<abstract xmlns="http://www.w3.org/1999/xhtml"><p>A novel customer batch service discipline for a single server queue is introduced and analyzed. Service to customers is offered in batches of a certain size. If the number of customers in the system at the service completion moment is less than this size, the server does not start the next service until the number of customers in the system reaches this size or a random limitation of the idle time of the server expires, whichever occurs first. Customers arrive according to a Markovian arrival process. An individual customer’s service time has a phase-type distribution. The service time of a batch is defined as the maximum of the individual service times of the customers which form the batch. The dynamics of such a system are described by a multi-dimensional Markov chain. An ergodicity condition for this Markov chain is derived, a stationary probability distribution of the states is computed, and formulas for the main performance measures of the system are provided. The Laplace–Stieltjes transform of the waiting time is obtained. Results are numerically illustrated.</p></abstract>

A novel customer batch service discipline for a single server queue is introduced and analyzed. Service to customers is offered in batches of a certain size. If the number of customers in the system at the service completion moment is less than this size, the server does not start the next service until the number of customers in the system reaches this size or a random limitation of the idle time of the server expires, whichever occurs first. Customers arrive according to a Markovian arrival process. An individual customer’s service time has a phase-type distribution. The service time of a batch is defined as the maximum of the individual service times of the customers which form the batch. The dynamics of such a system are described by a multi-dimensional Markov chain. An ergodicity condition for this Markov chain is derived, a stationary probability distribution of the states is computed, and formulas for the main performance measures of the system are provided. The Laplace–Stieltjes transform of the waiting time is obtained. Results are numerically illustrated.

Analysis of an MAP/PH/1 Queue with Flexible Group Service

International Journal of Applied Mathematics and Computer Science

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

{"article-title":"Analysis of an MAP/PH/1 Queue with Flexible Group Service"}

A novel customer batch service discipline for a single server queue is introduced and analyzed. Service to customers is offered in batches of a certain size....

Analysis of an MAP/PH/1 Queue with Flexible Group Service

Publié en ligne: 04 mai 2017

Pages: 119 - 131

Reçu: 19 juil. 2016

Accepté: 09 nov. 2016

DOI: https://doi.org/10.1515/amcs-2017-0009

Mots clés
queueing system, batch service, multi-rate service, stationary distribution, optimization

© by Rosanna Manzo

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

Analysis of an MAP/PH/1 Queue with Flexible Group Service

Publié en ligne: 04 mai 2017

Pages: 119 - 131

Reçu: 19 juil. 2016

Accepté: 09 nov. 2016

DOI: https://doi.org/10.1515/amcs-2017-0009

Mots clésqueueing system, batch service, multi-rate service, stationary distribution, optimization

© by Rosanna Manzo

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

Mots clés
queueing system, batch service, multi-rate service, stationary distribution, optimization