<abstract xmlns="http://www.w3.org/1999/xhtml"><p> We consider the discrete-time G/GI/1 queueing system with multiple exhaustive vacations. By a transform approach, we obtain an expression for the probability generating function of the waiting time of customers in such a system. We then show that the results can be used to assess the performance of G/GI/1 queueing systems with server breakdowns as well as that of the low-priority queue of a preemptive M<sup>X</sup>+G/GI/1 priority queueing system. By calculating service completion times of low-priority customers, various preemptive breakdown/priority disciplines can be studied, including preemptive resume and preemptive repeat, as well as their combinations. We illustrate our approach with some numerical examples.</p></abstract>

We consider the discrete-time G/GI/1 queueing system with multiple exhaustive vacations. By a transform approach, we obtain an expression for the probability generating function of the waiting time of customers in such a system. We then show that the results can be used to assess the performance of G/GI/1 queueing systems with server breakdowns as well as that of the low-priority queue of a preemptive MX+G/GI/1 priority queueing system. By calculating service completion times of low-priority customers, various preemptive breakdown/priority disciplines can be studied, including preemptive resume and preemptive repeat, as well as their combinations. We illustrate our approach with some numerical examples.

From Exhaustive Vacation Queues to Preemptive Priority Queues with General Interarrival Times

International Journal of Applied Mathematics and Computer Science

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

We consider the discrete-time G/GI/1 queueing system with multiple exhaustive vacations. By a transform approach, we obtain an expression for the probability...

From Exhaustive Vacation Queues to Preemptive Priority Queues with General Interarrival Times

Published Online: Jan 11, 2019

Page range: 695 - 704

Received: Jan 23, 2018

Accepted: Jun 20, 2018

DOI: https://doi.org/10.2478/amcs-2018-0053

Keywords
queueing system, preemptive priority, server interruption, server breakdown, exhaustive vacations

© 2019 Dieter Fiems, Stijn De Vuyst, published by Sciendo

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

From Exhaustive Vacation Queues to Preemptive Priority Queues with General Interarrival Times

Published Online: Jan 11, 2019

Page range: 695 - 704

Received: Jan 23, 2018

Accepted: Jun 20, 2018

DOI: https://doi.org/10.2478/amcs-2018-0053

Keywordsqueueing system, preemptive priority, server interruption, server breakdown, exhaustive vacations

© 2019 Dieter Fiems, Stijn De Vuyst, published by Sciendo

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

Keywords
queueing system, preemptive priority, server interruption, server breakdown, exhaustive vacations