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This article deals with asynchronous server vacation and customer retrialfacility in a multi-server queueing-inventory system. The Poisson processgoverns the arrival of a customer. The system is comprised of c identicalservers, a finite-size waiting area, and a storage area containing S items. Theservice time is distributed exponentially. If each server finds that there arean insufficient number of customers and items in the system after the busyperiod, they start a vacation. Once the servers vacation is over and itrecognizes there is no chance of getting busy, it goes into an idle state ifthe number of customers or items is not sufficient, otherwise, it will takeanother vacation. Furthermore, each server's vacation period occursindependently of the other servers. The system accepts a (s, Q) control policyfor inventory replenishment. For the steady state analysis, the Marcel F Neutsand B Madhu Rao matrix geometric approximation approach is used owing to thestructure of an infinitesimal generator matrix. The necessary stabilitycondition and R matrix are to be computed and presented. After calculating thesufficient system performance measures, an expected total cost of the system isto be constructed and numerically incorporated with the parameters.Additionally, numerical analyses will be conducted to examine the waiting timeof customers in the queue and in orbit, as well as the expected rate ofcustomer loss.

A Multi-Server Retrial Queueing Inventory System With Asynchronous Multiple Vacations