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Título : Effect of parameters on Geoa/Geob/1 Queues: theoretical analysis and simulation results
Autor : Lorente Marín, Ana
Sánchez Pastor, Mª Sagrario
Publicado en: Applied Mathematics. 2018, V. 9, n. 2, p. 153-170
Editorial : Scientific Research
Fecha de publicación : feb-2018
ISSN : 2152-7385
DOI: 10.4236/am.2018.92011
Resumen : This paper analyzes a discrete-time Geoa/Geob/1 queuing system with batch arrivals of fixed size a , and batch services of fixed size b. Both arrivals and services occur randomly following a geometric distribution. The steady-state queue length distribution is obtained as the solution of a system of difference equations. Necessary and sufficient conditions are given for the system to be stationary. Besides, the uniqueness of the root of the characteristic polynomial in the interval (0, 1) is proven which is the only root needed for the computation of the theoretical solution with the proposed procedure. The theoretical results are compared with the ones observed in some simulations of the queuing system under different sets of parameters. The agreement of the results encourages the use of simulation for more complex systems. Finally, we explore the effect of parameters on the mean length of the queue as well as on the mean waiting time.
Palabras clave: Discrete-Time Queuing System
Batch Arrivals
Batch Services
Stationary Systems
Materia: Matemáticas
Mathematics
Licencia: https://creativecommons.org/licenses/by/4.0/
URI : http://hdl.handle.net/10259/4751
Versión del editor: http://dx.doi.org/10.4236/am.2018.92011
Aparece en las colecciones: Artículos Q&C
Artículos GMAMMI

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