Efficient simulation of non-Poisson non-stationary point processes to study queueing approximations

A nonstationary point process can be efficiently simulated by exploiting a representation as the composition of a rate-one process and the cumulative arrival rate function, provided that an efficient algorithm is available for generating the rate-one process, as is the case for stationary renewal processes, Markov modulated Poisson processes and many other processes. Overall efficiency can be achieved by constructing a table of the inverse cumulative arrival rate function when it is not explicitly available.