The truncated normal distribution: Applications to queues with impatient customers

Motivated by heavy traffic approximations for single server queues with abandonment, we provide an exact expression for the moments of the truncated normal distribution using Stein’s lemma. Consequently, our moment expressions provide insight into the steady state skewness and kurtosis dynamics of single server queues with impatient customers. Moreover, based on the truncated normal distribution, we develop a new approximation for single server queues with abandonment in the nonstationary setting. Numerical examples illustrate that our approximation performs quite well.