Transient Solution of M [X]/G/1 Queue system with Balking and Re service

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S Shyamala, R Vijayaraj

Abstract

batch arrival non-Markovian queue system in where consumers arrival
are batches in accordance with Poisson process and customer are treated by first-comefirst-
served principle. When a customer’s service is completed, he or she has the
choice of requesting reservice for the same service or exiting the mode. Each
customer’s service duration follows a genaral (arbitrary) distribution. In addition, after
completing service, server takes vacation by having probability p or may be remain
with probability 1−p, if any, to serve a subsequent customer. One of the impatient
customers behavior balking, has also been added, indicating that a consumer can
choose whether or not to enter the system. Also, we suppose after every period the
server could not begin to providing service immediately, but rather requires some
startup time before giving service to the first consumer. After discussion of transiant
steady state system we can obtain closed-form system performance measurements

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