Steady state analysis and computation of the GI[x]/Mb/1/L queue with multiple working vacations and partial batch rejection

Authors:
Miao Miao Yu;Ying Hui Tang;Yong Hong Fu
Affiliations:
Department of Mathematics, Sichuan University of Science and Engineering, Zigong 643000, PR China;School of Mathematics & Software Science, Sichuan Normal University, Chengdu 610066, PR China;Department of Computer science, Sichuan University of Science and Engineering, Zigong 643000, PR China
Venue:
Computers and Industrial Engineering
Year:
2009

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Abstract

This paper analyzes a finite-buffer bulk-arrival bulk-service queueing system with multiple working vacations and partial batch rejection in which the inter-arrival and service times are, respectively, arbitrarily and exponentially distributed. Using the supplementary variable and the embedded Markov chain techniques, we obtain the waiting queue-length distributions at pre-arrival and arbitrary epochs. We also present Laplace-Stiltjes transform of the actual waiting-time distribution in the queue. Finally, several performance measures and a variety of numerical results in the form of tables and graphs are discussed.