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

<p>In this investigation, we establish a steady-state solution of an infinite-space single-server Markovian queueing system with working vacation (WV), Bernoulli schedule vacation interruption, and impatient customers. Once the system becomes empty, the server leaves the system and takes a vacation with probability p or a working vacation with probability 1 − p, where 0 ≤ p ≤ 1. The working vacation period is interrupted if the system is non empty at a service completion epoch and the server resumes its regular service period with probability 1 − q or carries on with the working vacation with probability q. During vacation and working vacation periods, the customers may be impatient and leave the system. We use a probability generating function technique to obtain the expected number of customers and other system characteristics. Stochastic decomposition of the queueing model is given. Then, a cost function is constructed by considering different cost elements of the system states, in order to determine the optimal values of the service rate during regular busy period, simultaneously, to minimize the total expected cost per unit time by using a quadratic fit search method (QFSM). Further, by taking illustration, numerical experiment is performed to validate the analytical results and to examine the impact of different parameters on the system characteristics.</p>
</abstract>

In this investigation, we establish a steady-state solution of an infinite-space single-server Markovian queueing system with working vacation (WV), Bernoulli schedule vacation interruption, and impatient customers. Once the system becomes empty, the server leaves the system and takes a vacation with probability p or a working vacation with probability 1 − p, where 0 ≤ p ≤ 1. The working vacation period is interrupted if the system is non empty at a service completion epoch and the server resumes its regular service period with probability 1 − q or carries on with the working vacation with probability q. During vacation and working vacation periods, the customers may be impatient and leave the system. We use a probability generating function technique to obtain the expected number of customers and other system characteristics. Stochastic decomposition of the queueing model is given. Then, a cost function is constructed by considering different cost elements of the system states, in order to determine the optimal values of the service rate during regular busy period, simultaneously, to minimize the total expected cost per unit time by using a quadratic fit search method (QFSM). Further, by taking illustration, numerical experiment is performed to validate the analytical results and to examine the impact of different parameters on the system characteristics.

Analysis and optimisation of a M/M/1/WV queue with Bernoulli schedule vacation interruption and customer’s impatience

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 4.0 International License.

In this investigation, we establish a steady-state solution of an infinite-space single-server Markovian queueing system with working vacation (WV), Bernoulli...

Analysis and optimisation of a M/M/1/WV queue with Bernoulli schedule vacation interruption and customer’s impatience

Published Online: Dec 30, 2021

Page range: 367 - 395

DOI: https://doi.org/10.2478/ausm-2021-0023

Keywords
queueing systems, working vacation, vacation interruption, impatient customers, probability generating function, optimization

© 2021 Shakir Majid et al., published by Sciendo

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

Analysis and optimisation of a M/M/1/WV queue with Bernoulli schedule vacation interruption and customer’s impatience

Published Online: Dec 30, 2021

Page range: 367 - 395

DOI: https://doi.org/10.2478/ausm-2021-0023

Keywordsqueueing systems, working vacation, vacation interruption, impatient customers, probability generating function, optimization

© 2021 Shakir Majid et al., published by Sciendo

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

Keywords
queueing systems, working vacation, vacation interruption, impatient customers, probability generating function, optimization