Time to Buffer Overflow in an MMPP Queue

Chydziñski, Andrzej

doi:10.1007/978-3-540-72606-7_75

Cited by 8 publications

(5 citation statements)

References 22 publications

(17 reference statements)

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“…As one may notice, the analytical results for distributions of the time to the buffer overflow in one-channel queues modelling singlemachine manufacturing lines, in fact, are restricted mainly to systems without machine breakdowns. In [3][4] the formulae for the time-to-buffer overflow period were obtained for models with BMAP (Batch Markovian Arrival Process) and MMPP (Markov-Modulated Poisson Process) input flows, respectively. One can find another results related to buffer overflow period and the loss process, e.g.…”

Section: Preliminariesmentioning

confidence: 99%

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Distribution of time to buffer overflow in a finite-buffer manufacturing model with unreliable machine

et al. 2017

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Abstract.One of the most important characteristic of each queueing model is time to buffer overflow. In the paper the distribution of that time in a single-channel manufacturing system, modelled by a Markovian finitebuffer queue with machine breakdowns, is studied. By using the analytical approach based on the idea of embedded Markov chain, total probability law and linear algebra, the formula for Laplace transform of the time to buffer overflow conditional distribution is found. Numerical illustration is presented. PreliminariesThe problem of finite buffer (magazine) capacity is a typical one in manufacturing engineering. Jobs arriving to the system being saturated are being lost or must be redirected to another destination. The in-depth investigation of the loss process cannot be based only on the well-known coefficient as the loss ratio, defined as the part of the total number of jobs being directed to the system (manufacturing line), which are lost due to the buffer overflow. To analyze the phenomenon more precisely from the probabilistic point of view, it is necessary to know, e.g. the probability distributions of buffer overflow durations and times of reaching them. The problem becomes more essential in the case of unreliable machine, where successive failure-free times are followed by repair periods during which the processing of jobs is suspended.In [1] and [2] the studies on the application of different-type queueing models in manufacturing engineering can be found. As one may notice, the analytical results for distributions of the time to the buffer overflow in one-channel queues modelling singlemachine manufacturing lines, in fact, are restricted mainly to systems without machine breakdowns. In [3][4] the formulae for the time-to-buffer overflow period were obtained for

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Section: Preliminariesmentioning

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Distribution of time to buffer overflow in a finite-buffer manufacturing model with unreliable machine

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“…and F (t) is the service time distribution function. From the practical point of view it is important that A k (s) and D k (s) can be computed effectively by means of the well-known uniformization method (see, for instance, [11], [18]).…”

Section: Arrival Process and Queueing Systemmentioning

confidence: 99%

Packet dropping characteristics in a queue with autocorrelated arrivals

Chydziñski

Wójcicki

Hryn

2008

JCOMSS

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This paper provides a detailed description of the packet dropping process connected with the buffer overflows in a network node. Namely, we show the formulas for the most important loss characteristics, both in the transient and the stationary regime and then illustrate them via numericalexamples. In order to make it possible to obtain the droppingcharacteristics for strongly autocorrelated arrivals, the Markovmodulated Poisson process is used as a traffic model.

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“…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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Time to Buffer Overflow in an MMPP Queue

Cited by 8 publications

References 22 publications

Distribution of time to buffer overflow in a finite-buffer manufacturing model with unreliable machine

Distribution of time to buffer overflow in a finite-buffer manufacturing model with unreliable machine

Packet dropping characteristics in a queue with autocorrelated arrivals

On the Transient Queue with the Dropping Function

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