Gaussian approximations for the probability mass function of the access delay for different backoff policies in S-ALOHA

In this letter, closed-form non-recursive expressions for the probability mass function (pmf) of the access delay are addressed. As the exact non-recursive expression for the pmf of the access delay are typically complex and have high computational requirements, Gaussian approximations are derived for the uniform, binary exponential and geometric backoff policies. Our approximations have a mean square error in the order of 10
^-7
compared to the exact recursive equations found in the literature