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.
Low Latency Queueing (LLQ) is an Internet Protocol (IP) router discipline that is being used to ensure that performance-sensitive high priority traffic, such as voice and video, receive their high level of performance, while allowing less performance-sensitive traffic, such as e-mail or best-effort IP, to receive some portion of the bandwidth. In this paper, we develop a simple analytic approximation for the buffer latency (expected buffer delay) for each traffic class using the LLQ system. The approximation is validated via a simulation model.
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