Design of rate-based controllers for active queue management in TCP/IP networks
Section snippets
Summary of our previous work
In our previous paper [1] we described an AQM scheme which uses traffic rate information for congestion control. Based on a non-linear fluid-flow model of TCP, we designed a proportional-integral (PI) controller for AQM. Starting with a linearized model of the non-linear TCP plant [2], [3], we derived a first-order linear plant model with time delay. We then discussed the problem of stabilizing the first-order system with time delay using a proportional-integral (PI) controller. Due to the
Dynamic model of TCP/AQM
In [2], [3], a rate-based fluid-flow model of a TCP source i accessing a single link is described by the following non-linear differential equation:where denotes the time-derivative of r, ri is rate of the TCP source (in packets per second), di is the round-trip time (RTT) of the TCP source (in s), p is the marking/dropping probability of a TCP packet at the link, and θ is a parameter characteristic of the type of TCP source. Similar to the model in
Simulation results
The objective of our simulation studies is to investigate how well the I controller and P-controller can maintain small queue sizes and target link utilization. The simulation results presented here were obtained using the OPNET Modeler simulation tool. Fig. 1 shows a simple bottleneck network configuration with two routers and a number of TCP flows which is the same configuration used in [1].
The routers are interconnected by a T3 (45 Mbps) link having a propagation delay of 1 ms. There are 10
Results for the integral controller
This section presents simulation results for the I-controlled TCP/AQM plant. We also discuss the properties of I-control of a first-order plant from a control theoretic perspective.
Results for the proportional controller
This section presents simulation results for the P-controlled TCP/AQM plant. Here we also discuss the properties of P-control of a first-order plant from a control theoretic perspective.
Remarks on PI control of a first-order system
A rate-based PI-controller of TCP/AQM system was described in our previous work [5]. Here we present control theoretic insights into why the PI-controller performed very well in the control the first-order plant. The PI-controller can be expressed aswhere kp and ki are proportional and integral gains, respectively. For the closed-loop system in Fig. 9, we get the following transfer functionsThe system is stable for positive
Conclusion
We have shown through simulations that properly designed I and P rate-based AQM scheme can maintain small queue sizes in the presence of long-lived FTP sources and short-lived web sources. Results were presented for networks with asymmetrical round-trip times, different link capacities and packets sizes. Maintaining small queue sizes is an attractive property for switches and routers that have very small buffers (typically much smaller than the bandwidth-delay product of the network). It is
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