Packet reordering in networks with heavy-tailed delays

Abstract

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. More generally, in many distributed applications 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 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.

Asymptotic behavior of generalized processor sharing queues under subexponential assumptions

“…Our framework is restricted to instantaneous inputs and extends results of Borst, Boxma and Jelenkovic [11]. Also our proof is new and inspired by the recent work of Baccelli and Foss [6] which has been applied to a variety of networks [8,12,7,20]. All these studies deal with networks which belong to the monotone separable framework.…”

“…Combining with (19), we get the equivalence (20). We now construct two specific sequences {K j n,x } and {η n } satisfying conditions 1 and 2 above and the conditions of the corollary.…”

Tail Asymptotics for Discrete Event Systems

“…Also under heavy-tailed assumptions on the distribution of the ζ (i) 's, results are available in Lelarge (2007a) and optimal values for the routing probabilities are computed when minimizing the resequencing delay or the size of the resequencing queue size. This model is certainly an oversimplification of the reality but it is intended to be of pedagogical interest.…”

Efficient traffic splitting in parallel TCP-based wireless networks: Modelling and experimental evaluation

“…For PS-based nodes that process the tasks of a job in parallel, the complex correlation structure between the sojourn times at the PS nodes makes an exact detailed mathematical analysis of the model impossible. In [24] and [25], the author analyzes a similar model but with FCFS queues and with probabilistic splitting. We further refer to Altman et al [26], who consider routing policies in a distributed versus centralized environment.…”