Volume 55, Number 5, September-October 2021
|Page(s)||2807 - 2825|
|Published online||20 September 2021|
Equilibrium analysis of cloud user request based on the Markov queue with variable vacation and vacation interruption
School of Economics and Management, Yanshan University, Hebei Qinhuangdao 066004, P.R. China
2 School of Science, Yanshan University, Hebei Qinhuangdao 066004, P.R. China
* Corresponding author: firstname.lastname@example.org
Accepted: 14 August 2021
This paper considers the equilibrium balking behavior of customers in a single-server Markovian queue with variable vacation and vacation interruption, where the server can switch across four states: vacation, working vacation, idle period, and busy period. Once the queue becomes empty, the server commences a working vacation and slows down its service rate. However, this period may be interrupted anytime by the vacation interruption. Upon the completion of a working vacation, the server takes a vacation in a probability-based manner and stops service if the system is empty. The system stays idle after a vacation until a new customer arrives. The comparisons between the equilibrium balking strategy of customers and the optimal expected social benefit per time unit for each type of queue are elucidated and the inconsistency between the individual optimization and the social optimization is revealed. Moreover, the sensitivity of the expected social benefit and the equilibrium threshold with respect to the several parameters as well as diverse precision levels is illustrated through numerical examples in a competitive cloud environment.
Mathematics Subject Classification: 60K25 / 90B22
Key words: Variable vacation / vacation interruption / equilibrium strategy / the expected social benefit
© The authors. Published by EDP Sciences, ROADEF, SMAI 2021
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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