Random-Access Channel Queuing Model

In the Long-Term Evolution (LTE) mobile communication standard, there is provision for a random-access channel (RACH), which provides users the opportunity to gain access to the network. Future fourth-generation and fifth-generation systems will undoubtedly also have some similar scheme. Therefore, better understanding of such systems is desirable. To this end, we present, in this paper, an abstract representation of the RACH queue that is in the form of a leaky Markov “ball and urn” model, where the number of balls in M successive bins represents the number of users contending for access after each of M attempts. We analyze this model by evolving a multidimensional probability distribution for the number of balls in each bin, from which the individual probabilities are then determined as marginals. In particular, the probability of the Mth bin will determine the probability of access or failure. An efficient computational scheme is developed to evolve the bin probabilities, and the results are shown to be in excellent agreement with Monte Carlo simulation, which, for M = 3, requires 10000 times longer run time.