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oai:riubu.ubu.es:10259/47512021-11-10T09:38:24Zcom_10259_4535com_10259_5086com_10259_2604com_10259_4249col_10259_4536col_10259_4250

Lorente Marín, Ana Sánchez Pastor, Mª Sagrario Discrete-Time Queuing System Batch Arrivals Batch Services Stationary Systems 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. 2018-03-19 2018-03-19 2018-02 info:eu-repo/semantics/article 2152-7385 http://hdl.handle.net/10259/4751 10.4236/am.2018.92011 eng Applied Mathematics. 2018, V. 9, n. 2, p. 153-170 http://dx.doi.org/10.4236/am.2018.92011 http://creativecommons.org/licenses/by/4.0/ info:eu-repo/semantics/openAccess Attribution 4.0 International Scientific Research