Loss rates for stochastic fluid models

O’Reilly, Małgorzata M.; Palmowski, Zbigniew

doi:10.1016/j.peva.2013.05.005

“…This allows us to exactly compute the metric π loss defined by (1) and corresponding to the fraction of lost information. In addition, we consider the stationary regime and study the state of the system, when a busy period starts; this aspect is not investigated in [10]. Finally, one outstanding result of this paper is that we have shown that the total loss duration and the total volume of information lost in a busy period have phase-type distributions.…”

Section: Resultsmentioning

confidence: 99%

“…https://doi.org/10.1239/jap/1445543849 Downloaded from https://www.cambridge.org/core. IP address: 44.224.250.200, on 03 Nov 2020 at 06:27:38, subject to the Cambridge Core terms of use, available Loss in finite buffer fluid queues 839Using(10) and(13), the mean duration of an idle period is given byE IP = (π − , 0)(−A ) −1 1 = π − (−Q −− ) −1 R−1 − (I + T −0 (−T 00 ) −1 )1.…”

mentioning

confidence: 99%

Volume and duration of losses in finite buffer fluid queues

Guillemin

¹

,

Séricola

²

2015

J. Appl. Probab.

2

0

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We study congestion periods in a finite fluid buffer when the net input rate depends upon a recurrent Markov process; congestion occurs when the buffer content is equal to the buffer capacity. Similarly to O'Reilly and Palmowski (2013), we consider the duration of congestion periods as well as the associated volume of lost information. While these quantities are characterized by their Laplace transforms in that paper, we presently derive their distributions in a typical stationary busy period of the buffer. Our goal is to compute the exact expression of the loss probability in the system, which is usually approximated by the probability that the occupancy of the infinite buffer is greater than the buffer capacity under consideration. Moreover, by using general results of the theory of Markovian arrival processes, we show that the duration of congestion and the volume of lost information have phase-type distributions.

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“…SFMs have been used in the analysis of a variety of real-life situations, including telecommunications systems [19], risk assessment [7], power generation systems [10] and congestion control [18]. The stationary and transient analysis of SFMs and powerful algorithms for the numerical evaluations of various performance measures can be found in [2,3,4,5,11,13,20].…”

Section: Sfmsmentioning

confidence: 99%

Construction of algorithms for discrete-time quasi-birth-and-death processes through physical interpretation

Samuelson

¹

,

O’Reilly

²

,

Bean

³

2020

Stochastic Models

2

0

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We apply physical interpretations to construct algorithms for the key matrix G in discrete-time quasi-birth-and-death (dtQBD) and its z-transform G(z) , motivated by the work on stochastic fluid models (SFMs) in [13]. In this methodology, we first write a summation expression for G(z) by considering a physical interpretation similar to that of an algorithm in [13]. Next, we construct the corresponding iterative scheme, and prove its convergence to G(z). In particular, here we consider the physical interpretation of Algorithm 1 for Ψ(s) in [13], and use a similar physical interpretation for G(z) partitioned into three sections, each expressed in terms of matrices analogous to block matrices in the fluid generator Q(s) in stochastic fluid models.

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“…Here, we extend the analysis provided in [14] by considering the loss of fluid occurring in finite buffer fluid queues. It is worth noting that the authors of [10] considered similar performance metrics via the use of Laplace transforms. The key difference with that paper is that we compute the distribution of the random variables under consideration instead of their Laplace transforms.…”

Section: Introductionmentioning

confidence: 99%

“…https://doi.org/10.1239/jap/1445543849 Downloaded from https://www.cambridge.org/core. IP address: 44.224.250.200, on 03 Nov 2020 at 06:29:13, subject to the Cambridge Core terms of use, available Loss in finite buffer fluid queues 839Using(10) and(13), the mean duration of an idle period is given byE IP = (π − , 0)(−A ) −1 1 = π − (−Q −− ) −1 R−1 − (I + T −0 (−T 00 ) −1 )1.…”

mentioning

confidence: 99%

Volume and duration of losses in finite buffer fluid queues

Guillemin¹,

Séricola²

2015

Journal of Applied Probability

View full text Add to dashboard Cite

We study congestion periods in a finite fluid buffer when the net input rate depends upon a recurrent Markov process; congestion occurs when the buffer content is equal to the buffer capacity. Similarly to O'Reilly and Palmowski (2013), we consider the duration of congestion periods as well as the associated volume of lost information. While these quantities are characterized by their Laplace transforms in that paper, we presently derive their distributions in a typical stationary busy period of the buffer. Our goal is to compute the exact expression of the loss probability in the system, which is usually approximated by the probability that the occupancy of the infinite buffer is greater than the buffer capacity under consideration. Moreover, by using general results of the theory of Markovian arrival processes, we show that the duration of congestion and the volume of lost information have phase-type distributions.

show abstract

Loss rates for stochastic fluid models

Cited by 9 publications

References 27 publications

Volume and duration of losses in finite buffer fluid queues

Volume and duration of losses in finite buffer fluid queues

Construction of algorithms for discrete-time quasi-birth-and-death processes through physical interpretation

Volume and duration of losses in finite buffer fluid queues

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