This paper investigates a discrete-time (s, S) perishable inventory system with positive service time and positive lead time. The system operates under a modified N-policy with two modes of service, where arrivals follow a Bernoulli process. During the stock-out period, the server goes on vacation. After the server vacation, the server initiates a batch service of size N only after N customer arrivals. During batch service, new individual arrivals were served separately. Service times are also assumed to be geometrically distributed. Lead times follow geometric distribution, where the maximum inventory level is S. The inventory items are perishable, with perishability following a geometric distribution, thereby adding an additional layer of complexity. The matrix analytic method is used to analyze system behavior in steady state, accounting for the arrival, service, and replenishment dynamics within the model. Numerical experiments are conducted to examine the impact of various system parameters and an optimal (s, S) pair is derived for fixed parameter values, highlighting practical applications and the efficiency of the modified N-policy in managing perishable items.