A Close Approximation of the Nonempty Buffer Probability Over Nakagami- $m$ Fading Channels

Based on the effective capacity model, the tail probability of backlog size in a wireless communication system can be characterized by two effective capacity functions, namely, the QoS exponent and the nonempty buffer probability. The QoS exponent is well understood in the literature; however, there is little known about the other function, i.e., the nonempty buffer probability, because this function has not been exactly derived. In this letter, we derive a new approximation formula for this function over Nakagami-
$\boldsymbol{m} $
fading channels. Simulation results indicate that our formula can closely approximate this function and is more accurate than existing approximation formulae.