Summary: We describe a method for carrying out Bayesian estimation for the double Pareto lognormal $(dPlN )$ distribution which has been proposed as a model for heavy-tailed phenomena. We apply our approach to estimate the $dPlN / M / 1$ and $M / dPlN / 1$ queueing systems. These systems cannot be analyzed using standard techniques due to the fact that the $dPlN$ distribution does not possess a Laplace transform in closed form. This difficulty is overcome using some recent approximations for the Laplace transform of the interarrival distribution for the Pareto$/M/1$ system. Our procedure is illustrated with applications in internet traffic analysis and risk theory.