Network Traffic Control Based-on Fractional-order PI～λD～μ

The characteristic of the Internet traffic flow should be analyzed and the model should be build before it controlled. The conventional network traffic models only describe the shot-time relations of it. It is found that network traffic has the characteristic of long-time relations and self-similar nature. FARIMA(p,d,q)model can describe the nature both of shot-time relations and of long-time relations.Through the research of fractional calculus, it is found that FARIMA(p,d,q) model is essentially a fractional differential, so network traffic control system is a fractional control system. For this kind of systems, some method based-on integer is suggested, such as PI,PID controller,auto-adaptive controller,forecast controller and so on. Because of long-time relations of uncontrolled network traffic, these integer-order controller can not get good purpose.The fractional-order PI~λD~μis used as the AQM controller and is used to manage the TCP queue. The fractional-order control system,the theory of fractional-order PI~λD~μand analysis method of stability are first discussed. Then the model of network traffic control system and its stability are introduced. In addition, the approximate formula for coefficient K p , Ki,Kd is also suggested by using characteristic index of forecast control. Finally, through emulation, the fractional-order PI~λD~μarithmetic is compared with the integer-order PID arithmetic.The availability of the strategies and stability of systems are proved by doing some analysis and simulation.