<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>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.</p>
</abstract>

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.

Queueing Systems with Random Volume Customers and a Sectorized Unlimited Memory Buffer

Cardinal Stefan Wyszyński University in Warsaw

Warsaw University of Life Sciences (SGGW)

Department of Mathematics Applications and Methods for Artificial Intelligence

International Journal of Applied Mathematics and Computer Science

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

In the present paper, we concentrate on basic concepts connected with the theory of queueing systems with random volume customers and a sectorized unlimited...

Queueing Systems with Random Volume Customers and a Sectorized Unlimited Memory Buffer

Data publikacji: 27 wrz 2021

Zakres stron: 471 - 486

Otrzymano: 17 mar 2021

Przyjęty: 16 lip 2021

DOI: https://doi.org/10.34768/amcs-2021-0032

Słowa kluczowe
queueing systems with random volume customers, sectorized memory buffer, total volume vector, Laplace and Laplace–Stieltjes transforms, multi-variate L’Hospital rule

© 2021 Oleg Tikhonenko et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Queueing Systems with Random Volume Customers and a Sectorized Unlimited Memory Buffer

Data publikacji: 27 wrz 2021

Zakres stron: 471 - 486

Otrzymano: 17 mar 2021

Przyjęty: 16 lip 2021

DOI: https://doi.org/10.34768/amcs-2021-0032

Słowa kluczowequeueing systems with random volume customers, sectorized memory buffer, total volume vector, Laplace and Laplace–Stieltjes transforms, multi-variate L’Hospital rule

© 2021 Oleg Tikhonenko et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Słowa kluczowe
queueing systems with random volume customers, sectorized memory buffer, total volume vector, Laplace and Laplace–Stieltjes transforms, multi-variate L’Hospital rule