In an attempt to provide a simple and computationally efficient method for the analysis of manufacturing systems, we have adopted the discrete-time analysis (DTA) approach to problems arising out of manufacturing. The subject of our study is the discrete -time G/G/1 queuing system with infinite waiting room. The time interval between the consecutive arrivals of customers is described in terms of a discrete probability mass function (p.m.f) a(k): a(k) is the probability of having an interval of an integer number of k time units between the arrival of customer number n and customer number n+1. The service time of customer n is given in terms of a discrete (p.m.f)b(k). The inter-arrival time and the service times are independent and identically distributed (i.i.d) random variables. The customers are served in the order of their arrival First-Come-First Served (FCFS). An explicit formulae are obtained for the distribution of the occupancy, just before and after the departure epoch by using discrete-time analysis. Time is assumption into equal intervals called slots. Further, some special cases of the model, numerical results, have been carried out in the form of a table and graphs.