Statistical mechanics approach for steady-state analysis in M/M/s queueing system with balking

Abstract

<p style='text-indent:20px;'>Behavior that a customer who has just arrived at a crowded queueing system leaves without joining the queue is known as the phenomenon of balking. Queueing systems with balking have been studied continually as one of significant subjects. In this paper, the theoretical approach for the steady-state analysis of the Markovian queueing systems with balking is considered based on the concept of the statistical mechanics. Here, it can be easily seen that the strength of balking is not constant but various in each queueing systems. Note that the strength of balking means how degree a customer who has just arrived at a crowded queueing system leaves without joining the queue. In our approach, under considering the difference of the strength of balking for each queueing systems, we have proposed a statistical mechanics model for analyzing the M/M/<inline-formula><tex-math id="M1">\begin{document}$ s $\end{document}</tex-math></inline-formula> queueing system with balking by introducing a parameter influencing the strength of balking. Further, we define a procedure for estimating the model parameter influencing the strength of balking. In addition, we consider a method of improving the performance of the M/M/<inline-formula><tex-math id="M2">\begin{document}$ s $\end{document}</tex-math></inline-formula> queueing system with balking by utilizing the statistical mechanics approach.</p>