Transient Solution of M [X]/G/1 Queue system with Balking and Re service (Turkish Journal of Computer and Mathematics Education (TURCOMAT), 2021)
batch arrival non-Markovian queue system in where consumers arrivalare 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 thechoice of requesting reservice for the same service or exiting the mode. Eachcustomer’s service duration follows a genaral (arbitrary) distribution. In addition, aftercompleting service, server takes vacation by having probability p or may be remainwith probability 1−p, if any, to serve a subsequent customer. One of the impatientcustomers behavior balking, has also been added, indicating that a consumer canchoose whether or not to enter the system. Also, we suppose after every period theserver could not begin to providing service immediately, but rather requires somestartup time before giving service to the first consumer. After discussion of transiantsteady state system we can obtain closed-form system performance measurements