Dynamics of Delay Equations, Theory and Applications - Abstract

Krisztin, Tibor

A differential equation with a queueing delay

We study a differential equation with a state-dependent delay motivated by a queueing process. The time delay is determined by an algebraic equation involving the length of the queue. For the length of the queue a discontinuous differential equation holds. We formulate an appropriate framework to study the problem. Within this framework we consider stability questions, and prove the existence of slowly oscillating periodic solutions. 1