Stationary solutions of stochastic recursions describing discrete event systems

Anantharam, Venkat; Konstantopoulos, Takis

doi:10.1016/s0304-4149(97)00019-7

Cited by 17 publications

(49 citation statements)

References 4 publications

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“…This result was proved in a similar way in [2], whereas an explicit construction of a stationary workload on × N was proposed in [9] and [13] (see also [12] for a generalization of this result to a dominated lattice-valued SRS).…”

Section: Theorem 3 Suppose That Either (5) or The Following Conditiomentioning

confidence: 69%

“…In this section we show how the techniques developed in [1] allow us to construct a stationary workload for the queue under weaker assumptions, on a probability space that is enriched with respect to the original one. This is done again using the stochastic comparison with the LRMST sequence (see (9)).…”

Section: Weak Stationaritymentioning

confidence: 99%

“…This is done again using the stochastic comparison with the LRMST sequence (see (9)). 506 P. MOYAL Throughout this section, we suppose without loss of generality that ( , F ) is Polish (see [1] for a precise definition). We work on the enlarged probability space × R, on which we define the shiftθ…”

Section: Weak Stationaritymentioning

confidence: 99%

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The queue with impatience: construction of the stationary workload under FIFO

Moyal

2010

Journal of Applied Probability

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In this paper we study the stability of queueing systems with impatient customers and a single server operating under a FIFO (first-in-first-out) discipline. We first give a sufficient condition for the existence of a stationary workload in the case of impatience until the beginning of service. We then provide a weaker condition of existence on an enriched probability space using the theory of Anantharam et al. (1997Anantharam et al. ( ), (1999. The case of impatience until the end of service is also investigated.

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Section: Theorem 3 Suppose That Either (5) or The Following Conditiomentioning

confidence: 69%

Section: Weak Stationaritymentioning

confidence: 99%

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The queue with impatience: construction of the stationary workload under FIFO

Moyal

2010

Journal of Applied Probability

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“…(2) is known as a stochastic recursive equation, see [1], [3], [5], [6], [9]. The loss process is assumed to be Poisson, hence it is independent of R n .…”

Section: A Stochastic Recursive Equationsmentioning

confidence: 99%

Analysis of AIMD protocols over paths with variable delay

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Abstract-The throughput of AIMD protocols in general and of TCP in particular, has been computed in many existing works by modeling the round-trip time as a constant and thus replacing the round-trip time by its expectation. There are however many scenarios in which the delays of packets vary, causing a variation of the round-trip time. Many typical scenarios occur in wireless and mobile networks. We propose in this paper an analytical model that accounts for the variability of delay, while computing the throughput of an AIMD protocol. We derive a closed-form expression for the throughput, that illustrates the impact of the variability of delay. We show by analysis and simulation, that an increase in the variability of delay improves the performance of an AIMD protocol. Thus, an analytical model that only considers the average delay could underestimate the performance of an AIMD protocol in scenarios where delay is variable.

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“…(1) is known as a stochastic recursive equation, see [1,3,5,6,9]. The loss process is assumed to be Poisson with an intensity that depends on the current round-trip time, and the process (…”

Section: $ and % ( 'mentioning

confidence: 99%

Analysis of AIMD protocols over paths with variable delay

2005

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Abstract:The throughput of AIMD protocols in general and of TCP in particular, has been computed in many existing works by modeling the round-trip time as a constant and thus replacing it by its expectation. There are however many scenarios in which the delays of packets vary, causing a variation of the round-trip time. Many typical scenarios occur in wireless and mobile networks. We propose in this paper an analytical model that accounts for the variability of delay, while computing the throughput of an AIMD protocol. We derive a closed-form expression for the throughput, that illustrates the impact of delay variability. We show by analysis and simulation, that an increase in the variability of delay improves the performance of an AIMD protocol. Thus, an analytical model that only considers the average delay could underestimate the performance of an AIMD protocol in scenarios where delay is variable. Key-words: TCP, delay variability, stochastic recursive equations.This is an extension of a paper that appeared at INFOCOM'04 which was restricted to a Poisson loss process with fixed parameter. £University of Nice-Sophia Antipolis. ¤Also with Universidad Autónoma Metropolitana, Mexico. Analyse de protocoles AIMD sur des trajectoires à délai variableRésumé : Les modèles traditionnels des protocoles AIMD, et en particulier ceux du protocole TCP, calculent le débit en modélisant le délai d'aller-retour comme étant une constante, ainsi celui-ci est remplacé par son espérance. Pourtant, il existe plusieurs scénarios pour lesquels le délai des paquets varie, ce qui cause une variation du temps d'aller-retour. Les réseaux mobiles et les réseaux sans fil sont les meilleurs exemples de ce type de scénario. Nous proposons dans ce papier, un modèle analytique prenant en compte la variabilité du délai pour calculer le débit d'un protocole AIMD. Nous obtenons une expression close pour le débit, et montrons par analyse et simulation qu'une augmentation de la variabilité du délai améliore les performances d'un protocole AIMD. En conséquence, un modèle analytique qui ne considère que le délai moyen pourrait sous-estimer les performances de ce type de protocole dans des scénarios où le délai est variable. Mots-clés :TCP, variabilité du délai, équations récursives stochastiques. AIMD protocols over paths with variable delay3

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Stationary solutions of stochastic recursions describing discrete event systems

Cited by 17 publications

References 4 publications

The queue with impatience: construction of the stationary workload under FIFO

The queue with impatience: construction of the stationary workload under FIFO

Analysis of AIMD protocols over paths with variable delay

Analysis of AIMD protocols over paths with variable delay

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