This paper analyzes a
discrete-time multi-server queue in which service capacity of each
server is a minimum of one and a maximum of b customers. The
interarrival- and service-times are assumed to be independent and
geometrically distributed. The queue is analyzed under the
assumptions of early arrival system and late arrival system with
delayed access. Besides, obtaining state probabilities at
arbitrary and outside observer's observation epochs, some
performance measures and waiting-time distribution in the queue
have also been discussed. Finally, it is shown that in limiting
case the results obtained in this
paper tend to the continuous-time counterpart.