An optional arrival process of the oscillatory demands in the inventory system with queue dependent service rate

In this paper, we study a classical retrial queueing-inventory system (CRQIS) with an optional arrival process of an oscillatory customer (OC) who may enter into the waiting hall or an infinite orbit directly under Bernoulli trials. The orbital customer emulates their requirements through the waiting hall only over the classical retrial policy (ClRP) whenever it is less than its capacity and the service rate of customer depends on the queue length at an epoch. This system contains a perishing item too, and replenishment can be done following the (s, Q) ordering policy. The server can do an orbital search which follows Bernoulli process. Neuts approach is applied for the matrix-geometric approximation (MGA) to find a stationary probability vector and the Laplace-Stieltjes transform method (LSTM) is used to derive waiting time of both arrivals. Also, sufficient numerical problems are to be explored for the assumed model.