<abstract xmlns="http://www.w3.org/1999/xhtml"><p>This paper concerns the analysis of a Markovian queueing system with Bernoulli feedback, single vacation, waiting server and impatient customers. We suppose that whenever the system is empty the sever waits for a random amount of time before he leaves for a vacation. Moreover, the customer’s impatience timer depends on the states of the server. If the customer’s service has not been completed before the impatience timer expires, the customer leaves the system, and via certain mechanism, impatient customer may be retained in the system. We obtain explicit expressions for the steady-state probabilities of the queueing model, using the probability generating function (PGF). Further, we obtain some important performance measures of the system and formulate a cost model. Finally, an extensive numerical study is illustrated.</p></abstract>

This paper concerns the analysis of a Markovian queueing system with Bernoulli feedback, single vacation, waiting server and impatient customers. We suppose that whenever the system is empty the sever waits for a random amount of time before he leaves for a vacation. Moreover, the customer’s impatience timer depends on the states of the server. If the customer’s service has not been completed before the impatience timer expires, the customer leaves the system, and via certain mechanism, impatient customer may be retained in the system. We obtain explicit expressions for the steady-state probabilities of the queueing model, using the probability generating function (PGF). Further, we obtain some important performance measures of the system and formulate a cost model. Finally, an extensive numerical study is illustrated.

Performance and economic analysis of Markovian Bernoulli feedback queueing system with vacations, waiting server and impatient customers

Djillali Liabes University of Sidi Bel Abbes

Laboratory of Stochastic Models, Statistic and Applications

Acta Universitatis Sapientiae, Mathematica

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

This paper concerns the analysis of a Markovian queueing system with Bernoulli feedback, single vacation, waiting server and impatient customers. We suppose...

Performance and economic analysis of Markovian Bernoulli feedback queueing system with vacations, waiting server and impatient customers

Published Online: Mar 04, 2019

Page range: 218 - 241

Received: Jul 21, 2017

DOI: https://doi.org/10.2478/ausm-2018-0018

Keywords
Markovian queueing models, vacations, impatience, Bernoulli feedback, waiting server, probability generating function, cost model

© 2018 Amina Angelika Bouchentouf et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Performance and economic analysis of Markovian Bernoulli feedback queueing system with vacations, waiting server and impatient customers

Published Online: Mar 04, 2019

Page range: 218 - 241

Received: Jul 21, 2017

DOI: https://doi.org/10.2478/ausm-2018-0018

KeywordsMarkovian queueing models, vacations, impatience, Bernoulli feedback, waiting server, probability generating function, cost model

© 2018 Amina Angelika Bouchentouf et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
Markovian queueing models, vacations, impatience, Bernoulli feedback, waiting server, probability generating function, cost model