A note on an analytic model for slow start in TCP

Absmct-Sikdar et a1 111 has pmvided a formula to model the window increase pattem given the mechanics of delayed ackuowledgemeuts. In this paper, we show that their sum formula significantly underestimates the iterated sum fur rounds mater than seven. m e approximation e m r gmws exponentially. We also derive a more accurate sum formula whose approximation e m r is linearly bounded. We show that with use of the i n c o m t sum formula, cases arise where it is impossible to time out as the initial loss indication in slow start, which can have signlcant impact nu TCP latency, assuming a comlated loss model. We show that our more accurate sum fumula greatly reduces the number of cases showing this behaviour, further improving upon the accuracy of the model. I. BACKGROUND Analytic models are very useful to gain an in-depth understanding of the fundamental behaviour of TCP protocols. Recently , some efforts have been made to build analytic models for TCP performance using round-trip time and packet loss probability [1][2][3]. In [l], comprehensive analytic models are provided for TCP behaviour. However, their model for packet sums in slow start has little theoretical background, and no indication of how the formula was obtained. Their analytic sum formula i s also provided to calculate the total number of packets transmitted in the first k rounds in the slow start phase of TCP. We will show that their sum formula significantly underestimates the iterated sum for k > 7. We also derive a more accurate sum formula. In this note, the same notations from [l] are adopted. In [l], Sikdar et al have presented a formula to model the window increase pattern, given the mechanics of delayed acknowledgements. This is presented as w (n) = p+ +e], (1) where 1 J is the floor function. Equation (1) is used to determine the number of packets transmitted in the nlh round. This forms the basis of further models to eventually determine the number of rounds required, and hence the transfer latency, for a slow start period ending in either packet loss or reaching the