A Stochastic Model for Multi-Operational-Mode TCP in High-Speed Networks

A Stochastic Model for Multi-Operational-Mode TCP in High-Speed Networks

Talal A. Edwan


This paper presents a stochastic model for a multi-operational-mode TCP variant optimised to effectively utilise the bandwidth in high-speedlong-delay networks. Particularly, a model for a TCP variant that increases its rate as power function of the current congestion window, and uses multiplicative and subtractive decrease to reduce the congestion window upon packet loss. The power function is adapted dynamically using powers of {0.5, 1, 2} according to the level of congestion in the network. The proposed model can be generalised to other powers; it captures the dynamics of the congestion window size evolution and sending rate under the influence of random packet loss by providing a closed-form expression for both the congestion window size and the normalised sending rate. We show that depending on the increase/decrease rules adopted for the congestion window size evolution, the congestion window size can be modelled either as function of exponential random variable or a Markov chain. Simulation results validate the analytical model and show that the multiplicative decrease factor has more impact on the rate especially when a quadratic – instead of linear – increase rule is adopted under heavy packet loss rate. In addition to that, results show that the initial value of additive increase when a square-root rule is adopted has minimal effect on the average congestion window size.


TCP, Congestion control, Markov chain, Performance modelling, Stochastic model, High-Speed networks