1. Uncooperative Flow Control
Xingzhe Fan
M. Arcak, J. T. Wen, K. Candrayana and S. Kalyanaraman
Electrical, Computer, and Systems Engineering Department
Rensselaer Polytechnic Institute

2. Outline Network flow control
Detection and rectification of uncooperative users
Primal algorithm
Dual algorithm

3. Objective: Maximize utilization subject to link capacity constraints
Network Flow Model (Kelly et al., 1998)
Objective: Maximize utilization subject to link capacity constraints
Kelly model Network as the interconnection of information sources and communication links through the routing matrices as shown in this Fig. Packets from each source are routed through the links with the aggregate link rates y equal to Rx. Each link has a fixed capacity c, and based on its congestion and queue size, a link price p is generated. The link price information is then sent back to the sources with the aggregate source price, denoted by q which is = RT p since the links only feed back price information to the sources that utilize them.
The objective is then to maximize the utilization of the whole network subject to the link constraints. Here Ui is concave function, which is a measure of the utility of each source and the sum of them is regarded as the utilization of the whole network. The constraint is because each link has a fixed capacity c and link rates can not be greater than it. For this static optimization problem, we can not solve it directly because it will need global information which are not locally available. Kelly come up with two dynamic algorithms, generalized later by Low and Srikant. which solve this optimization problem in a decentralized and dynamic way, that is, … The first one is called primal which use a dynamic rate control algorithm and a static link price update. This h basically is a penalty or barrier function to force the link rates not greater than link capacity. Here we use + to denote projection, which keep all the variable non-negative and in…. The second algorithm called dual use a static rate update and a dynamic link control algorithm, which essentially come from applying the gradient projection algorithm to the dual problem.

4. Uncooperative flow control (detecting and rectifying cheating users)

5. Ideal uncooperative flow control for primal algorithm
In the primal algorithm, let us suppose the cheating user uses… Ideally if …However,

6. Uncooperative flow control for primal algorithm

7. Uncooperative flow control for primal algorithm
Rigorously, we prove that…

8. Ideal uncooperative flow control for dual algorithm

9. Uncooperative flow control for dual algorithm

10. Uncooperative flow control for dual algorithm

11. NS2 simulation

12. NS2 simulations
Caveat: Too small or too large ρ may deteriorate the performance:
Small ρ disallowed to achieve desired two-time-scale behavior
Arbitrarily large ρ leads to saturation of dropping or marking
ρ can be determined experimentally
or by automatic tuning.