This paper represents an analysis of the Geo / G / 1 / K / N system in which the capacity of the service facility is less than N the total quantity of messages in the system. Consider the Geo / G / 1 / K / N system without a server holiday, assuming a late-arrival model with partial acceptance and a belated substitution rule, then a Geo / G / 1 / K /N Consider n systems with multiple servers. The service arrives at the end of each slot with a message probability in the source.