Heavy Traffic Analysis of AIMD Models

We study heavy traffic asymptotics of many Additive Increase Multiplicative Decrease AIMD connections sharing a common router in the presence of other uncontrolled traffic, called mice. The system is scaled by speed and average number of sources. With appropriate scalings of the packet rate and buffer content, an approximating delayed diffusion model is derived. By heavy traffic we mean that there is relatively little spare capacity in the operating regime. In contrast to previous scaled models, the randomness due to the mice or number of connections is not averaged, and plays its natural and dominant role. The asymptotic heavy traffic model allows us to analyze buffer and loss management policies of early marking or discarding as a function of the queue size andor the total input rate and to choose a nearly optimal function via use of an appropriate limiting optimal control problem, captures the essential features of the physical problem, and can guide us to good operating policies. After studying the asymptotics of a large number of persistent AIMD connections we also handle the asymptotic of finite AIMD connections whose number varies as connections arrive and leave. The data illustrate some of the advantages of the approach.