The Untraceable Events Method for Absorbing Processes

In this paper we propose a new method of determining the stability of queueing systems. We attain it using the absorbing process and introduce the untraceable events method to show the existence of the absorbing process. The advantage of our method is that we are able to discuss the stability of various variables for both discrete and continuous parameters in a general framework with nonstationary input. An untraceable event has the property that the state loses the memory of its origin. In a concrete model, we use the boundedness of the state at an epoch in time with respect to the initial condition and choose the form of the untraceable event corresponding to the input distribution.