The interrupted poisson process as an overflow process

Abstract

Traffic overflowing a first-choice trunk group can be approximated accurately by a simple renewal process called an interrupted Poisson process–a Poisson process which is alternately turned on for an exponentially distributed time and then turned off for another (independent) exponentially distributed time. The approximation is obtained by matching either the first two or three moments of an interrupted Poisson process to those of an overflow process. Numerical investigation of errors in the approximation and subsequent experience has shown that this method of generating overflow traffic is accurate and very useful in both simulations and analyses of traffic systems.