Geo m /G/1/n system with LIFO discipline without interrupts and constrained total amount of customers

Cascone, A.; Manzo, Rosanna; Pechinkin, A. V.; Shorgin, Sergey

doi:10.1134/s0005117911010085

Cited by 8 publications

(4 citation statements)

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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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“…This mechanism is called a synchronised or triggered motion (e.g., [3], [4] and [5]). If we take into account the inverse order discipline, that is, a Last-Come-First-served (LCFS), we refer to [6], [7] as well as [8].…”

Section: Introductionmentioning

confidence: 99%

A discrete-time queueing system with three different strategies

Atencia

Galán–García

Aguilera–Venegas

et al. 2021

Journal of Computational and Applied Mathematics

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“…This mechanism is called a synchronized or triggered motion (e.g., Artalejo, 2000;Gelenbe and Label, 1998). For the inverse order discipline, we refer to (Pechinkin and Svischeva 2004;Pechinkin and Shorgin 2008) as well as (Cascone et al 2011).…”

Section: Introductionmentioning

confidence: 99%

A Discrete-Time Retrial Queueing System With Service Upgrade

Atencia

Ruiz²,

Sánchez³

2015

ECMS 2015 Proceedings Edited By: Valeri M. Mladenov, Petia Georgieva, Grisha Spasov, Galidiya Petrova

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This paper considers a discrete-time retrial queueing system with displacements. The arriving customers can opt to go directly to the server obtaining immediately its service or to join the orbit. In the first case, the displaced customer goes directly to the orbit. The arrivals follow a geometrical law and the service times are general.We study the Markov chain underlying the considered queueing system obtaining the generating function of the number of customers in the orbit and in the system as well as the stationary distribution of the time that a customer spends in the server. We derive the stochastic decomposition law and as an application we give bounds for the proximity between the steady-state distributions for our queueing system and its corresponding standard system.

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Geo m /G/1/n system with LIFO discipline without interrupts and constrained total amount of customers

Cited by 8 publications

References 0 publications

Bulletin of the Polish Academy of Sciences: Technical Sciences

Bulletin of the Polish Academy of Sciences: Technical Sciences

A discrete-time queueing system with three different strategies

A Discrete-Time Retrial Queueing System With Service Upgrade

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