Rate of convergence for the 'square root formula' in the Internet transmission control protocol. (8th September 2016)

• Record Type: Journal Article
• Authors: Ott, Teunis J.
• Is Part Of: Advances in applied probability. Volume 38:Number 4(2006)
• Page Start: 1132
• Page End: 1154
• Publication Date: 2016-09-08
• Subjects: Computer networking, -- transport protocol, -- stochastic process, -- square root law, -- stationary distribution, -- stochastic dominance, -- rate of convergence, -- coupled stochastic processes; 60F99, -- 60G10, -- 60G99, -- 60K30, -- 60K99, -- 68U99; Probabilities -- Periodicals; Stochastic models -- Periodicals; Electronic journals; Periodicals; 519.2
• DOI: 10.1017/S0001867800001488
• Languages: English
• ISSNs: 0001-8678

Abstract

Abstract : The 'square root formula' in the Internet transmission control protocol (TCP) states that if the probability p of packet loss becomes small and there is independence between packets, then the stationary distribution of the congestion window W is such that the distribution of W √ p is almost independent of p and is completely characterizable. This paper gives an elementary proof of the convergence of the stationary distributions for a much wider class of processes that includes classical TCP as well as T. Kelly's 'scalable TCP'. This paper also gives stochastic dominance results that translate to a rate of convergence.