Analysis on Partial Overflow Queueing Systems with Two Kinds of Calls

In this paper, the traffic model of one kind of the partial overflow system is presented and theoretically analyzed, which has remained unsolved up to today. In the partial overflow systems, the considered overflow traffic stream is a part of the traffic stream overflowing from a common trunks group with multiinput calls. The systems with two kinds of calls are treated. Both of the two input traffic streams are assumed to follow the Poisson process and the holding times of the calls are assumed to be identical and follow an exponential distribution. Under these assumptions, analytical formulas are derived to calculate the individual traffic characteristics for both the loss-loss partial overflow system and the wait-loss partial overflow system. With these results, the accuracy of the well-used equivalent random theory in approximating the traffic model offered with partial overflow stream is investigated. The two-input model is a general one and can be used for analyzing the model with more than two inputs. It is expected that the formulas derived in this paper can be Used to improve the accuracy of ERT method as well as used directly.