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

作　　者：A. Lorente M. S. Sánchez 

机构地区：[1]Departamento de Matemáticas y Computación, Universidad de Burgos, Escuela Politécnica Superior, Avda. Cantabria s/n, 09006 Burgos, Spain [2]Departamento de Matemáticas y Computación, Universidad de Burgos, Facultad de Ciencias, Pza. Misael Bañ uelos s/n, 09001 Burgos, Spain

出　　处：《Applied Mathematics》2018年第2期153-170,共18页应用数学（英文）

摘　　要：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.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.

关 键 词：DISCRETE-TIME QUEUING System BATCH Arrivals BATCH Services STATIONARY Systems 

分 类 号：O1[理学—数学]