Counting preimages of TCP reordering patterns

Packet reordering is an important property of network traffic that should be captured by analytical models of the Transmission Control Protocol (TCP). We study a combinatorial problem motivated by RESTORED [1], a TCP modeling methodology that incorporates information about packet dynamics. A significant component of this model is a many-to-one mapping B that transforms sequences of packet IDs into buffer sequences in a manner that is compatible with TCP semantics. We show that the following hold: • There exists a linear time algorithm that, given a buffer sequence W of length n, decides whether there exists a permutation A of {1, 2, . . . , n} such that A ∈ B(W ) (and constructs such a permutation, when it exists). • The problem of counting the number of permutations in B(W ) has a polynomial time algorithm. • We also show how to extend these results to sequences of IDs that contain repeated packets.