Abstract
The performance analysis of the classical M / G / 1 queue, under a general mixed joining/balking strategy was carried out recently by Kerner (Stoch Mod 24:364–375, 2008), who used an analytic approach based on the supplementary variable method. The tractability of the corresponding queueing system with state-dependent arrival rates is particularly significant, as it has important applications in situations where the customers are strategic. In this paper, we present an alternative path for the analysis of the same system, using purely probabilistic arguments.
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Acknowledgments
We would like to mention the inspiring papers of Kerner (2008), Abouee-Mehrizi et al. (2012) and the relevant talks of B. Balcioglu, O. Baron and Y. Kerner at the 1st European Conference on Queueing Theory, Ghent, Belgium, 20–22 August 2014. These works underlined the significance and the applications of the study of the \(M_n/G/1\) queue and constitute the main inspiration of the present work. This research has been financed by the European Union (European Social Fund—ESF) and Greek national funds through the Operational Program “Education and Lifelong Learning” of the National Strategic Reference Framework (NSRF)-Research Funding Program: Thalis-Athens University of Economics and Business-New Methods in the Analysis of Market Competition: Oligopoly, Networks and Regulation.
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Economou, A., Manou, A. A probabilistic approach for the analysis of the \(M_n/G/1\) queue. Ann Oper Res 317, 19–27 (2022). https://doi.org/10.1007/s10479-015-1943-0
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DOI: https://doi.org/10.1007/s10479-015-1943-0