Performance Analysis of Reliable Internet Protocols (TCP) Using a Fixed Point Algorithm

The feedback nature of reliable Internet protocols can be represented by a fixed point algorithm (FPA). The network signals congestion based on the aggregate traffic offered to it and each source adjusts its sending rate based on the feedback from the network to reach the network operating regime. The algorithms of reliable (transport) protocols are based on this fact. The FPA has been one of the most useful ways of solving analytical models of Internet performance. Apart from implementing the FPA for simple networks with few bottleneck links, no implementation algorithm of this complex procedure is given to the best of our knowledge. In this paper I develop an implementation algorithm of the FPA for analytical models of the Transmission Control Protocol (TCP) which is the most widely used transport protocol on the Internet and show how the FPA emulates TCP. Even though the algorithm considers TCP it can be easily generalized to any reliable Internet protocol. The implementation algorithm can be used to develop efficient and comprehensive analytical tools for the performance investigation of networks (the Internet) with an arbitrary number of bottleneck links and sources. Such tools help to analyze existing protocols and propose more efficient ones. In this paper I also briefly discuss important ideas which can be used to prove the convergence of the FPA (and hence TCP) and the uniqueness of the fixed points. These ideas can be used to easily study the stability of the TCP protocol. Unlike previous proofs of convergence which apply to only specific network scenarios, our approach applies to different network scenarios.