Exact Time-Dependent Queue-Length Solution to a Discrete-Time Geo / D /1 Queue

Jung Woo Baek and Yun Han Bae
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Jung Woo Baek: Department of Industrial Engineering, Chosun University, Gwangju 61452, Korea
Yun Han Bae: Department of Mathematics Education, Sangmyung University, Seoul 03016, Korea

Mathematics, 2019, vol. 7, issue 8, 1-8

Abstract: Time-dependent solutions to queuing models are beneficial for evaluating the performance of real-world systems such as communication, transportation, and service systems. However, restricted results have been reported due to mathematical complexity. In this study, we present a time-dependent queue-length formula for a discrete-time G e o / D / 1 queue starting with a positive number of initial customers. We derive the time-dependent formula in closed form.

Keywords: time-dependent queue-length probability; discrete-time Geo / D /1 queue; closed-form solution (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
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