Wyniki wyszukiwania - BazTech

1

On applications of computer algebra systems in queueing theory calculations

Ziółkowski Marcin

Bulletin of the Polish Academy of Sciences. Technical Sciences

|

2024

|

Vol. 72, nr 4

art. no. e150199

EN

In the present paper, the most important aspects of computer algebra systems applications in complicated calculations for classical queueing theory models and their novel modifications are discussed. We mainly present huge computational possibilities of Mathematica environment and effective methods of obtaining symbolic results connected with the most important performance characteristics of queueing systems. First of all, we investigate effective solutions to computational problems appearing in queueing theory such as: finding final probabilities for Markov chains with a huge number of states, calculating derivatives of complicated rational functions of one or many variables with the use of classical and generalized L’Hospital’s rules, obtaining exact formulae of Stieltjes convolutions, calculating chosen integral transforms used often in the above-mentioned theory and possible applications of generalized density function of random variables and vectors in these computations. Some exemplary calculations for practical models belonging both to classical models and their generalizations are attached as well.

2

Multi–server loss queueing system with random volume customers, non–identical servers and a limited sectorized memory buffer

Ziółkowski Marcin

Bulletin of the Polish Academy of Sciences. Technical Sciences

|

2023

|

Vol. 71, nr 5

art. no. e146764

EN

In the present paper, the model of multi–server queueing system with random volume customers, non–identical (heterogeneous) servers and a sectorized memory buffer has been investigated. In such system, the arriving customers deliver some portions of information of a different type which means that they are additionally characterized by some random volume vector. This multidimensional information is stored in some specific sectors of a limited memory buffer until customer ends his service. In analyzed model, the arrival flow is assumed to be Poissonian, customers’ service times are independent of their volume vectors and exponentially distributed but the service parameters may be different for every server. Obtained results include general formulae for the steady–state number of customers distribution and loss probability. Special cases analysis and some numerical computations are attached as well.

3

M/G/n/(0, V) Erlang queueing system with non-homogeneous customers, non-identical servers and limited memory space

Tikhonenko O., Ziółkowski M., Kurkowski M.

Bulletin of the Polish Academy of Sciences. Technical Sciences

|

2019

|

Vol. 67, nr 3

489--500

EN

In the present paper, we investigate a?multi-server Erlang queueing system with heterogeneous servers, non-homogeneous customers and limited memory space. The arriving customers appear according to a?stationary Poisson process and are additionally characterized by some random volume. The service time of the customer depends on his volume and the joint distribution function of the customer volume and his service time can be different for different servers. The total customers volume is limited by some constant value. For the analyzed model, steady-state distribution of number of customers present in the system and loss probability are calculated. An analysis of some special cases and some numerical examples are attached as well.

4

Multiline queueing system with random time limitations and limited buffer space

Tikhonenko O., Zając P.

Journal of Applied Mathematics and Computational Mechanics

|

2018

|

Vol. 17, nr 4

99--106

EN

In the paper, we investigate multi-server queueing systems with demands of random space requirements (volumes), in which buffer space is limited by constant value and queueing ore (and) service time are limited by exponentially distributed random variables. For such systems, stationary demands number distribution and loss probability are determined. Some numerical results are attached as well.

5

Multi-server closed queueing system with limited buffer space

Tikhonenko A., Tikhonenko-Kędziak A.

Journal of Applied Mathematics and Computational Mechanics

|

2017

|

Vol. 16, nr 1

117--125

EN

In the paper, we investigate multi-server closed queueing systems with identical servers and a finite number of terminals. Requests from each terminal are characterized by a random space requirement (volume), the request service time doesn’t depend on its volume and has an exponential distribution. The total requests capacity in the system is limited by a positive value (buffer space memory volume) V. For such systems, stationary requests number distribution and loss probability are determined. The analogous results for open multi-server systems are obtained as a limit case. Some numerical results are attached as well.