<abstract xmlns="http://www.w3.org/1999/xhtml"><p> This paper discusses a discrete-time queueing system with starting failures in which an arriving customer follows three different strategies. Two of them correspond to the LCFS (Last Come First Served) discipline, in which displacements or expulsions of customers occur. The third strategy acts as a signal, that is, it becomes a negative customer. Also examined is the possibility of failures at each service commencement epoch. We carry out a thorough study of the model, deriving analytical results for the stationary distribution. We obtain the generating functions of the number of customers in the queue and in the system. The generating functions of the busy period as well as the sojourn times of a customer at the server, in the queue and in the system, are also provided. We present the main performance measures of the model. The versatility of this model allows us to mention several special cases of interest. Finally, we prove the convergence to the continuous-time counterpart and give some numerical results that show the behavior of some performance measures with respect to the most significant parameters of the system</p></abstract>

This paper discusses a discrete-time queueing system with starting failures in which an arriving customer follows three different strategies. Two of them correspond to the LCFS (Last Come First Served) discipline, in which displacements or expulsions of customers occur. The third strategy acts as a signal, that is, it becomes a negative customer. Also examined is the possibility of failures at each service commencement epoch. We carry out a thorough study of the model, deriving analytical results for the stationary distribution. We obtain the generating functions of the number of customers in the queue and in the system. The generating functions of the busy period as well as the sojourn times of a customer at the server, in the queue and in the system, are also provided. We present the main performance measures of the model. The versatility of this model allows us to mention several special cases of interest. Finally, we prove the convergence to the continuous-time counterpart and give some numerical results that show the behavior of some performance measures with respect to the most significant parameters of the system

A discrete-time system with service control and repairs

Department of Applied Mathematics University of Malaga, Campus de Teatinos, 29071 Malaga, Spain

International Journal of Applied Mathematics and Computer Science

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

{"article-title":"A discrete-time system with service control and repairs"}

This paper discusses a discrete-time queueing system with starting failures in which an arriving customer follows three different strategies. Two of them...

A discrete-time system with service control and repairs

Publié en ligne: 25 sept. 2014

Pages: 471 - 484

Reçu: 19 août 2013

DOI: https://doi.org/10.2478/amcs-2014-0035

Mots clés
discrete-time queue, unreliable server, negative customers, busy period, sojourn times, continuous-time counterpart

© by Ivan Atencia

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

A discrete-time system with service control and repairs

Publié en ligne: 25 sept. 2014

Pages: 471 - 484

Reçu: 19 août 2013

DOI: https://doi.org/10.2478/amcs-2014-0035

Mots clésdiscrete-time queue, unreliable server, negative customers, busy period, sojourn times, continuous-time counterpart

© by Ivan Atencia

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

Mots clés
discrete-time queue, unreliable server, negative customers, busy period, sojourn times, continuous-time counterpart