, because the 6G mURLLC mobile users are served by time-varying wireless channel and the deterministic upper-bounded AoI is difficult to guarantee. To overcome this challenge, in this paper we propose and develop the analytical modeling techniques to identify and characterize the statistical-bounded-AoI theory to efficiently support mURLLC services over 6G mobile wireless networks. First, we introduce the θ-envelope rate of the maximum AoI (i.e. peak AoI) to represent the envelope's average changing rate for the stochastic sequence of the maximum AoI. Then, we derive the upper-bound and lower-bound on the distribution of the maximum AoI. Third, we define and model the statistical-bounded AoI by developing the AoI-exponent to measure the exponential decaying rate of the AoI violation probability. Finally, we validate and evaluate our derived results of the AoI evolution in mURLLC networks through numerical analyses.
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