Diffusion Model of a Non-Integer Order <em>PI^γ</em> Controller with TCP/UDP Streams

Abstract

In this article, a way to employ the diffusion approximation to model interplay between TCP and UDP flows is presented. In order to control traffic congestion, an environment of IP routers applying AQM (Active Queue Management) algorithms has been introduced. Furthermore, the impact of the fractional controller PIγ and its parameters on the transport protocols is investigated. The controller has been elaborated in accordance with the control theory. The TCP and UDP flows are transmitted simultaneously and are mutually independent. Only the TCP is controlled by the AQM algorithm. Our diffusion model allows a single TCP or UDP flow to start or end at any time, which distinguishes it from those previously described in the literature.

Keywords

• active queue management
• diffusion approximation
• fractional controller <i>PI^γ</i>
• internet
• TCP/IP and UDP