Some remarks regarding asymptotic packet loss in the Pareto/M/1/K queueing system

Many asymptotic results and numerical techniques have appeared in literature to evaluate the packet loss of GI/M/1/K queueing systems and some of them are applicable to heavy-tail distributed interarrival times. We have found a closed-form expression for the Laplace transform of Pareto probability distributions and it allows us to have a better setting to evaluate different performance measures of Pareto queueing systems. Particularly, in this paper we consider the evaluation of the asymptotic packet loss for the Pareto distributed interarrival times, i.e., Pareto/M/1/K queueing systems, through the use of the Pareto Laplace transform and its derivative.