Further Investigations of the Priority Queuing System with Preemptive Priority and Randomized Push-Out Mechanism

Abstract

This article is written about a queuing theory models with limited buffer size and one service channel with two incoming flows. One of the flows is more important than another flow. In this article we prefer to call packets of these flows as priority and non-priority packets. This priority can be realized as a preemptive priority, which allows high-priority packets to take place in system queue closer to service channel and push-out low-priority packets out of service channel or as a randomized push-out, which allows to push out non-priority packets out of the system when it is full. Authors present in this article algorithm for computing statistical characteristics of the model for all values of push-out probability α. For getting solution is used generating functions method. This method reduces size of linear equations system from k(k+1)/2 to (k+1). Using this method allowed authors to study model behavior for all load values from 0 to 4 by first and second incoming flows. In this article provided zones of model “closing” for non-priority packets. Also authors considered a relative deviation of loss probability and it’s approximation by linear law depending on push-out probability α to get areas of possible using linear law for approximating results of changing this push-out probability.