RT info:eu-repo/semantics/article
T1 Effect of parameters on Geoa/Geob/1 Queues: theoretical analysis and simulation results
A1 Lorente Marín, Ana
A1 Sánchez Pastor, Mª Sagrario
K1 Discrete-Time Queuing System
K1 Batch Arrivals
K1 Batch Services
K1 Stationary Systems
K1 Matemáticas
K1 Mathematics
AB This paper analyzes a discrete-time Geoa/Geob/1 queuing system with batcharrivals of fixed size a , and batch services of fixed size b. Both arrivals and servicesoccur randomly following a geometric distribution. The steady-statequeue length distribution is obtained as the solution of a system of differenceequations. Necessary and sufficient conditions are given for the system to bestationary. Besides, the uniqueness of the root of the characteristic polynomialin the interval (0, 1) is proven which is the only root needed for the computationof the theoretical solution with the proposed procedure. The theoreticalresults are compared with the ones observed in some simulations of thequeuing system under different sets of parameters. The agreement of the resultsencourages the use of simulation for more complex systems. Finally, weexplore the effect of parameters on the mean length of the queue as well as onthe mean waiting time.
PB Scientific Research
SN 2152-7385
YR 2018
FD 2018-02
LK http://hdl.handle.net/10259/4751
UL http://hdl.handle.net/10259/4751
LA eng
DS Repositorio Institucional de la Universidad de Burgos
RD 24-abr-2024