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http://dx.doi.org/10.7737/JKORMS.2014.39.3.001

A Note on the M/G/1/K Queue with Two-Threshold Hysteresis Strategy of Service Intensity Switching  

Choi, Doo Il (Division of Liberal arts and Teaching, Halla University)
Kim, Bo Keun (Samsung SDS)
Lee, Doo Ho (SW.Content Research Laboratory, ETRI)
Publication Information
Journal of the Korean Operations Research and Management Science Society / v.39, no.3, 2014 , pp. 1-5 More about this Journal
Abstract
We study the paper Zhernovyi and Zhernovyi [Zhernovyi, K.Y. and Y.V. Zhernovyi, "An $M^{\Theta}/G/1/m$ system with two-threshold hysteresis strategy of service intensity switching," Journal of Communications and Electronics, Vol.12, No.2(2012), pp.127-140]. In the paper, authors used the Korolyuk potential method to obtain the stationary queue length distribution. Instead, our note makes an attempt to apply the most frequently used methods : the embedded Markov chain and the supplementary variable method. We derive the queue length distribution at a customer's departure epoch and then at an arbitrary epoch.
Keywords
M/G/1/K Queue; Queue Length Dependent Service Rate; Thresholds; Finite Buffer;
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1 Zhernovyi, K.Y. and Y.V. Zhernovyi, "An M $\theta$/G/1/m system with two-threshold hysteresis strategy of service intensity switching," Journal of Communications and Electronics, Vol.12, No.2(2012), pp.127-140.
2 Choi, D.I., T.S. Kim, and S. Lee, "Analysis of a queueing system with a general service scheduling function, with applications to telecommunication network traffic control," European Journal of Operational Research, Vol.178, No.2(2007), pp.463-471.   DOI