Tails for (max, plus) recursions under subexponentiality

Dieker, A. B.; Lelarge, Marc

doi:10.1007/s11134-006-7730-5

Cited by 7 publications

(16 citation statements)

References 28 publications

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“…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.…”

Section: Introductionmentioning

confidence: 82%

Asymptotic behavior of generalized processor sharing queues under subexponential assumptions

Lelarge

2009

Queueing Syst

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Abstract:We analyze the behavior of Generalized Processor Sharing (GPS) queues with heavy-tailed service times. We compute the exact tail asymptotics of the stationary workload of an individual class and give new conditions for reduced-load equivalence and induced burstiness to hold. We also show that both phenomena can occur simultaneously. Our proofs rely on the single big event theorem and new fluid limits obtained for the GPS system that can be of interest by themselves.

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Section: Introductionmentioning

confidence: 82%

Asymptotic behavior of generalized processor sharing queues under subexponential assumptions

Lelarge

2009

Queueing Syst

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“…We give some heuristic rules for optimal balancing. Concerning the resequencing delay, the results are derived from Dieker and Lelarge (2006). The cases that are not covered in this reference are proved in Sect.…”

Section: Motivationmentioning

confidence: 99%

“…One of our main tool in our analysis will be the work of and the subsequent works done in and Dieker and Lelarge (2006). We briefly describe how we can model the system described above thanks to the (max,plus) algebra.…”

Section: Mathematical Modelmentioning

confidence: 99%

“…This formalism is not essential in our paper and we refer to Baccelli et al (1992) for more references. However, we stress that (max,plus) formalism is crucial for the proof of Theorem 1 below (that can be found in Dieker and Lelarge 2006). In view of the key role of this theorem for our analysis, we chose to show the connection between our model and (max,plus) algebra.…”

Section: Mathematical Modelmentioning

confidence: 99%

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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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“…Baccelli, Lelarge, and Foss [11] compute the exact tail asymptotics of stationary response times for both irreducible and reducible open stochastic event graphs under the assumptions of renewal input and independent identically distributed subexponential service times. In a recent paper, Dieker and Lelarge [15] study the tail asymptotics for functionals of the stationary solution of (max,+) linear recursions under subexponentiality assumptions in more complex networks; for example, the networks which have a FIFO event graph instead of a single server in each subnetwork. In addition, they apply the results to analyze the tail asymptotics of the resequencing delay.…”

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confidence: 99%

Tandem queues with subexponential service times and finite buffers

Kim

Ayhan

2010

Queueing Syst

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We focus on tandem queues with subexponential service time distributions. We assume that number of customers in front of the first station is infinite and there is infinite room for finished customers after the last station but the size of the buffer between two consecutive stations is finite. Using (max,+) linear recursions, we investigate the tail asymptotics of transient response times and waiting times under both communication blocking and manufacturing blocking schemes. We also discuss under which conditions these results can be generalized to the tail asymptotics of stationary response times and waiting times. Finally, we provide numerical examples to investigate the convergence of the tail probabilities of transient response times and waiting times to their asymptotic counter parts.

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Tails for (max, plus) recursions under subexponentiality

Cited by 7 publications

References 28 publications

Asymptotic behavior of generalized processor sharing queues under subexponential assumptions

Asymptotic behavior of generalized processor sharing queues under subexponential assumptions

Packet reordering in networks with heavy-tailed delays

Tandem queues with subexponential service times and finite buffers

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