Distribution of the number of customers served during a busy period in a discrete time single server queue

In this paper, a discrete-time single server queueing system with infinite buffer size and geometrically distributed arrivals is considered. We derive the functional equations and analyze the distribution of the number of customers served during a busy period for geometrically distributed service time as well as for deterministic service time. We also show that in the limiting case the results obtained in this paper are consistent with the corresponding continuous-time counterparts by Medhi [1].