# Semi-Markov-based approach for the analysis of open tandem networks with blocking and truncation

• Volume: 19, Issue: 1, page 151-163
• ISSN: 1641-876X

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## Abstract

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This paper describes an analytical study of open two-node (tandem) network models with blocking and truncation. The study is based on semi-Markov process theory, and network models assume that multiple servers serve each queue. Tasks arrive at the tandem in a Poisson fashion at the rate λ, and the service times at the first and the second node are nonexponentially distributed with means sA and sB , respectively. Both nodes have buffers with finite capacities. In this type of network, if the second buffer is full, the accumulation of new tasks by the second node is temporarily suspended (a blocking factor) and tasks must wait on the first node until the transmission process is resumed. All new tasks that find the first buffer full are turned away and are lost (a truncation factor). First, a Markov model of the tandem is investigated. Here, a twodimensional state graph is constructed and a set of steady-state equations is created. These equations allow calculating state probabilities for each graph state. A special algorithm for transforming the Markov model into a semi-Markov process is presented. This approach allows calculating steady-state probabilities in the semi-Markov model. Next, the algorithms for calculating the main measures of effectiveness in the semi-Markov model are presented. In the numerical part of this paper, the author investigates examples of several semi-Markov models. Finally, the results of calculating both the main measures of effectiveness and quality of service (QoS) parameters are presented.

## How to cite

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Walenty Oniszczuk. "Semi-Markov-based approach for the analysis of open tandem networks with blocking and truncation." International Journal of Applied Mathematics and Computer Science 19.1 (2009): 151-163. <http://eudml.org/doc/207916>.

@article{WalentyOniszczuk2009,
abstract = {This paper describes an analytical study of open two-node (tandem) network models with blocking and truncation. The study is based on semi-Markov process theory, and network models assume that multiple servers serve each queue. Tasks arrive at the tandem in a Poisson fashion at the rate λ, and the service times at the first and the second node are nonexponentially distributed with means sA and sB , respectively. Both nodes have buffers with finite capacities. In this type of network, if the second buffer is full, the accumulation of new tasks by the second node is temporarily suspended (a blocking factor) and tasks must wait on the first node until the transmission process is resumed. All new tasks that find the first buffer full are turned away and are lost (a truncation factor). First, a Markov model of the tandem is investigated. Here, a twodimensional state graph is constructed and a set of steady-state equations is created. These equations allow calculating state probabilities for each graph state. A special algorithm for transforming the Markov model into a semi-Markov process is presented. This approach allows calculating steady-state probabilities in the semi-Markov model. Next, the algorithms for calculating the main measures of effectiveness in the semi-Markov model are presented. In the numerical part of this paper, the author investigates examples of several semi-Markov models. Finally, the results of calculating both the main measures of effectiveness and quality of service (QoS) parameters are presented.},
author = {Walenty Oniszczuk},
journal = {International Journal of Applied Mathematics and Computer Science},
keywords = {two-node network with blocking and truncation; semi-Markov model; Markov exact algorithm},
language = {eng},
number = {1},
pages = {151-163},
title = {Semi-Markov-based approach for the analysis of open tandem networks with blocking and truncation},
url = {http://eudml.org/doc/207916},
volume = {19},
year = {2009},
}

TY - JOUR
AU - Walenty Oniszczuk
TI - Semi-Markov-based approach for the analysis of open tandem networks with blocking and truncation
JO - International Journal of Applied Mathematics and Computer Science
PY - 2009
VL - 19
IS - 1
SP - 151
EP - 163
AB - This paper describes an analytical study of open two-node (tandem) network models with blocking and truncation. The study is based on semi-Markov process theory, and network models assume that multiple servers serve each queue. Tasks arrive at the tandem in a Poisson fashion at the rate λ, and the service times at the first and the second node are nonexponentially distributed with means sA and sB , respectively. Both nodes have buffers with finite capacities. In this type of network, if the second buffer is full, the accumulation of new tasks by the second node is temporarily suspended (a blocking factor) and tasks must wait on the first node until the transmission process is resumed. All new tasks that find the first buffer full are turned away and are lost (a truncation factor). First, a Markov model of the tandem is investigated. Here, a twodimensional state graph is constructed and a set of steady-state equations is created. These equations allow calculating state probabilities for each graph state. A special algorithm for transforming the Markov model into a semi-Markov process is presented. This approach allows calculating steady-state probabilities in the semi-Markov model. Next, the algorithms for calculating the main measures of effectiveness in the semi-Markov model are presented. In the numerical part of this paper, the author investigates examples of several semi-Markov models. Finally, the results of calculating both the main measures of effectiveness and quality of service (QoS) parameters are presented.
LA - eng
KW - two-node network with blocking and truncation; semi-Markov model; Markov exact algorithm
UR - http://eudml.org/doc/207916
ER -

## References

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