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A better numerical approach for finding the steady-state waiting time and the average queue length of a system for the arithmetic GI/G/1 queue

University of British Columbia

In this research, an efficient numerical method is developed to determine the steady-state waiting time distribution of a GI/G/1 queue by solving the discrete-time version of Lindley’s equation, when the queue is bounded on a finite interval. Then, by using Little’s Formula, we calculate the stationary distribution for the total number of customers in the queue. The derivations are based on the Wiener-Hopf factorization of random walks. The method is carried out using a successive approximation method, by improving the weighted average. Finally, to prove the effectiveness of our method, we apply the algorithm for Uniform, Geometric, and Gamma distributions, to find an approximation. An analytical interpretation is also presented to find the waiting time distribution for the Geom/Geom/1 queue, which is not based on a finite interval, as an example of the GI/G/1 queue. Moreover, compare to the other related methods it has been proven that our method is numerically stable, simple, and robust.

Text

2011-12-19

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/39784

Mathematics

University of British Columbia

UBCO

http://creativecommons.org/licenses/by-nc-nd/4.0/