Piecewise polynomial approximations for heavy-tailed distributions in queueing analysis

A basic difficulty in dealing with heavy-tailed distributions is that they may not have explicit Laplace transforms. This makes numerical methods that use the Laplace transform more challenging. This paper generalizes an existing method for approximating heavy-tailed distributions, for use in queueing analysis. The generalization involves fitting Chebyshev polynomials to a probability density function g(t) at specified points t(1), t(2), - - -, t(N). By choosing points ti, which rapidly get far out in the tail, it is possible to capture the tail behavior with relatively few points, and to control the relative error in the approximation. We give numerical examples to evaluate the performance of the method in simple queueing problems.