Dynamic TCP Acknowledgment with Sliding Window

The dynamic TCP acknowledgement problem formulated by Dooly et al. has been intensively studied in the area of competitive analysis. However, their framework does not consider the sliding window that restricts the maximum number of packets that the sender can inject into the network without an acknowledgement in TCP protocol. This paper proposes a new problem in which the sliding window is realistically integrated. We study how the ability of on-line algorithms change, depending on whether the receiver knows the window size. We show that a deterministic on-line algorithm extended from the optimal on-line algorithm for Dooly’s framework achieves the best competitive ratio of 2, if the window size is given. By contrast, if the window size is not given, the lower bound of the competitive ratio for an algorithm class which contains the algorithm by Dooly et al. depends on the peak packet rate from the sender and the window size. Significantly, our problem models the situation in which an on-line algorithm involuntarily transforms the input and processes the modified input without noticing the transformation.