Simulation of nonhomogeneous Poisson processes with log linear rate function

An efficient method for simulating a nonhomogeneous Poisson process with rate function λ(t) = exp(α0+α1t) is given. The method ia based on an identity relating the nonhomogeneous Poisson process to the gap statistics from a random number of exponential random variables with suitably chosen parameters; it avoids costly ordering and taking of logarithms required by direct simulation methods and is more efficient than time scale transformations of a homogeneous Poisson process.