<abstract xmlns="http://www.w3.org/1999/xhtml"><p> A single-server queueing system with a marked Markovian arrival process of heterogeneous customers is considered. Type-1 customers have limited preemptive priority over type-2 customers. There is an infinite buffer for type-2 customers and no buffer for type-1 customers. There is also a finite buffer (stock) for consumable additional items (semi-products, half-stocks, etc.) which arrive according to the Markovian arrival process. Service of a customer requires a fixed number of consumable additional items depending on the type of the customer. The service time has a phase-type distribution depending on the type of the customer. Customers in the buffer are impatient and may leave the system without service after an exponentially distributed amount of waiting time. Aiming to minimize the loss probability of type-1 customers and maximize throughput of the system, a threshold strategy of admission to service of type-2 customers is offered. Service of type-2 customer can start only if the server is idle and the number of consumable additional items in the stock exceeds the fixed threshold. Stationary distributions of the system states and the waiting time are computed. In the numerical example, we show some interesting effects and illustrate a possibility of application of the presented results for solution of optimization problems.</p></abstract>

A single-server queueing system with a marked Markovian arrival process of heterogeneous customers is considered. Type-1 customers have limited preemptive priority over type-2 customers. There is an infinite buffer for type-2 customers and no buffer for type-1 customers. There is also a finite buffer (stock) for consumable additional items (semi-products, half-stocks, etc.) which arrive according to the Markovian arrival process. Service of a customer requires a fixed number of consumable additional items depending on the type of the customer. The service time has a phase-type distribution depending on the type of the customer. Customers in the buffer are impatient and may leave the system without service after an exponentially distributed amount of waiting time. Aiming to minimize the loss probability of type-1 customers and maximize throughput of the system, a threshold strategy of admission to service of type-2 customers is offered. Service of type-2 customer can start only if the server is idle and the number of consumable additional items in the stock exceeds the fixed threshold. Stationary distributions of the system states and the waiting time are computed. In the numerical example, we show some interesting effects and illustrate a possibility of application of the presented results for solution of optimization problems.

A Queueing System with Heterogeneous Impatient Customers and Consumable Additional Items

International Journal of Applied Mathematics and Computer Science

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

A single-server queueing system with a marked Markovian arrival process of heterogeneous customers is considered. Type-1 customers have limited preemptive...

A Queueing System with Heterogeneous Impatient Customers and Consumable Additional Items

Published Online: Jul 08, 2017

Page range: 367 - 384

Received: Sep 07, 2016

Accepted: Jan 31, 2017

DOI: https://doi.org/10.1515/amcs-2017-0026

Keywords
marked Markovian arrival process, consumable additional items, phase-type distribution, impatient customers

© by Chesoong Kim

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

A Queueing System with Heterogeneous Impatient Customers and Consumable Additional Items

Published Online: Jul 08, 2017

Page range: 367 - 384

Received: Sep 07, 2016

Accepted: Jan 31, 2017

DOI: https://doi.org/10.1515/amcs-2017-0026

Keywordsmarked Markovian arrival process, consumable additional items, phase-type distribution, impatient customers

© by Chesoong Kim

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

Keywords
marked Markovian arrival process, consumable additional items, phase-type distribution, impatient customers