TCP Stability and Resource Allocation: Part II

Issues with TCP

Scalability Problem - I

Scalability Problem - II

Scalability Problem - III

Proposed Solutions

High Throughput TCP (Vinnicombe)

High-Throughput TCP - II

Linear System

Stability

Nyquist Test

Nyquist Plot (a=0.5)

Sufficient Condition for Stability

Source and Router Conditions

Decomposition for a Particular Price Function

Network Analysis

Extension to Networks

Global Stability - I

Global Stability - II

Razumikhin’s theorem

What does it mean?

Global Stability Results

Stochastic Models

Discrete-Time Stochastic Models

Model at the Link

Large Number of Sources Limit

Arrivals and Departures

 Connection-Level Model

Necessary Condition for Stability

Priority

What if we use TCP for resource allocation?

A Class of Utility Functions

Connection-Level Fluid Model

Proof of Stability

Some Open Problems