Article ID: | iaor20063680 |
Country: | United States |
Volume: | 16 |
Issue: | 2 |
Start Page Number: | 152 |
End Page Number: | 161 |
Publication Date: | Mar 2004 |
Journal: | INFORMS Journal On Computing |
Authors: | Fischer Martin J., Gross Donald, Brill Percy H., Shortle John F., Masi Denise M.B. |
Keywords: | M/G/1 queues |
In many modern applications of queueing theory, the classical assumption of exponentially decaying service distributions does not apply. In particular, Internet and insurance risk problems may involve heavy-tailed distributions. A difficulty with heavy-tailed distributions is that they may not have closed-form, analytic Laplace transforms. This makes numerical methods, which use the Laplace transform, challenging. In this paper, we develop a method for approximating Laplace transforms. Using the approximation, we give algorithms to compute the steady state probability distribution of the waiting time of an M/G/1 queue to a desired accuracy. We give several numerical examples, and we validate the approximation with known results where possible or with simulations otherwise. We also give convergence proofs for the methods.