Response time of the queue with the dropping function

Chydziñski, Andrzej; Adamczyk, Blazej

doi:10.1016/j.amc.2020.125164

Cited by 2 publications

(4 citation statements)

References 38 publications

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“…Finally, there are papers that deal with the response or waiting time and do involve active queue management, but with a simplified arrival process, which either lacks group arrivals [34] or autocorrelation [35]. A general arrival process with powerful modeling capabilities is an essential feature of the model examined here.…”

Section: Related Workmentioning

confidence: 99%

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Response Time of Queueing Mechanisms

Chydzinski,

Adamczyk

2024

Symmetry

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We study response time, a key performance characteristic of queueing mechanisms. The studied model incorporates both active and passive queue management, arbitrary service time distribution, as well as a complex model of arrivals. Therefore, the obtained formulas can be used to calculate the response time of many real queueing mechanisms with different features, by parameterizing adequately the general model considered here. The paper consists of two parts. In the first, mathematical part, we derive the distribution function for the response time, its density, and the mean value. This is done by constructing two systems of integral equations, for the distribution function and the mean value, respectively, and solving these systems with transform techniques. All the characteristics are derived both in the time-dependent and steady-state cases. In the second part, we present numerical values of the response time for a few system parameterizations and point out several of its properties, some rather counterintuitive.

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Section: Related Workmentioning

confidence: 99%

“…To find (35), we have to calculate the derivative of Q(s, x), which requires the derivative of V(n, s, x), which in turn requires the derivative of W(n, l, s, x), which requires the derivative of g(k, t, x). In the last two steps, we need to employ the Leibniz integral rule, necessary for differentiation under integrals.…”

Section: Response Timementioning

confidence: 99%

Response Time of Queueing Mechanisms

Chydzinski,

Adamczyk

2024

Symmetry

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“…They represent the most popular dropping function classes proposed in the active queue management literature. Importantly, all these dropping functions were parameterized in [ 28 ] in such a way that they provide the average stationary response time of exactly 20.0 for

. The average response time is arguably the single most important stationary performance measure of a queueing system, thus in some sense, these five dropping functions provide the same stationary behavior of the queue.…”

Section: Examplesmentioning

confidence: 99%

“…To the best of the author’s knowledge, the results presented herein are new. For studies on other characteristics (the queue size, loss probability, response time) of systems with the dropping function, or carried out under different assumptions on the arrival process and service times, we refer the reader to [ 18 , 19 , 20 , 21 , 22 , 23 , 24 , 25 , 26 , 27 , 28 ]. On the other hand, there are several papers on the time to reach a given level in classic queueing models, i.e., without the dropping function—see, for example, [ 29 , 30 , 31 , 32 , 33 ] and the references given there.…”

Section: Introductionmentioning

confidence: 99%

On the Transient Queue with the Dropping Function

Chydziñski

2020

Entropy

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We deal with a queueing system, in which arriving packets are being dropped with the probability depending on the queue size. Such a scheme is used in several active queue management schemes proposed for Internet routers. In this paper, we derive and analyze a selected transient characteristic of the model, i.e., the probability that in a given time interval the queue size is kept under a predefined level. As the main purpose of the discussed queueing scheme is to maintain the queue size low, this is a natural characteristic to study. In addition to that, the average time to reach a given level is derived. Theoretical results for both characteristics are accompanied by numerical examples. Among other things, they demonstrate that the transient behavior of the queue may vary significantly with the shape of the dropping function, even if the steady-state performance remains unaltered.

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Response time of the queue with the dropping function

Cited by 2 publications

References 38 publications

Response Time of Queueing Mechanisms

Response Time of Queueing Mechanisms

On the Transient Queue with the Dropping Function

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