In this paper, we analyze and compare three (s, S) inventory systems with positive service time and retrial of customers. In all these systems, arrivals of customers form a Poisson process and service times are exponentially distributed. When the inventory level depletes to s due services, an order of replenishment is placed. The leadtime follows an exponential distribution. In model I, an arriving customer, encountering the inventory dry or server, busy proceeds to an orbit with probability γ and is lost forever with probability (1−γ) . A retrial customer in the orbit, finding the inventory dry or server busy, returns to the orbit with probability δ and is lost forever with probability (1−δ) .In addition to the description in the model I, we provide a buffer of varying (finite) capacity equal to the current inventory level for model II and another having capacity equal to the maximum inventory level S for model III. In models II and III, an arriving customer, encountering the buffer full, proceeds to an orbit with probability γ and is lost forever with probability (1−γ). A retrial customer in the orbit, finding the buffer full, returns to the orbit with probability δ and is lost forever with probability (1−δ). In all these models, the inter-retrial times are exponentially distributed with linear rate. Using Matrix Analytic Method we study these inventory models. Some measures of the system performance in the steady state are derived. A suitable cost function is defined for all three cases and it is analyzed using graphical illustrations.
