Response time of the queue with the dropping function

摘要

In many active queue management algorithms, the dropping function, which associates the probability of dropping a packet with the buffer occupancy, is used. Several different forms of the dropping function has been considered so far, from a simple linear one, to the newest three-range polynomials. In this paper, an analysis of the response time of the queue with the dropping function is presented. In particular, theorems on the distribution of the response time and its average value and variance are proven. The assumed model of the queue is general – it allows arbitrary form of the dropping function, arbitrary form of the service time distribution and infinite buffer. Theoretical results are illustrated with numerical results for five popular types of dropping functions.