Individual Traffic Characteristics Queueing Systems with Multiple Poisson and Overflow Inputs

A theoretical method for analyzing overflow problems in queueing systems is presented. An interrupted Poisson process (IPP) approximation of overflow traffic is employed. An overflow stream is replaced by an IPP using the three-moment matching method. For a three-input model, to which one Poisson and two IPP streams are offered simultaneously, explicit and iterative formulas are derived to calculate the mean waiting time, overflow probability, and moments of overflow traffic intensity from the system for each of the three input streams. This three-input model is a general one, and can be used for analyzing complex problems such as multistage overflow models and individual traffic characteristics for a model with more than three inputs. By setting the capacity of the waiting room of the three-input model to 0, this method can cover loss systems. For both queueing and loss systems, several numerical examples of typical traffic models are shown. Comparisons are made between theoretical values and experimental values by computer simulations, and it is demonstrated that the accuracy of the method is excellent.