An investigation of an 𝑀^{𝜃}/𝐺/1/𝑚 queueing system with service mode switching

Zhernovyĭ, K.

doi:10.1090/S0094-9000-2013-00889-8

An investigation of an $\text {M}^{\theta }\text {/G/1/m}$ queueing system with service mode switching

Author: K. Yu. Zhernovyĭ
Translated by: N. Semenov
Journal: Theor. Probability and Math. Statist. 86 (2013), 65-78
MSC (2010): Primary 60K25; Secondary 60K20
DOI: https://doi.org/10.1090/S0094-9000-2013-00889-8
Published electronically: August 20, 2013
MathSciNet review: 2986450
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Abstract | References | Similar Articles | Additional Information

Abstract: We consider an $\mathrm {M^{\theta }/G/1/m}$ queueing system with two service modes. The server switches between the modes when the number of customers present at the beginning of service is larger than $h$. Laplace transforms for the distributions of the number of customers in the system during the busy period and for the distribution function of the busy period are found. The average duration of the busy period is obtained. Formulas for the stationary distribution of the number of customers in the system and for the stationary characteristics of the system are established.

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