An important characteristic of any TCP connection is the sequencing of packets within that connection. Out-of sequence packets indicate that the connection suffers from loss, duplication or reordering. It is thus of interest to study the magnitude of out-of sequence packets within Internet TCP connection and to identify their causes. More generally, in many distributed applications (e.g., remote computations, database manipulations, or data transmission over a computer network), information integrity requires that data exchanges between different nodes of a system be performed in a specific order. However, due to random delays over different paths in a system, the packets or updates may arrive at the receiver in a different order than their chronological order. In such a case, a resequencing buffer at the receiver has to store disordered packets temporarily. We analyze both the waiting time of a packet in the resequencing buffer and the size of this resequencing queue. We derive the exact asymptotics for the large deviation of these quantities under heavy-tailed assumptions. In contrast with results obtained for light-tailed distributions, we show that there exists several ``typical paths'' that lead to the large deviation. We derive explicitly these different ``typical paths'' and give heuristic rules for an optimal balancing.