Preemptive queueing system with randomized push-out mechanism

• New preemptive queueing system with randomised push-out mechanism is studied.
• The system was classified using Kendall’s and Basharin’s notations.
• The system was solved numerically using generating function method.
• Numerical results and graphs were presented.

In this article considered a queueing theory model with limited buffer size, one service channel, and two incoming flows. In this model one of the flows has a power to preempt other tasks. We call it a high-priority flow. Another one is low-priority. This priority mechanism is realized in a two different ways. The first one is a preemptive priority, which allows high-priority packets to interrupt low-priority packets in service channel and push them out. The second one is a randomized push-out mechanism with probability α, which allows us to choose what type of packets should be pushed out of the system when it is full. In this article we provide an algorithm for computing statistical characteristics of the model for all values of push-out probability α. We have used generating functions method to simplify the system of linear equations. This method allows us to reduce the order of linear equations system from k(k + 1)/2 to (k + 1). As the result we have got two effects in this model. The first one is a linear behavior of loss probabilities in the model with low overload. The second one is a “closing” of a system for low-priority packets with high overload.