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The connection establishment in Long-Term Evolution Advanced (LTE-A) is often executed for distributed user equipment (UE) nodes with frequent small data sets for transmission to the central enhanced Node B. LTE-A connection establishment consists mainly of an access barring check (ABC) followed by preamble transmission (contention). Previous studies of connection establishment have often assumed Poisson characteristics (without verifying the Poisson assumption). In this paper, we introduce a simple equilibrium analysis framework for comprehensively evaluating the LTE-A connection establishment, including both access barring and preamble contention. We conduct a detailed analysis of the backlog arising from the uniform backoff over up to T max o slots by UE requests that failed the barring check or collided in the preamble contention. We verify that the process representing the numbers of backlogged UE requests rejoining the connection establishment tends to Poisson process characteristics for high barring probability and long maximum timeout T max o . We present numerical comparisons of our equilibrium model with simulations for practical parameter settings. The comparisons illustrate the effects of the parameter settings on the convergence of the LTE-A connection establishment dynamics to Poisson characteristics for nonsynchronized and synchronized request arrivals. Index Terms-Access barring check (ABC), backlog model, Long-Term Evolution Advanced (LTE-A), Markov modulated poisson process, Poisson process, preamble contention, uniform backoff.

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