Cost Optimization in Sintering Process on the Basis of Bulk Queueing System with Diverse Services Modes and Vacation

Subramani Palani Niranjan, Suthanthira Raj Devi Latha () and Sorin Vlase ()
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Subramani Palani Niranjan: Department of Mathematics, Vel Tech Rangarajan Dr. Sagunthala R&D Institute of Science and Technology, Chennai 600062, India
Suthanthira Raj Devi Latha: Department of Mathematics, Vel Tech Rangarajan Dr. Sagunthala R&D Institute of Science and Technology, Chennai 600062, India
Sorin Vlase: Department of Mechanical Engineering, Transilvania University of Brasov, Romania, B-dul Eroilor, 29, 500036 Brașov, Romania

Mathematics, 2024, vol. 12, issue 22, 1-19

Abstract: This research investigated a single bulk server queuing model where service modes and server vacations are dependent on the number of clients. The server operates in three different service modes: single service, fixed batch service, and variable batch service. Modes will be determined by queue length. The service starts only when the minimum number of customers, say ‘ a ’, has accumulated in the queue. At this point, the server selects one of three service modes. Transitions between duty modes are permitted only at the beginning of a duty period. At the end of the service, the server can go on vacation if the queue length drops below ‘ a ’. When returning from vacation, if threshold ‘ a ’ is not reached, the server will remain inactive until it is reached. A special technique called the Supplementary Variables Technique (SVT) was used to determine the probability-generating function when estimating the queue size at a given time. Appropriate numerical examples exemplify the method developed in the paper. An optimal cost analysis was performed to set the threshold values for different server modes with the intention of minimizing the aggregate average cost.

Keywords: bulk arrival; dormant period; fixed batch service; varying batch service; vacation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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