Parallel queues with resequencing

Jean-Marie, Alain; Gün, Levent

doi:10.1145/174147.169748

Cited by 45 publications

(34 citation statements)

References 3 publications

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“…In our model, misordering is caused by (random) multi-path routing. A similar framework has been studied by Jean-Marie and Gün [18], where the misordering network consists of K parallel M/GI/1 queues and the corresponding distribution…”

Section: Motivationmentioning

confidence: 98%

Tails for (max, plus) recursions under subexponentiality

Dieker

Lelarge

2006

Queueing Syst

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We study the stationary solution to a (max, plus)-linear recursion. Under subexponentiality assumptions on the input to the recursion, we obtain the tail asymptotics of certain (max, plus)-linear functionals of this solution.(Max, plus)-linear recursions arise in FIFO queueing networks; more specifically, in stochastic event graphs. In the event graph setting, two special cases of our results are of particular interest and have already been investigated in the literature. Firstly, the functional may correspond to the end-to-end response time of the event graph. Secondly, for two queues in tandem, the functional may correspond to the sojourn time in the second queue. Our results allow for more general networks; we illustrate this by studying the asymptotics of the resequencing delay due to multi-path routing.

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Section: Motivationmentioning

confidence: 98%

Tails for (max, plus) recursions under subexponentiality

Dieker

Lelarge

2006

Queueing Syst

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“…To the best of our knowledge, there are very few results on this problem under heavy-tailed assumptions. A similar framework has been studied by Jean-Marie and Gün (1993), where the disordering network consists of K parallel M/G I /1 queues and the corresponding distribution of the resequencing delay is derived. A survey is given in Baccelli and Makowski (1989).…”

Section: Motivationmentioning

confidence: 99%

Packet reordering in networks with heavy-tailed delays

Lelarge

2007

Math Meth Oper Res

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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.

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“…The study of resequencing problem in queueing networks is not without history [5,8,2,4,13,7]. Recently, large deviations results have been obtained for the size of the resequencing buffer for a system of two parallel M |M |1 queues [15].…”

Section: B a Simple Model Of Mis-ordering And Multi-path Routingmentioning

confidence: 99%

“…Recently, large deviations results have been obtained for the size of the resequencing buffer for a system of two parallel M |M |1 queues [15]. The analysis given here has its point of departure in the work of [8] where the distributions of the resequencing and end-toend delays were derived for a system of parallel M |GI|1 queues. Unfortunately, most of the closed-form results rely on the service times being exponentially distributed, while general service time distributions do not always give nice form solutions.…”

Section: B a Simple Model Of Mis-ordering And Multi-path Routingmentioning

confidence: 99%

“…Unfortunately, most of the closed-form results rely on the service times being exponentially distributed, while general service time distributions do not always give nice form solutions. For our purpose this limits somewhat the usefulness of the results from [8] since in many circumstances, it may not be appropriate to assume that the service times are exponentially distributed. For instance, in the Internet, traffic coming to a router arises as the aggregation of many flows from many different sources, and the impact of the admission control and scheduling policies is far from understood.…”

Section: B a Simple Model Of Mis-ordering And Multi-path Routingmentioning

confidence: 99%

See 1 more Smart Citation

Resequencing Delays Under Multipath Routing - Asymptotics in a Simple Queueing Model

Han¹,

Makowski²

2005

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Abstract-We study the resequencing delay caused by multipath routing. We use a queueing model which consists of parallel queues to model the network routing behavior. We define a new metric, denoted by γ, to study the impact of resequencing on the customer end-to-end delay. Our results characterize some properties of γ with respect to different service time distributions. In particular, the resequencing delay can be negligible when the delay along each path is light-tailed, but can be of major concern when it is heavy-tailed.

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Parallel queues with resequencing

Cited by 45 publications

References 3 publications

Tails for (max, plus) recursions under subexponentiality

Tails for (max, plus) recursions under subexponentiality

Packet reordering in networks with heavy-tailed delays

Resequencing Delays Under Multipath Routing - Asymptotics in a Simple Queueing Model

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