Effect of Parameters on Geoa/Geob/1 Queues: Theoretical Analysis and Simulation Results

Autor:	M. S. Sánchez, A. Lorente
Rok vydání:	2018
Předmět:	Discrete-Time Queuing System Queue management system Matemáticas Batch Services Computation Complex system General Medicine Interval (mathematics) Geometric distribution Stationary Systems Applied mathematics Batch Arrivals Uniqueness Queue Mathematics Characteristic polynomial
Zdroj:	Repositorio Institucional de la Universidad de Burgos (RIUBU) instname
ISSN:	2152-7393 2152-7385
Popis:	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.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_dedup___::fb0e9288d94146f98d85d8baf910b635 https://doi.org/10.4236/am.2018.92011 Zobrazit plný text záznamu