• AMAN GUPTA
• Dr. Ranjeet Singh Pundhir

This paper focuses on the batch arriving and batch service queuing system where customers arriving according to the general bulk rule (a1, b1) and follows the Poisson distribution. Customers are served in bulk manner according to the different four types of optional distribution. If there are not sufficient number of customers for receiving the service, then may or may not go for the vacations until the available numbers of customers are lies between a1 and b1. Server comes back for the vacation if arrived numbers of customers are sufficient for giving the service. Here we have also included the balking and reneging behaviors of customers due to have insufficient amount of time. Here we have determined the dependent probability generating function by using the corresponding steady static equations and number of customer waiting in the system.

bulk rule, probability generation function, Poisson distribution

"A BATCH ARRIVING QUEUING SYSTEM WITH FOUR TYPES OF OPTIONAL SERVICES AND VACATIONS", International Journal of Emerging Technologies and Innovative Research (www.jetir.org), ISSN:2349-5162, Vol.10, Issue 9, page no.d760-d770, September-2023, Available :http://www.jetir.org/papers/JETIR2309383.pdf

"A BATCH ARRIVING QUEUING SYSTEM WITH FOUR TYPES OF OPTIONAL SERVICES AND VACATIONS", International Journal of Emerging Technologies and Innovative Research (www.jetir.org | UGC and issn Approved), ISSN:2349-5162, Vol.10, Issue 9, page no. ppd760-d770, September-2023, Available at : http://www.jetir.org/papers/JETIR2309383.pdf