A time-varying Poisson arrival process generator

Abstract

Frequently an arrival process is acceptably Poisson, but the ar rival rate varies with time. This note uses inversion to derive a time-varying Poisson generator whose rate function is continuous and piecewise-linear. The piecewise-linear function includes the piecewise constant arrival rate while involving only slightly more computations and represents a reasonable compromise between flexibility and practicality. In this case, inversion is efficient while being highly compatible with correlation induction variance reduction methods. The generator has been implemented for routine use in the INSIGHT simulation language providing a useful new input process while promoting variance reduction through common and antithetic variates.