Analysis is a discrete time queueing-inventory model with back-order of items

This paper analyses a discrete-time (s, S) queueing inventory model with service time and back-order in inventory. The arrival of customers is assumed to be the Bernoulli process. Service follows geometric distribution. As soon as level reaches pre-assigned due demands, an order for replenishment placed. Replenishment also When reduces zero or non-replenishment items, maximum k are allowed system remaining completely lost till replenishment. Matrix-Analytic Method (MAM) used analyze model. Stability conditions, various performance measures system, waiting-time distribution reorder-time obtained. Numerical experiments incorporated.