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A Heuristic Derivation of the Waiting Time Distribution of a GI/G/1 Queue
Dae Eun Lim(임대은),Bokeun Kim(김보근),Nam K. Kim(김남기),Kyung C. Chae(채경철) 한국경영과학회 2015 한국경영과학회지 Vol.40 No.1
This paper presents a heuristic approach to derive the Laplace-Stieltjes transform (LST) and the probability generating function (PGF) of the waiting time distributions of a continuous- and a discrete-time GI/G/1 queue, respectively. This is a new idea to derive the well-known results, the waiting time distribution of GI/G/1 queue, in a different way.
A Modified Supplementary Variable Technique Applied to the GI/G/1/K Queue
Kim, Nam K.,Chae, Kyung C. 한국경영과학회 2001 한국경영과학회 학술대회논문집 Vol.- No.1(1)
In this paper, we introduce an unconventional approach of using the supplementary variable technique. We use the GI/G/1/K queue as an example queueing system to which we apply this approach. As a result, we obtain transform-free expressions for the steady-state queue-length distributions at arrival, departure, and arbitrary times. We also discuss how to utilize these expressions.