Average Connection Establishment Time in Random Access Channel with Limited Resources

In 4G and 5G cellular networks, a 4-step random access procedure is used. A significant challenge arises when a large number of users attempt to connect within a short period of time. To address this issue, the access class barring mechanism is employed. There are numerous studies that analyze the average connection time for users within the random access framework that includes access class barring. However, these studies primarily offer approximate calculations for the average connection time. In this work, the connection process is modeled using a Markov chain. The problem of calculating the average connection time is reduced to finding the average time to reach an absorbing state. An iterative algorithm is proposed to compute the exact value of this metric both for a system using the access class barring mechanism and without its use. It is demonstrated that, under certain conditions, the approximate calculations presented in other works significantly underestimate the average connection time.