The potentials method for the M/G/1/m queue with customer dropping and hysteretic strategy of the service time change

Zhernovyi, Yuriy; Kopytko, Bohdan

doi:10.17512/jamcm.2016.1.20

Cited by 4 publications

(2 citation statements)

References 7 publications

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“…Some interesting investigations can be found e.g. in [14][15][16][17][18][19][20][21][22][23][24][25][26][27][28] but we must emphasize that in many of cited papers service time of a customer is still often treated as independent with regard to his volume which does not let us use the results in many practical systems, and the others include only approximate analysis and do not deal with calculating exact total volume characteristics (even in steady state).…”

Section: Introductionmentioning

confidence: 99%

Bulletin of the Polish Academy of Sciences: Technical Sciences

Ziółkowski,

Tikhonenko

2022

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In the present paper, we analyze the model of a single-server queueing system with limited number of waiting positions, random volume customers and unlimited sectorized memory buffer. In such a system, the arriving customer is additionally characterized by a nonnegative random volume vector whose indications usually represent the portions of unchanged information of a different type that are located in sectors of unlimited memory space dedicated for them during customer presence in the system. When the server ends the service of a customer, information immediately leaves the buffer, releasing resources of the proper sectors. We assume that in the investigated model, the service time of a customer is dependent on his volume vector characteristics. For such defined model, we obtain a general formula for steady-state joint distribution function of the total volume vector in terms of Laplace-Stieltjes transforms. We also present practical results for some special cases of the model together with formulae for steady-state initial moments of the analyzed random vector, in cases where the memory buffer is composed of at most two sectors. Some numerical computations illustrating obtained theoretical results are attached as well.

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Section: Introductionmentioning

confidence: 99%

Bulletin of the Polish Academy of Sciences: Technical Sciences

Ziółkowski,

Tikhonenko

2022

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“…Their popularity and number of applications increase mainly because of the headway in computer science, which is a basic discipline of their existence. Interesting analyses are presented, e.g., by Juneja et al (2012), Naumov et al (2015;, Naumov and Samuilov (2018), , Lisovskaya et al (2017;, Zhernovyi and Kopytko (2016), Matalytsky and Zaj ąc (2019), Cascone et al (2010), Rumyantsev and Morozov (2017), Kerobyan et al (2018), or Nowak et al (2020). It is worth highlighting that, in the cited papers, the service time of a customer is still often treated as independent with regard to his volume so the obtained results can be applied in real systems in a limited range.…”

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confidence: 99%

Queueing systems with random volume customers and a sectorized unlimited memory buffer

Tikhonenko¹,

Ziółkowski²,

Kempa³

2021

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In the present paper, we concentrate on basic concepts connected with the theory of queueing systems with random volume customers and a sectorized unlimited memory buffer. In such systems, the arriving customers are additionally characterized by a non-negative random volume vector. The vector's indications can be understood as the sizes of portions of information of a different type that are located in the sectors of memory space of the system during customers' sojourn in it. This information does not change while a customer is present in the system. After service termination, information immediately leaves the buffer, releasing its resources. In analyzed models, the service time of a customer is assumed to be dependent on his volume vector characteristics, which has influence on the total volume vector distribution. We investigate three types of such queueing systems: the Erlang queueing system, the single-server queueing system with unlimited queue and the egalitarian processor sharing system. For these models, we obtain a joint distribution function of the total volume vector in terms of Laplace (or Laplace-Stieltjes) transforms and formulae for steady-state initial mixed moments of the analyzed random vector, in the case when the memory buffer is composed of two sectors. We also calculate these characteristics for some practical case in which the service time of a customer is proportional to the customer's length (understood as the sum of the volume vector's indications). Moreover, we present some numerical computations illustrating theoretical results.

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Determining Stationary Characteristics of Two-Channel Queueing Systems with Erlangian Distribution of Service Time

Zhernovyi

2017

Cybern Syst Anal

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The potentials method for the M/G/1/m queue with customer dropping and hysteretic strategy of the service time change

Cited by 4 publications

References 7 publications

Bulletin of the Polish Academy of Sciences: Technical Sciences

Bulletin of the Polish Academy of Sciences: Technical Sciences

Queueing systems with random volume customers and a sectorized unlimited memory buffer

Determining Stationary Characteristics of Two-Channel Queueing Systems with Erlangian Distribution of Service Time

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