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A discrete-time single-server queue with balking: economic applications

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Lozano, Macarena; Moreno, Pilar

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Abstract This paper studies a discrete-time single-server queue with finite and infinite buffer where the users have the option to leave the queue upon arrival (balking). We consider two variants of the model in accordance with the balking policies. Firstly, all the arriving customers balk with a constant probability. Secondly, arriving customers increase their balking probabilities as more customers join the system. Specifically, we find the ergodicity condition and closed form expressions for the stationary distribution of the system size, of the waiting/spending time in the FCFS system and of the unfinished work. The mathematical model is applied in order to resolve several real-life problems in the economic field; in this sense, practical applications in the secondary and tertiary sector are shown. We also develop a cost model to determine the buffer capacity that minimizes certain cost function and give some numerical examples.
Classification Economic Statistics, Econometrics, Business Informatics
Free Keywords Balking; Discrete-time queue; Ergodicity; Markov chain; Optimal control; Practical applications; Unfinished work; Waiting/ spending time; C60; C69; C65
Document language English
Publication Year 2008
Page/Pages p. 735-748
Journal Applied Economics, 40 (2008) 6
Status Postprint; peer reviewed
Licence PEER Licence Agreement (applicable only to documents from PEER project)