D. Anandakumar, S. Palaniammal and N. Nagaveni.
The Analysis of M|M^(A,B)|1 on Unobservable and Partially Observable Waiting Line With Repeated Vacations
Dynamic Systems and Applications 30 (2021) No. 9, 1503 – 1518

https://doi.org/10.46719/dsa202130.09.07

ABSTRACT.
The General Bulk Service Rule (GBSR) is implemented on M|M^(a,b)|1 for the ardent customers. The model is designed for the system with single server and repeated vacations. The high priority batch is contributed with better service and the First Come First Served (FCFS) queuing manner is applied to the batches. The server begins to serve when ‘a’ customers are available in the queue and after completing the service if the server identifies at most ‘b’ customers in the queue then server takes all the customers and put them in a batch and when the server discovers more than b customers in the waiting line, the server will provide the service for the first ‘b’ customers in a batch and rest of the customers are put in the waiting line. The customers get in the queue in the poison fashion and service time of every batch area is presumed to be distributed exponentially with respect to mean dependent batch area and customers may eschew or break if the waiting line of the customers are tend to be very large. In this method, server can take vacation when less than ‘a’ customers are present in the queue. The diverse performance metrics on effectiveness are examined and the model is inspected based on eschewing and breaking probability.

Keywords: General bulk service, First Come First Serve, eschew and break, repeated vacation, poison process, and performance metrics