Analysis of Stochastic State-Dependent Arrivals in a Queueing-Inventory System with Multiple Server Vacation and Retrial Facility

This article analyses a four-dimensional stochastic queueing-inventory system with multiple server vacations and state-dependent arrival process. The can start at random time only when there is no customer in the waiting hall inventory level zero. flow of customers state-dependent. Whenever arriving finds that full, they enter into infinite orbit retry to hall. If least one space hall, orbital enters When on vacation, primary (retrial) rate λ1(θ1). not occurs λ2(θ2). Each follows an independent Poisson distribution. service provided by positive μ, which exponential drops fixed s, reorder Q items triggered immediately under (s,Q) ordering policy. stability has been analysed, using Neuts matrix geometric approach, stationary probability vectors have obtained. Moreover, various performance measures are derived. expected total cost analysis explores verifies characteristics assumed parameters this model. average investigated all parameters. monotonicity verified its numerical simulation. discussion about fraction being vacation suggests as server’s duration reduces, also reduces. mean number reduced whenever per replenishment reduced.