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Fluid model for multiple TCP and UDP connections through a network of queues in a random environment

Banff International Research Station for Mathematical Innovation and Discovery

The Transmission Control Protocol (TCP) is one of the main protocols of the Internet protocol suite and major internet applications rely on it. The TCP protocol provides reliability, flow control and congestion control. Alongside the TCP, the User Datagram Protocol (UDP) is another transport protocol which, in contrast to TCP, is a simplified request-response protocol that does not have any connection setup time and does not provide any flow, congestion or error controls. We consider in this presentation a fluid model for multiple TCP and UDP connections interacting through a network of queues. We suppose that the connections are randomly routed according to a dynamical routing table protocol which takes into account the topology of the network and adapts the routing dynamically. Our model extends the multi-class model studied in Graham et al (2009). The dynamic of the TCP flows follows the additive increase/multiplicative-decrease (AIMD) protocol and is represented by a stochastic differential equation w.r.t. a Poisson random measure and the UDP flows are represented by simple point processes. Using an adequate scaling, a mean-field result is proved where, as the number of connections goes to infinity, the behaviour of the different connections can be represented by the solution of an original nonlinear stochastic differential equation. The existence and uniqueness of the solution of this equation are derived. Moreover, we discuss some open problems and possible extensions. This talk is based on a current ongoing joint work with Donald A.Dawson and Yiqiang Q.Zhao.

Mathematics; Mathematics

video/mp4

Author affiliation: Carleton University

2021-02-19

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/77345

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/